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Lepri S, Livi R, Politi A. Too Close to Integrable: Crossover from Normal to Anomalous Heat Diffusion. PHYSICAL REVIEW LETTERS 2020; 125:040604. [PMID: 32794827 DOI: 10.1103/physrevlett.125.040604] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/08/2020] [Accepted: 07/08/2020] [Indexed: 06/11/2023]
Abstract
Energy transport in one-dimensional chains of particles with three conservation laws is generically anomalous and belongs to the Kardar-Parisi-Zhang dynamical universality class. Surprisingly, some examples where an apparent normal heat diffusion is found over a large range of length scales were reported. We propose a novel physical explanation of these intriguing observations. We develop a scaling analysis that explains how this may happen in the vicinity of an integrable limit, such as, but not only, the famous Toda model. In this limit, heat transport is mostly supplied by quasiparticles with a very large mean free path ℓ. Upon increasing the system size L, three different regimes can be observed: a ballistic one, an intermediate diffusive range, and, eventually, the crossover to the anomalous (hydrodynamic) regime. Our theoretical considerations are supported by numerical simulations of a gas of diatomic hard-point particles for almost equal masses and of a weakly perturbed Toda chain. Finally, we discuss the case of the perturbed harmonic chain, which exhibits a yet different scenario.
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Affiliation(s)
- Stefano Lepri
- Consiglio Nazionale delle Ricerche, Istituto dei Sistemi Complessi, Via Madonna del Piano 10, I-50019 Sesto Fiorentino, Italy
- Istituto Nazionale di Fisica Nucleare, Sezione di Firenze, via G. Sansone 1, I-50019 Sesto Fiorentino, Italy
| | - Roberto Livi
- Consiglio Nazionale delle Ricerche, Istituto dei Sistemi Complessi, Via Madonna del Piano 10, I-50019 Sesto Fiorentino, Italy
- Istituto Nazionale di Fisica Nucleare, Sezione di Firenze, via G. Sansone 1, I-50019 Sesto Fiorentino, Italy
- Dipartimento di Fisica e Astronomia and CSDC, Università di Firenze, via G. Sansone 1, I-50019 Sesto Fiorentino, Italy
| | - Antonio Politi
- Institute for Complex Systems and Mathematical Biology & SUPA University of Aberdeen, Aberdeen AB24 3UE, United Kingdom
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2
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Li N. Energy and spin diffusion in the one-dimensional classical Heisenberg spin chain at finite and infinite temperatures. Phys Rev E 2019; 100:062104. [PMID: 31962512 DOI: 10.1103/physreve.100.062104] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/25/2019] [Indexed: 06/10/2023]
Abstract
The energy and spin diffusion behaviors in the one-dimensional classical Heisenberg spin chain have been systematically investigated using the equilibrium diffusion method. The spatiotemporal autocorrelation functions for energy and spin are calculated at finite and infinite temperatures. As conserved quantities, the spreading of excess energy and spin can be used to determine their actual diffusion behaviors. At low temperatures, the energy diffusion shows almost ballistic behavior, and spin shows superdiffusion behavior for finite chain size. For energy diffusion, normal diffusion behavior can be obtained when the temperature is higher than 0.75. For spin diffusion, normal diffusion behavior is observed at infinite temperature.
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Affiliation(s)
- Nianbei Li
- Institute of Systems Science and Department of Physics, College of Information Science and Engineering, Huaqiao University, Xiamen 361021, China
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3
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Liao W, Li N. Energy and momentum diffusion in one-dimensional periodic and asymmetric nonlinear lattices with momentum conservation. Phys Rev E 2019; 99:062125. [PMID: 31330609 DOI: 10.1103/physreve.99.062125] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/16/2019] [Indexed: 11/07/2022]
Abstract
The energy diffusion in one-dimensional (1D) momentum conserving nonlinear lattices usually exhibits anomalous superdiffusion, except the coupled rotator lattice with symmetric and periodic interacting potential which has normal energy diffusion corresponding to normal heat conduction. For nonperiodic 1D lattices with momentum conservation, it has been argued that the asymmetric potential can induce normal heat conduction. Later results indicate the observed normal behavior might be the finite size effect and the anomalous behavior will appear in the thermodynamical limit. Here we propose asymmetric and periodic 1D nonlinear lattices with momentum conservation. The energy and momentum diffusion behaviors will be investigated in detail and the same normal diffusion behaviors for both energy and momentum can be observed. These results confirm that the periodicity is the key for normal transport behavior in 1D momentum conserving lattices, whether the potential is symmetric or asymmetric.
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Affiliation(s)
- Wenshan Liao
- Institute of Systems Science and Department of Physics, College of Information Science and Engineering, Huaqiao University, Xiamen 361021, China
| | - Nianbei Li
- Institute of Systems Science and Department of Physics, College of Information Science and Engineering, Huaqiao University, Xiamen 361021, China
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G R A, Barik D. Temperature-dependent divergence of thermal conductivity in momentum-conserving one-dimensional lattices with asymmetric potential. Phys Rev E 2019; 99:022103. [PMID: 30934250 DOI: 10.1103/physreve.99.022103] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/17/2018] [Indexed: 06/09/2023]
Abstract
In this study we used a nonequilibrium simulation method to investigate the temperature dependent divergence of thermal conductivity in a one-dimensional momentum conserving system with an asymmetric double well nearest-neighbor interaction potential. We show that across all temperatures thermal conductivity exhibits power-law divergence with the chain length and the value of the divergence exponent (α) depends on the temperature of the system. At low and high temperatures α reaches close to ∼0.5 and ∼0.33, respectively. Whereas in the intermediate temperature the divergence of thermal conductivity with the chain length saturates with α∼0.07. Subsequent analysis showed that the estimated value of α in the intermediate temperature may not have reached its thermodynamic limit. Further calculations of local α revealed that its approach towards the thermodynamic limit is crucially dependent on the temperature of the system. At low and high temperatures local α reaches its thermodynamic limits in shorter chain lengths. On the contrary, in the case of intermediate temperature its progress towards the asymptotic limit is nonmonotonic.
