1
|
Fu W, Zhang Y, Zhao H. Effect of pressure on thermalization of one-dimensional nonlinear chains. Phys Rev E 2021; 104:L032104. [PMID: 34654109 DOI: 10.1103/physreve.104.l032104] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/31/2021] [Accepted: 08/30/2021] [Indexed: 11/07/2022]
Abstract
Pressure plays a vital role in changing the transport properties of matter. To understand this phenomenon at a microscopic level, we here focus on a more fundamental problem, i.e., how pressure affects the thermalization properties of solids. As illustrating examples, we study the thermalization behavior of the monatomic chain and the mass-disordered chain of Fermi-Pasta-Ulam-Tsingou-β under different strains in the thermodynamic limit. It is found that the pressure-induced change in integrability results in qualitatively different thermalization processes for the two kinds of chains. However, for both cases, the thermalization time follows the same law-it is inversely proportional to the square of the nonintegrability strength. This result suggests that pressure can significantly change the integrability of a system, which provides a new perspective for understanding the pressure-dependent thermal transport behavior.
Collapse
Affiliation(s)
- Weicheng Fu
- Department of Physics, Tianshui Normal University, Tianshui 741001, Gansu, China.,Lanzhou Center for Theoretical Physics, Key Laboratory of Theoretical Physics of Gansu Province, Lanzhou University, Lanzhou, Gansu 730000, China
| | - Yong Zhang
- Department of Physics, Xiamen University, Xiamen 361005, Fujian, China.,Lanzhou Center for Theoretical Physics, Key Laboratory of Theoretical Physics of Gansu Province, Lanzhou University, Lanzhou, Gansu 730000, China
| | - Hong Zhao
- Department of Physics, Xiamen University, Xiamen 361005, Fujian, China.,Lanzhou Center for Theoretical Physics, Key Laboratory of Theoretical Physics of Gansu Province, Lanzhou University, Lanzhou, Gansu 730000, China
| |
Collapse
|
2
|
Chakraborti S, Ganapa S, Krapivsky PL, Dhar A. Blast in a One-Dimensional Cold Gas: From Newtonian Dynamics to Hydrodynamics. PHYSICAL REVIEW LETTERS 2021; 126:244503. [PMID: 34213930 DOI: 10.1103/physrevlett.126.244503] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/02/2021] [Accepted: 05/20/2021] [Indexed: 06/13/2023]
Abstract
A gas composed of a large number of atoms evolving according to Newtonian dynamics is often described by continuum hydrodynamics. Proving this rigorously is an outstanding open problem, and precise numerical demonstrations of the equivalence of the hydrodynamic and microscopic descriptions are rare. We test this equivalence in the context of the evolution of a blast wave, a problem that is expected to be at the limit where hydrodynamics could work. We study a one-dimensional gas at rest with instantaneous localized release of energy for which the hydrodynamic Euler equations admit a self-similar scaling solution. Our microscopic model consists of hard point particles with alternating masses, which is a nonintegrable system with strong mixing dynamics. Our extensive microscopic simulations find a remarkable agreement with Euler hydrodynamics, with deviations in a small core region that are understood as arising due to heat conduction.
Collapse
Affiliation(s)
- Subhadip Chakraborti
- International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bengaluru 560089, India
| | - Santhosh Ganapa
- International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bengaluru 560089, India
| | - P L Krapivsky
- Department of Physics, Boston University, Boston, Massachusetts 02215, USA
- Skolkovo Institute of Science and Technology, 143026 Moscow, Russia
| | - Abhishek Dhar
- International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bengaluru 560089, India
| |
Collapse
|
3
|
Luo R, Huang L, Lepri S. Heat conduction in a three-dimensional momentum-conserving fluid. Phys Rev E 2021; 103:L050102. [PMID: 34134304 DOI: 10.1103/physreve.103.l050102] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/28/2021] [Accepted: 04/28/2021] [Indexed: 11/07/2022]
Abstract
Size dependence of energy transport and the effects of reduced dimensionality on transport coefficients are of key importance for understanding nonequilibrium properties of matter on the nanoscale. Here, we perform nonequilibrium and equilibrium simulations of heat conduction in a three-dimensional (3D) fluid with the multiparticle collision dynamics, interacting with two thermal walls. We find that the bulk 3D momentum-conserving fluid has a finite nondiverging thermal conductivity. However, for large aspect ratios of the simulation box, a crossover from 3D to one-dimensional (1D) abnormal behavior of the thermal conductivity occurs. In this case, we demonstrate a transition from normal to abnormal transport by a suitable decomposition of the energy current. These results not only provide a direct verification of Fourier's law, but also further confirm the validity of existing theories for 3D fluids. Moreover, they indicate that abnormal heat transport persists also for almost 1D fluids over a large range of sizes.
Collapse
Affiliation(s)
- Rongxiang Luo
- Department of Physics, Fuzhou University, Fuzhou 350108, Fujian, China.,Fujian Science and Technology Innovation Laboratory for Optoelectronic Information of China, Fuzhou 350108, Fujian, China
| | - Lisheng Huang
- Department of Physics, Fuzhou University, Fuzhou 350108, Fujian, China.,Fujian Science and Technology Innovation Laboratory for Optoelectronic Information of China, Fuzhou 350108, Fujian, China
| | - 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
| |
Collapse
|
4
|
Luo R. Heat conduction in two-dimensional momentum-conserving and -nonconserving gases. Phys Rev E 2020; 102:052104. [PMID: 33327068 DOI: 10.1103/physreve.102.052104] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/30/2020] [Accepted: 10/18/2020] [Indexed: 06/12/2023]
Abstract
Compared to that for two-dimensional (2D) lattices, our understanding of heat conduction in 2D gases is still limited. Here we study heat conduction behavior of 2D gas systems with momentum-conserving and -nonconserving interparticle interactions by using the nonequilibrium and equilibrium molecular dynamics methods. For the momentum-conserving system, we find that when the dimensionality of the system is changed from 2D