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Affiliation(s)
- Archana G R
- School of Chemistry, University of Hyderabad, Gachibowli 500046, Hyderabad, India
| | - Debashis Barik
- School of Chemistry, University of Hyderabad, Gachibowli 500046, Hyderabad, India
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Guo BQ, Liu T, Yu CS. Quantum thermal transistor based on qubit-qutrit coupling. Phys Rev E 2018; 98:022118. [PMID: 30253594 DOI: 10.1103/physreve.98.022118] [Citation(s) in RCA: 30] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/09/2018] [Indexed: 11/07/2022]
Abstract
A quantum thermal transistor is designed by the strong coupling between one qubit and one qutrit which are in contact with three heat baths with different temperatures. The thermal behavior is analyzed based on the master equation by both the numerical and the approximately analytic methods. It is shown that the thermal transistor, as a three-terminal device, allows a weak modulation heat current (at the modulation terminal) to switch on and off and effectively modulate the heat current between the other two terminals. In particular, the weak modulation heat current can induce the strong heat current between the other two terminals with the multiple-region amplification of heat current. Furthermore, the heat currents are quite robust to the temperature (current) fluctuation at the lower-temperature terminal within a certain range of temperature, and so it can behave as a heat current stabilizer.
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Affiliation(s)
- Bao-Qing Guo
- School of Physics, Dalian University of Technology, Dalian 116024, China
| | - Tong Liu
- School of Physics, Dalian University of Technology, Dalian 116024, China
| | - Chang-Shui Yu
- School of Physics, Dalian University of Technology, Dalian 116024, China
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6
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Ming Y, Ye L, Chen HS, Mao SF, Li HM, Ding ZJ. Solitons as candidates for energy carriers in Fermi-Pasta-Ulam lattices. Phys Rev E 2018; 97:012221. [PMID: 29448422 DOI: 10.1103/physreve.97.012221] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/25/2017] [Indexed: 11/07/2022]
Abstract
Currently, effective phonons (renormalized or interacting phonons) rather than solitary waves (for short, solitons) are regarded as the energy carriers in nonlinear lattices. In this work, by using the approximate soliton solutions of the corresponding equations of motion and adopting the Boltzmann distribution for these solitons, the average velocities of solitons are obtained and are compared with the sound velocities of energy transfer. Excellent agreements with the numerical results and the predictions of other existing theories are shown in both the symmetric Fermi-Pasta-Ulam-β lattices and the asymmetric Fermi-Pasta-Ulam-αβ lattices. These clearly indicate that solitons are suitable candidates for energy carriers in Fermi-Pasta-Ulam lattices. In addition, the root-mean-square velocity of solitons can be obtained from the effective phonons theory.
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Affiliation(s)
- Yi Ming
- School of Physics and Material Science, Anhui University, Hefei, Anhui 230601, China
| | - Liu Ye
- School of Physics and Material Science, Anhui University, Hefei, Anhui 230601, China
| | - Han-Shuang Chen
- School of Physics and Material Science, Anhui University, Hefei, Anhui 230601, China
| | - Shi-Feng Mao
- School of Nuclear Science and Technology, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Hui-Min Li
- Supercomputing Center, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Ze-Jun Ding
- Department of Physics and Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei, Anhui 230026, China.,Key Laboratory of Strongly-coupled Quantum Matter Physics, Chinese Academy of Sciences, Hefei, Anhui 230026, China
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Xiong D. Observing golden-mean universality class in the scaling of thermal transport. Phys Rev E 2018; 97:022116. [PMID: 29548205 DOI: 10.1103/physreve.97.022116] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/06/2017] [Indexed: 11/07/2022]
Abstract
We address the issue of whether the golden-mean [ψ=(sqrt[5]+1)/2≃1.618] universality class, as predicted by several theoretical models, can be observed in the dynamical scaling of thermal transport. Remarkably, we show strong evidence that ψ appears to be the scaling exponent of heat mode correlation in a purely quartic anharmonic chain. This observation seems to somewhat deviate from the previous expectation and we explain it by the unusual slow decay of the cross correlation between heat and sound modes. Whenever the cubic anharmonicity is included, this cross correlation gradually dies out and another universality class with scaling exponent γ=5/3, as commonly predicted by theories, seems recovered. However, this recovery is accompanied by two interesting phase transition processes characterized by a change of symmetry of the potential and a clear variation of the dynamic structure factor, respectively. Due to these transitions, an additional exponent close to γ≃1.580 emerges. All this evidence suggests that, to gain a full prediction of the scaling of thermal transport, more ingredients should be taken into account.
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Affiliation(s)
- Daxing Xiong
- Department of Physics, Fuzhou University, Fuzhou 350108, Fujian, China
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Xu L, Wang L. Response and correlation functions of nonlinear systems in equilibrium states. Phys Rev E 2018; 96:052139. [PMID: 29347673 DOI: 10.1103/physreve.96.052139] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/23/2017] [Indexed: 11/07/2022]
Abstract
In this paper, we study systematically a serial of correlation functions in some one-dimensional nonlinear lattices. Due to the energy conservation law, they are implicitly interdependent. Various transport coefficients are thus also connected. In the studies of the autocorrelations of local energy density and of local heat current, a general relation between diverging heat conduction and super heat diffusion has been proposed recently. We clarify that such a relation is valid only in systems without temperature pressure. In those with temperature pressure, a constant but nontrivial term appears. This term explains a previously observed fact that heat diffusion in such systems is always ballistic but heat conduction can diverge very slowly. Such a result not only disproves the existence of any general relation between diverging heat conduction and super heat diffusion, but it also breaks the long-term presumption that ballistic heat conduction and diffusion always coexist.
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Affiliation(s)
- Lubo Xu
- Department of Physics and Beijing Key Laboratory of Opto-electronic Functional Materials and Micro-Nano Devices, Renmin University of China, Beijing 100872, People's Republic of China
| | - Lei Wang
- Department of Physics and Beijing Key Laboratory of Opto-electronic Functional Materials and Micro-Nano Devices, Renmin University of China, Beijing 100872, People's Republic of China
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Xiong D, Saadatmand D, Dmitriev SV. Crossover from ballistic to normal heat transport in the ϕ^{4} lattice: If nonconservation of momentum is the reason, what is the mechanism? Phys Rev E 2017; 96:042109. [PMID: 29347584 DOI: 10.1103/physreve.96.042109] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/15/2017] [Indexed: 11/07/2022]
Abstract
Anomalous (non-Fourier) heat transport is no longer just a theoretical issue since it has been observed experimentally in a number of low-dimensional nanomaterials, such as SiGe nanowires, carbon nanotubes, and others. To understand these anomalous behaviors, exploring the microscopic origin of normal (Fourier) heat transport is a fascinating theoretical topic. However, this issue has not yet been fully understood even for one-dimensional (1D) model chains, in spite of a great amount of thorough studies done to date. From those studies, it has been widely accepted that the conservation of momentum is a key ingredient to induce anomalous heat transport, while momentum-nonconserving systems usually support normal heat transport where Fourier's law is valid. But if the nonconservation of momentum is the reason, what is the underlying microscopic mechanism for the observed normal heat transport? Here we carefully revisit a typical 1D momentum-nonconserving ϕ^{4} model, and we present evidence that the mobile discrete breathers, or, in other words, the moving intrinsic localized modes with frequency components above the linear phonon band, can be responsible for that.
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Affiliation(s)
- Daxing Xiong
- Department of Physics, Fuzhou University, Fuzhou 350108, Fujian, China
| | - Danial Saadatmand
- Department of Physics, University of Sistan and Baluchestan, Zahedan, Iran
| | - Sergey V Dmitriev
- Institute for Metals Superplasticity Problems of RAS, Khalturin St. 39, 450001 Ufa, Russia.,National Research Tomsk State University, Lenin Avenue 36, 634050 Tomsk, Russia
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Xu L, Wang L. Resonance phonon approach to phonon relaxation time and mean free path in one-dimensional nonlinear lattices. Phys Rev E 2017; 95:042138. [PMID: 28505770 DOI: 10.1103/physreve.95.042138] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/17/2017] [Indexed: 11/07/2022]
Abstract
We extend a previously proposed resonance phonon approach that is based on the linear response theory. By studying the complex response function in depth, we work out the phonon relaxation time besides the oscillating frequency of the phonons in a few one-dimensional nonlinear lattices. The results in the large wave-number-k regime agree with the expectations of the effective phonon theory. However, in the small-k limit they follow different scaling laws. The phonon mean free path can also be calculated indirectly. It coincides well with that derived from the anharmonic phonon approach. A power-law divergent heat conduction, i.e., the heat conductivity κ depends on lattice length N by κ∼N^{β} with β>0, then is supported for the momentum-conserving lattices. Furthermore, this approach can be applied to diatomic lattices. So obtained relaxation time quantitatively agrees with that from the effective phonon theory. As for the mean free path, the resonance phonon approach can detect both the acoustic and the optical branches, whereas the anharmonic phonon approach can only detect a combined branch, i.e., the acoustic branch for small k and the optical branch for large k.
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Affiliation(s)
- Lubo Xu
- Department of Physics and Beijing Key Laboratory of Opto-electronic Functional Materials and Micro-Nano Devices, Renmin University of China, Beijing 100872, People's Republic of China
| | - Lei Wang
- Department of Physics and Beijing Key Laboratory of Opto-electronic Functional Materials and Micro-Nano Devices, Renmin University of China, Beijing 100872, People's Republic of China
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Xiong D. Anomalous temperature-dependent heat transport in one-dimensional momentum-conserving systems with soft-type interparticle interaction. Phys Rev E 2017; 95:042127. [PMID: 28505818 DOI: 10.1103/physreve.95.042127] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/12/2016] [Indexed: 06/07/2023]
Abstract
We numerically investigate the heat transport problem in a one-dimensional momentum-conserving lattice with a soft-type (ST) anharmonic interparticle interaction. It is found that with the increase of the system's temperature, while the introduction of ST anharmonicity softens phonons and decreases their velocities, this type of nonlinearity like its hard type (HT) counterpart, can still not be able to fully damp the longest wavelength phonons. Therefore, a usual anomalous temperature dependence of heat transport with certain scaling properties similarly to those shown in the Fermi-Pasta-Ulam-β-like systems with HT interactions can be seen. Our detailed examination from simulations verifies this temperature-dependent behavior well.
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Affiliation(s)
- Daxing Xiong
- Department of Physics, Fuzhou University, Fuzhou 350108, Fujian, China
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12
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Bagchi D. Thermal transport in the Fermi-Pasta-Ulam model with long-range interactions. Phys Rev E 2017; 95:032102. [PMID: 28415308 DOI: 10.1103/physreve.95.032102] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/16/2016] [Indexed: 06/07/2023]
Abstract
We study the thermal transport properties of the one-dimensional Fermi-Pasta-Ulam model (β type) with long-range interactions. The strength of the long-range interaction decreases with the (shortest) distance between the lattice sites as distance^{-δ}, where δ≥0. Two Langevin heat baths at unequal temperatures are connected to the ends of the one-dimensional lattice via short-range harmonic interactions that drive the system away from thermal equilibrium. In the nonequilibrium steady state the heat current, thermal conductivity, and temperature profiles are computed by solving the equations of motion numerically. It is found that the conductivity κ has an interesting nonmonotonic dependence with δ with a maximum at δ=2.0 for this model. Moreover, at δ=2.0,κ diverges almost linearly with system size N and the temperature profile has a negligible slope, as one expects in ballistic transport for an integrable system. We demonstrate that the nonmonotonic behavior of the conductivity and the nearly ballistic thermal transport at δ=2.0 obtained under nonequilibrium conditions can be explained consistently by studying the variation of largest Lyapunov exponent λ_{max} with δ, and excess energy diffusion in the equilibrium microcanonical system.
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Affiliation(s)
- Debarshee Bagchi
- Centro Brasileiro de Pesquisas Fisicas, Rio de Janeiro-RJ, Brazil
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Gendelman OV, Savin AV. Heat conduction in a chain of colliding particles with a stiff repulsive potential. Phys Rev E 2016; 94:052137. [PMID: 27967160 DOI: 10.1103/physreve.94.052137] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/02/2016] [Indexed: 11/07/2022]
Abstract
One-dimensional billiards, i.e., a chain of colliding particles with equal masses, is a well-known example of a completely integrable system. Billiards with different particle masses is generically not integrable, but it still exhibits divergence of a heat conduction coefficient (HCC) in the thermodynamic limit. Traditional billiards models imply instantaneous (zero-time) collisions between the particles. We relax this condition of instantaneous impact and consider heat transport in a chain of stiff colliding particles with the power-law potential of the nearest-neighbor interaction. The instantaneous collisions correspond to the limit of infinite power in the interaction potential; for finite powers, the interactions take nonzero time. This modification of the model leads to a profound physical consequence-the probability of multiple (in particular triple) -particle collisions becomes nonzero. Contrary to the integrable billiards of equal particles, the modified model exhibits saturation of the heat conduction coefficient for a large system size. Moreover, the identification of scattering events with triple-particle collisions leads to a simple definition of the characteristic mean free path and a kinetic description of heat transport. This approach allows us to predict both the temperature and density dependencies for the HCC limit values. The latter dependence is quite counterintuitive-the HCC is inversely proportional to the particle density in the chain. Both predictions are confirmed by direct numerical simulations.
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Affiliation(s)
- Oleg V Gendelman
- Faculty of Mechanical Engineering, Technion-Israel Institute of Technology, Haifa 32000, Israel
| | - Alexander V Savin
- Semenov Institute of Chemical Physics, Russian Academy of Sciences, Moscow 119991, Russia
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Xu L, Wang L. Dispersion and absorption in one-dimensional nonlinear lattices: A resonance phonon approach. Phys Rev E 2016; 94:030101. [PMID: 27739752 DOI: 10.1103/physreve.94.030101] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/27/2016] [Indexed: 11/07/2022]
Abstract
Based on the linear response theory, we propose a resonance phonon (r-ph) approach to study the renormalized phonons in a few one-dimensional nonlinear lattices. Compared with the existing anharmonic phonon (a-ph) approach, the dispersion relations derived from this approach agree with the expectations of the effective phonon (e-ph) theory much better. The application is also largely extended, i.e., it is applicable in many extreme situations, e.g., high frequency, high temperature, etc., where the existing one can hardly work. Furthermore, two separated phonon branches (one acoustic and one optical) with a clear gap in between can be observed by the r-ph approach in a diatomic anharmonic lattice. While only one combined branch can be detected in the same lattice with both the a-ph approach and the e-ph theory.
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Affiliation(s)
- Lubo Xu
- Department of Physics and Beijing Key Laboratory of Optoelectronic Functional Materials and Micro-Nano Devices, Renmin University of China, Beijing 100872, People's Republic of China
| | - Lei Wang
- Department of Physics and Beijing Key Laboratory of Optoelectronic Functional Materials and Micro-Nano Devices, Renmin University of China, Beijing 100872, People's Republic of China
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Sato DS. Pressure-induced recovery of Fourier's law in one-dimensional momentum-conserving systems. Phys Rev E 2016; 94:012115. [PMID: 27575085 DOI: 10.1103/physreve.94.012115] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/11/2015] [Indexed: 06/06/2023]
Abstract
We report the two typical models of normal heat conduction in one-dimensional momentum-conserving systems. They show the Arrhenius and the non-Arrhenius temperature dependence. We construct the two corresponding phenomenologies, transition-state theory of thermally activated dissociation and the pressure-induced crossover between two fixed points in fluctuating hydrodynamics. Compressibility yields the ballistic fixed point, whose scaling is observed in Fermi-Pasta-Ulam (FPU) β lattices.
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Affiliation(s)
- Dye Sk Sato
- Earthquake Research Institute, University of Tokyo, 1-1-1 Yayoi, Bunkyo, Tokyo 113-0032, Japan
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Gao Z, Li N, Li B. Heat conduction and energy diffusion in momentum-conserving one-dimensional full-lattice ding-a-ling model. Phys Rev E 2016; 93:022102. [PMID: 26986283 DOI: 10.1103/physreve.93.022102] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/13/2015] [Indexed: 06/05/2023]
Abstract
The ding-a-ling model is a kind of half lattice and half hard-point-gas (HPG) model. The original ding-a-ling model proposed by Casati et al. does not conserve total momentum and has been found to exhibit normal heat conduction behavior. Recently, a modified ding-a-ling model which conserves total momentum has been studied and normal heat conduction has also been claimed. In this work, we propose a full-lattice ding-a-ling model without hard point collisions where total momentum is also conserved. We investigate the heat conduction and energy diffusion of this full-lattice ding-a-ling model with three different nonlinear inter-particle potential forms. For symmetrical potential lattices, the thermal conductivities diverges with lattice length and their energy diffusions are superdiffusive signaturing anomalous heat conduction. For asymmetrical potential lattices, although the thermal conductivity seems to converge as the length increases, the energy diffusion is definitely deviating from normal diffusion behavior indicating anomalous heat conduction as well. No normal heat conduction behavior can be found for the full-lattice ding-a-ling model.
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Affiliation(s)
- Zhibin Gao
- Center for Phononics and Thermal Energy Science, School of Physics Science and Engineering, Tongji University, 200092 Shanghai, People's Republic of China
| | - Nianbei Li
- Center for Phononics and Thermal Energy Science, School of Physics Science and Engineering, Tongji University, 200092 Shanghai, People's Republic of China
| | - Baowen Li
- Department of Mechanical Engineering, University of Colorado Boulder, Colorado 80309, USA
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Zhang Z, Tang C, Tong P. Dynamical thermalization of Frenkel-Kontorova model in the thermodynamic limit. Phys Rev E 2016; 93:022216. [PMID: 26986340 DOI: 10.1103/physreve.93.022216] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/25/2015] [Indexed: 06/05/2023]
Abstract
We study numerically the process of dynamical thermalization in the Frenkel-Kontorova (FK) model with weak nonlinearity. The total energy has initially equidistributed among some of the lowest frequency linear modes. It is found that the energy transfers continuously to the high-frequency modes and finally evolves towards energy equipartition in the FK model. However, the metastable state, which was found in Fermi-Pasta-Ulam (FPU) model and φ(4) model in a relatively short time scale, is not found in the FK model. We further perform a very accurate systematic study of the equipartition time T(eq) as functions of the particle number N, the nonlinear parameter β, and the energy density ɛ. In the thermodynamic limit, the dependence of T(eq) on β and ɛ is found to display a power law behavior: T(eq)∝β(a)ɛ(b). The exponents a and b are numerically found to be approximately -2.0 and 1.43. This scaling law is also quite different from those of the FPU-β model and φ(4) model.
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Affiliation(s)
- Zhenjun Zhang
- College of Science, Hohai University, Nanjing, Jiangsu 210098, People's Republic of China
| | - Chunmei Tang
- College of Science, Hohai University, Nanjing, Jiangsu 210098, People's Republic of China
| | - Peiqing Tong
- School of Physics Science and Technology, Nanjing Normal University, Nanjing, Jiangsu 210023, People's Republic of China
- Jiangsu Provincial Key Laboratory for Numerical Simulation of Large Scale Complex Systems, Nanjing Normal University, Nanjing, Jiangsu 210023, People's Republic of China
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19
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Di Cintio P, Livi R, Bufferand H, Ciraolo G, Lepri S, Straka MJ. Anomalous dynamical scaling in anharmonic chains and plasma models with multiparticle collisions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:062108. [PMID: 26764633 DOI: 10.1103/physreve.92.062108] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/29/2015] [Indexed: 06/05/2023]
Abstract
We study the anomalous dynamical scaling of equilibrium correlations in one-dimensional systems. Two different models are compared: the Fermi-Pasta-Ulam chain with cubic and quartic nonlinearity and a gas of point particles interacting stochastically through multiparticle collision dynamics. For both models-that admit three conservation laws-by means of detailed numerical simulations we verify the predictions of nonlinear fluctuating hydrodynamics for the structure factors of density and energy fluctuations at equilibrium. Despite this, violations of the expected scaling in the currents correlation are found in some regimes, hindering the observation of the asymptotic scaling predicted by the theory. In the case of the gas model this crossover is clearly demonstrated upon changing the coupling constant.
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Affiliation(s)
- Pierfrancesco Di Cintio
- Dipartimento di Fisica e Astronomia and CSDC, Universitá di Firenze, via G. Sansone 1, I-50019 Sesto Fiorentino, Italy
- Istituto Nazionale di Fisica Nucleare, Sezione di Firenze, via G. Sansone 1, I-50019 Sesto Fiorentino, Italy
| | - Roberto Livi
- Dipartimento di Fisica e Astronomia and CSDC, Universitá di Firenze, via G. Sansone 1, I-50019 Sesto Fiorentino, Italy
- Istituto Nazionale di Fisica Nucleare, Sezione di Firenze, via G. Sansone 1, I-50019 Sesto Fiorentino, Italy
| | - Hugo Bufferand
- Aix-Marseille Université, CNRS, PIIM, UMR 7345, F-13397 Marseille Cedex 20, France
| | | | - Stefano Lepri
- Istituto Nazionale di Fisica Nucleare, Sezione di Firenze, via G. Sansone 1, I-50019 Sesto Fiorentino, Italy
- Consiglio Nazionale delle Ricerche, Istituto dei Sistemi Complessi via Madonna del piano 10, I-50019 Sesto Fiorentino, Italy
| | - Mika J Straka
- IMT Institute for Advanced Studies Lucca, Piazza S. Francesco 19, I-55100 Lucca, Italy
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20
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Zhao H, Wang L. Deviation from the Maxwell-Cattaneo law: Role of asymmetric interparticle interactions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:042136. [PMID: 26565197 DOI: 10.1103/physreve.92.042136] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/31/2015] [Indexed: 06/05/2023]
Abstract
Nonstationary heat conduction in a few one-dimensional nonlinear lattices is studied numerically based on the Maxwell-Cattaneo (MC) law. We simulate the relaxation process and calculate the magnitudes of the temperature oscillation A(T)(t) and the local heat current oscillation A(j)(t). A phase difference between A(T)(t) and A(j)(t) is observed, which not only verifies the existence of the time lag τ in the MC law but also provides a better way of determining the critical wavelength L(*) that separates between oscillatory and diffusive relaxation modes. However, clear deviations from the MC law are observed. Not only do the decay exponents differ from the theoretical expectations, but, more importantly, suboscillation in the diffusive regime, which is not expected by the MC law, is found in the lattices with asymmetric interactions as well. These findings imply that higher-order effects must be considered in order to well describe the nonstationary heat conduction process in these systems.
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Affiliation(s)
- Huizhu Zhao
- Department of Physics and Beijing Key Laboratory of Optoelectronic Functional Materials and Micro-nano Devices, Renmin University of China, Beijing 100872, People's Republic of China
| | - Lei Wang
- Department of Physics and Beijing Key Laboratory of Optoelectronic Functional Materials and Micro-nano Devices, Renmin University of China, Beijing 100872, People's Republic of China
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21
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Wang J, He D, Zhang Y, Wang J, Zhao H. Effects of interaction symmetry on delocalization and energy transport in one-dimensional disordered lattices. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:032138. [PMID: 26465457 DOI: 10.1103/physreve.92.032138] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/22/2015] [Indexed: 06/05/2023]
Abstract
We study effects of interaction symmetry in one-dimensional, momentum-conserving disordered lattices. It is found that asymmetric and symmetric interparticle interactions may result in significant difference: localized modes can be delocalized by very weak asymmetric interactions but survive much stronger symmetric interactions. Moreover, in the delocalization regime, asymmetric and symmetric interactions also have qualitatively different effects on transport: the former (the latter) may lead to a fast decaying (slow power-law decaying) heat current correlation function and in turn a convergent (divergent) heat conductivity. A method for detecting delocalization in systems at a nonzero temperature is proposed as well.
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Affiliation(s)
- Jianjin Wang
- Department of Physics and Institute of Theoretical Physics and Astrophysics, Xiamen University, Xiamen 361005, Fujian, China
| | - Dahai He
- Department of Physics and Institute of Theoretical Physics and Astrophysics, Xiamen University, Xiamen 361005, Fujian, China
| | - Yong Zhang
- Department of Physics and Institute of Theoretical Physics and Astrophysics, Xiamen University, Xiamen 361005, Fujian, China
| | - Jiao Wang
- Department of Physics and Institute of Theoretical Physics and Astrophysics, Xiamen University, Xiamen 361005, Fujian, China
| | - Hong Zhao
- Department of Physics and Institute of Theoretical Physics and Astrophysics, Xiamen University, Xiamen 361005, Fujian, China
- Collaborative Innovation Center of Chemistry for Energy Materials, Xiamen University, Xiamen 361005, Fujian, China
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22
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Chen S, Wang J, Casati G, Benenti G. Thermoelectricity of interacting particles: a numerical approach. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:032139. [PMID: 26465458 DOI: 10.1103/physreve.92.032139] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/12/2015] [Indexed: 06/05/2023]
Abstract
A method for computing the thermopower in interacting systems is proposed. This approach, which relies on Monte Carlo simulations, is illustrated first for a diatomic chain of hard-point elastically colliding particles and then in the case of a one-dimensional gas with (screened) Coulomb interparticle interaction. Numerical simulations up to N>10^{4} particles confirm the general theoretical arguments for momentum-conserving systems and show that the thermoelectric figure of merit increases linearly with the system size.
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Affiliation(s)
- Shunda Chen
- Center for Nonlinear and Complex Systems, Università degli Studi dell'Insubria, via Valleggio 11, 22100 Como, Italy
- Istituto Nazionale di Fisica Nucleare, Sezione di Milano, via Celoria 16, 20133 Milano, Italy
| | - Jiao Wang
- Department of Physics and Institute of Theoretical Physics and Astrophysics, Xiamen University, Xiamen 361005, Fujian, China
| | - Giulio Casati
- Center for Nonlinear and Complex Systems, Università degli Studi dell'Insubria, via Valleggio 11, 22100 Como, Italy
- International Institute of Physics, Federal University of Rio Grande do Norte, Natal, Brazil
| | - Giuliano Benenti
- Center for Nonlinear and Complex Systems, Università degli Studi dell'Insubria, via Valleggio 11, 22100 Como, Italy
- Istituto Nazionale di Fisica Nucleare, Sezione di Milano, via Celoria 16, 20133 Milano, Italy
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23
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Wang L, Wu Z, Xu L. Super heat diffusion in one-dimensional momentum-conserving nonlinear lattices. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:062130. [PMID: 26172684 DOI: 10.1103/physreve.91.062130] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/02/2015] [Indexed: 06/04/2023]
Abstract
Heat diffusion processes in various one-dimensional total-momentum-conserving nonlinear lattices with symmetric interaction and asymmetric interaction are systematically studied. It is revealed that the asymmetry of interaction largely enhances the heat diffusion; while according to our existing studies for heat conduction in the same lattices, it slows the divergence of heat conductivity in a wide regime of system size. These findings violate the proposed relations that connect anomalous heat conduction and super heat diffusion. The generality of those expectations is thus questioned.
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Affiliation(s)
- Lei Wang
- Department of Physics and Beijing Key Laboratory of Opto-electronic Functional Materials and Micro-nano Devices, Renmin University of China, Beijing 100872, People's Republic of China
| | - Zhiyuan Wu
- Department of Physics and Beijing Key Laboratory of Opto-electronic Functional Materials and Micro-nano Devices, Renmin University of China, Beijing 100872, People's Republic of China
| | - Lubo Xu
- Department of Physics and Beijing Key Laboratory of Opto-electronic Functional Materials and Micro-nano Devices, Renmin University of China, Beijing 100872, People's Republic of China
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24
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Liu J, Liu S, Li N, Li B, Wu C. Renormalized phonons in nonlinear lattices: A variational approach. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:042910. [PMID: 25974565 DOI: 10.1103/physreve.91.042910] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/19/2015] [Indexed: 06/04/2023]
Abstract
We propose a variational approach to study renormalized phonons in momentum-conserving nonlinear lattices with either symmetric or asymmetric potentials. To investigate the influence of pressure for phonon properties, we derive an inequality which provides both the lower and upper bound of the Gibbs free energy as the associated variational principle. This inequality is a direct extension to the Gibbs-Bogoliubov inequality. Taking the symmetry effect into account, the reference system for the variational approach is chosen to be harmonic with an asymmetric quadratic potential which contains variational parameters. We demonstrate the power of this approach by applying it to one-dimensional nonlinear lattices with a symmetric or asymmetric Fermi-Pasta-Ulam-type potential. For a system with a symmetric potential and zero pressure, we recover existing results. For other systems which are beyond the scope of existing theories, including those having symmetric potential and pressure and those having the asymmetric potential with or without pressure, we also obtain accurate sound velocity.
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Affiliation(s)
- Junjie Liu
- State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai 200433, China
| | - Sha Liu
- Department of Physics and Centre for Computational Science and Engineering, National University of Singapore, 117546 Singapore
| | - Nianbei Li
- Center for Phononics and Thermal Energy Science, School of Physics Science and Engineering, Tongji University, Shanghai 200092, China
| | - Baowen Li
- Department of Physics and Centre for Computational Science and Engineering, National University of Singapore, 117546 Singapore
- Center for Phononics and Thermal Energy Science, School of Physics Science and Engineering, Tongji University, Shanghai 200092, China
- NUS Graduate School for Integrative Sciences and Engineering, 117456 Singapore
- Graphene Research Centre, Faculty of Science, National University of Singapore, 117542 Singapore
| | - Changqin Wu
- State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai 200433, China
- Collaborative Innovation Center of Advanced Microstructures, Fudan University, Shanghai 200433, China
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25
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Wang L, Xu L, Zhao H. Heat-current correlation loss induced by finite-size effects in a one-dimensional nonlinear lattice. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:012110. [PMID: 25679573 DOI: 10.1103/physreve.91.012110] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/22/2014] [Indexed: 06/04/2023]
Abstract
The Green-Kubo formula provides a mathematical expression for heat conductivity in terms of integrals of the heat-current correlation function, which should be calculated in the thermodynamic limit. In finite systems this function generally decreases, i.e., it decays faster than it does in infinite systems. We compared the values of the correlation function in a one-dimensional purely quartic lattice with various lengths, and found that this loss is much smaller than is conventionally estimated. By studying the heat diffusion process in this lattice, we found that, in contrast to the conventional belief, the collisions between sound modes do not noticeably affect the current correlation function. Therefore, its loss being surprisingly small can be well understood. This finding allows one to calculate the heat conductivity in a very large system with desirable accuracy by performing simulations in a system with much smaller size, and thus greatly broadens the application of the Green-Kubo method.
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Affiliation(s)
- Lei Wang
- Department of Physics and Beijing Key Laboratory of Opto-electronic Functional Materials and Micro-nano Devices, Renmin University of China, Beijing 100872, People's Republic of China
| | - Lubo Xu
- Department of Physics and Beijing Key Laboratory of Opto-electronic Functional Materials and Micro-nano Devices, Renmin University of China, Beijing 100872, People's Republic of China
| | - Huizhu Zhao
- Department of Physics and Beijing Key Laboratory of Opto-electronic Functional Materials and Micro-nano Devices, Renmin University of China, Beijing 100872, People's Republic of China
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26
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Yang L, Li N, Li B. Temperature-dependent thermal conductivities of one-dimensional nonlinear Klein-Gordon lattices with a soft on-site potential. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:062122. [PMID: 25615059 DOI: 10.1103/physreve.90.062122] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/19/2014] [Indexed: 06/04/2023]
Abstract
The temperature-dependent thermal conductivities of one-dimensional nonlinear Klein-Gordon lattices with soft on-site potential (soft-KG) are investigated systematically. Similarly to the previously studied hard-KG lattices, the existence of renormalized phonons is also confirmed in soft-KG lattices. In particular, the temperature dependence of the renormalized phonon frequency predicted by a classical field theory is verified by detailed numerical simulations. However, the thermal conductivities of soft-KG lattices exhibit the opposite trend in temperature dependence in comparison with those of hard-KG lattices. The interesting thing is that the temperature-dependent thermal conductivities of both soft- and hard-KG lattices can be interpreted in the same framework of effective phonon theory. According to the effective phonon theory, the exponents of the power-law dependence of the thermal conductivities as a function of temperature are only determined by the exponents of the soft or hard on-site potentials. These theoretical predictions are consistently verified very well by extensive numerical simulations.
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Affiliation(s)
- Linlin Yang
- Center for Phononics and Thermal Energy Science, School of Physics Science and Engineering, Tongji University, 200092 Shanghai, People's Republic of China
| | - Nianbei Li
- Center for Phononics and Thermal Energy Science, School of Physics Science and Engineering, Tongji University, 200092 Shanghai, People's Republic of China
| | - Baowen Li
- Center for Phononics and Thermal Energy Science, School of Physics Science and Engineering, Tongji University, 200092 Shanghai, People's Republic of China and Department of Physics and Centre for Computational Science and Engineering, National University of Singapore, Singapore 117546, Republic of Singapore and NUS Graduate School for Integrative Sciences and Engineering, Singapore 117456, Republic of Singapore
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27
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Chen S, Wang J, Casati G, Benenti G. Nonintegrability and the Fourier heat conduction law. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:032134. [PMID: 25314422 DOI: 10.1103/physreve.90.032134] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/07/2014] [Indexed: 06/04/2023]
Abstract
We study in momentum-conserving systems, how nonintegrable dynamics may affect thermal transport properties. As illustrating examples, two one-dimensional (1D) diatomic chains, representing 1D fluids and lattices, respectively, are numerically investigated. In both models, the two species of atoms are assigned two different masses and are arranged alternatively. The systems are nonintegrable unless the mass ratio is one. We find that when the mass ratio is slightly different from one, the heat conductivity may keep significantly unchanged over a certain range of the system size and as the mass ratio tends to one, this range may expand rapidly. These results establish a new connection between the macroscopic thermal transport properties and the underlying dynamics.
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Affiliation(s)
- Shunda Chen
- CNISM and Center for Nonlinear and Complex Systems, Università degli Studi dell'Insubria, via Valleggio 11, I-22100 Como, Italy and Istituto Nazionale di Fisica Nucleare, Sezione di Milano, via Celoria 16, I-20133 Milano, Italy
| | - Jiao Wang
- Department of Physics and Institute of Theoretical Physics and Astrophysics, Xiamen University, Xiamen 361005, Fujian, China
| | - Giulio Casati
- CNISM and Center for Nonlinear and Complex Systems, Università degli Studi dell'Insubria, via Valleggio 11, I-22100 Como, Italy and Istituto Nazionale di Fisica Nucleare, Sezione di Milano, via Celoria 16, I-20133 Milano, Italy and International Institute of Physics, Federal University of Rio Grande do Norte, Natal, Brasil
| | - Giuliano Benenti
- CNISM and Center for Nonlinear and Complex Systems, Università degli Studi dell'Insubria, via Valleggio 11, I-22100 Como, Italy and Istituto Nazionale di Fisica Nucleare, Sezione di Milano, via Celoria 16, I-20133 Milano, Italy
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28
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Morgado WAM, Duarte Queirós SM. Thermostatistics of small nonlinear systems: Gaussian thermal bath. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:022110. [PMID: 25215692 DOI: 10.1103/physreve.90.022110] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/22/2013] [Indexed: 06/03/2023]
Abstract
We discuss the statistical properties of small mechanothermodynamic systems (one- and two-particle cases) subject to nonlinear coupling and in contact with standard Gaussian reservoirs. We use a method that applies averages in the Laplace-Fourier space, which relates to a generalization of the final-value theorem. The key advantage of this method lies in the possibility of eschewing the explicit computation of the propagator, traditionally required in alternative methods like path integral calculations, which is hardly obtainable in the majority of the cases. For one-particle equilibrium systems we are able to compute the instantaneous (equilibrium) probability density functions of injected and dissipated power as well as the respective large deviation functions. Our thorough calculations explicitly show that for such models nonlinearities are irrelevant in the long-term statistics, which preserve the exact same values as computed for linear cases. Actually, we verify that the thermostatistical effect of the nonlinearities is constricted to the transient towards equilibrium, since it affects the average total energy of the system. For the two-particle system we consider each element in contact with a heat reservoir, at different temperatures, and focus on the problem of heat flux between them. Contrarily to the one-particle case, in this steady state nonequilibrium model we prove that the heat flux probability density function reflects the existence of nonlinearities in the system. An important consequence of that it is the temperature dependence of the conductance, which is unobserved in linear(harmonic) models. Our results are complemented by fluctuation relations for the injected power (equilibrium case) and heat flux (nonequilibrium case).
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Affiliation(s)
- Welles A M Morgado
- Department of Physics, PUC-Rio, and National Institute of Science and Technology for Complex Systems, Rua Marquês de São Vicente 225, 22453-900 Rio de Janeiro, RJ, Brazil
| | - Sílvio M Duarte Queirós
- Centro Brasileiro de Pesquisas Físicas and National Institute of Science and Technology for Complex Systems, Rua Dr Xavier Sigaud, 150, 22290-180 Rio de Janeiro, RJ, Brazil
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29
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Xiong D, Zhang Y, Zhao H. Temperature dependence of heat conduction in the Fermi-Pasta-Ulam-β lattice with next-nearest-neighbor coupling. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:022117. [PMID: 25215699 DOI: 10.1103/physreve.90.022117] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/03/2013] [Indexed: 06/03/2023]
Abstract
We show numerically that introducing the next-nearest-neighbor interactions (of appropriate strength) into the one-dimensional (1D) Fermi-Pasta-Ulam-β (FPU-β) lattice can result in an unusual, nonmonotonic temperature dependent divergence behavior in a wide temperature range, which is in clear contrast to the universal divergence manner independent of temperature as suggested previously in the conventional 1D FPU-β models with nearest-neighbor (NN) coupling only. We also discuss the underlying mechanism of this finding by analyzing the temperature variations of the properties of discrete breathers, especially that with frequencies having the intraband components. The results may provide useful information for establishing the connection between the macroscopic heat transport properties and the underlying dynamics in general 1D systems with interactions beyond NN couplings.
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Affiliation(s)
- Daxing Xiong
- Department of Physics, Fuzhou University, Fuzhou 350002, Fujian, China
| | - Yong Zhang
- Department of Physics and Institute of Theoretical Physics and Astrophysics, Xiamen University, Xiamen 361005, Fujian, China
| | - Hong Zhao
- Department of Physics and Institute of Theoretical Physics and Astrophysics, Xiamen University, Xiamen 361005, Fujian, China
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30
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Das SG, Dhar A, Saito K, Mendl CB, Spohn H. Numerical test of hydrodynamic fluctuation theory in the Fermi-Pasta-Ulam chain. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:012124. [PMID: 25122268 DOI: 10.1103/physreve.90.012124] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/16/2014] [Indexed: 06/03/2023]
Abstract
Recent work has developed a nonlinear hydrodynamic fluctuation theory for a chain of coupled anharmonic oscillators governing the conserved fields, namely, stretch, momentum, and energy. The linear theory yields two propagating sound modes and one diffusing heat mode, all three with diffusive broadening. In contrast, the nonlinear theory predicts that, at long times, the sound mode correlations satisfy Kardar-Parisi-Zhang scaling, while the heat mode correlations have Lévy-walk scaling. In the present contribution we report on molecular dynamics simulations of Fermi-Pasta-Ulam chains to compute various spatiotemporal correlation functions and compare them with the predictions of the theory. We obtain very good agreement in many cases, but also some deviations.
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Affiliation(s)
- Suman G Das
- Raman Research Institute, CV Raman Avenue, Sadashivanagar, Bangalore 560080, India
| | - Abhishek Dhar
- International Center for Theoretical Sciences, TIFR, IISC Campus, Bangalore 560012, India
| | - Keiji Saito
- Department of Physics, Keio University, Yokohama 223-8522, Japan
| | - Christian B Mendl
- Zentrum Mathematik, TU München, Boltzmannstraße 3, 85747 Garching, Germany
| | - Herbert Spohn
- Institute for Advanced Study, Einstein Drive, Princeton, New Jersey 08540, USA
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31
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Gill-Comeau M, Lewis LJ. Cross-correlations between phonon modes in anharmonic oscillator chains: role in heat transport. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:042114. [PMID: 24827200 DOI: 10.1103/physreve.89.042114] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/28/2014] [Indexed: 06/03/2023]
Abstract
We have computed current-current correlation functions in chains of anharmonic oscillators described by various models (FPU-β, FPU-αβ, ϕ4), considering both the total current and the currents associated with individual phonon modes, which are important in view of the Green-Kubo relation for heat conductivity. Our simulations show that, contrary to the common hypothesis, there are, under some circumstances, significant correlations between neighboring modes. These cross-mode correlations are the dominant contribution to the conductivity in the low anharmonicity regime. The inverse of the timescale over which they are significant, 1/τc, is related to the anharmonicity level in a way similar to the largest Lyapunov exponent, suggesting that the two quantities are related. Cross-mode correlations exist in both anomalous and regular heat-conducting systems although we are unable to observe a transition to the independent-mode regime in the latter case.
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Affiliation(s)
- Maxime Gill-Comeau
- Département de Physique et Regroupement Québécois sur les Matériaux de Pointe (RQMP), Université de Montréal, C.P. 6128, Succursale Centre-Ville, Montréal, Québec H3C 3J7, Canada
| | - Laurent J Lewis
- Département de Physique et Regroupement Québécois sur les Matériaux de Pointe (RQMP), Université de Montréal, C.P. 6128, Succursale Centre-Ville, Montréal, Québec H3C 3J7, Canada
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32
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Savin AV, Kosevich YA. Thermal conductivity of molecular chains with asymmetric potentials of pair interactions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:032102. [PMID: 24730785 DOI: 10.1103/physreve.89.032102] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/30/2013] [Indexed: 06/03/2023]
Abstract
We provide molecular-dynamics simulation of heat transport in one-dimensional molecular chains with different interparticle pair potentials. We show that the thermal conductivity is finite in the thermodynamic limit in chains with the potentials that allow for bond dissociation. The Lennard-Jones, Morse, and Coulomb potentials are such potentials. The convergence of the thermal conductivity is provided by phonon scattering on the locally strongly stretched loose interatomic bonds at low temperature and by the many-particle scattering at high temperature. On the other hand, chains with a confining pair potential, which does not allow for bond dissociation, possess anomalous thermal conductivity, diverging with the chain length. We emphasize that chains with a symmetric or asymmetric Fermi-Pasta-Ulam potential or with combined potentials, containing a parabolic and/or a quartic confining potential, all exhibit anomalous heat transport.
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Affiliation(s)
- Alexander V Savin
- Semenov Institute of Chemical Physics, Russian Academy of Sciences, Moscow 119991, Russia
| | - Yuriy A Kosevich
- Semenov Institute of Chemical Physics, Russian Academy of Sciences, Moscow 119991, Russia and Laboratoire d'Energétique Moléculaire et Macroscopique, CNRS UPR 288, Ecole Centrale Paris, Grande Voie des Vignes, 92295 Châtenay-Malabry, France
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33
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Savin AV, Gendelman OV. Mechanical control of heat conductivity in molecular chains. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:012134. [PMID: 24580199 DOI: 10.1103/physreve.89.012134] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/06/2013] [Indexed: 06/03/2023]
Abstract
We discuss a possibility to control heat conductivity in molecular chains by means of external mechanical loads. To illustrate such possibilities we consider first well-studied one-dimensional chain with degenerate double-well potential of the nearest-neighbor interaction. We consider varying lengths of the chain with fixed number of particles. Number of possible energetically degenerate ground states strongly depends on the overall length of the chain, or, in other terms, on average length of the link between neighboring particles. These degenerate states correspond to mechanical equilibria; therefore, one can say that formation of such structures mimics a process of plastic deformation. We demonstrate that such modification of the chain length can lead to quite profound (almost fivefold) reduction of the heat conduction coefficient. Even more profound effect is revealed for a model with a single-well nonconvex potential. It is demonstrated that in a certain range of constant external forcing, this model becomes effectively double-well and has a multitude of possible states of equilibrium for fixed value of the external load. Due to this degeneracy, the heat-conduction coefficient can be reduced by two orders of magnitude. We suggest a mechanical model of a chain with periodic double-well potential, which allows control of the heat transport. The models considered may be useful for description of heat transfer in biological macromolecules and for control of the heat transport in microsystems. The possibility of the heat transport control in more realistic three-dimensional systems is illustrated by simulation of a three-dimensional model of polymer α-helix. In this model, the mechanical stretching also brings about the structural inhomogeneity and, in turn, to essential reduction of the heat conductivity.
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Affiliation(s)
- A V Savin
- Semenov Institute of Chemical Physics, Russian Academy of Sciences, Moscow 119991, Russia
| | - O V Gendelman
- Faculty of Mechanical Engineering, Technion-Israel Institute of Technology, Haifa 32000, Israel
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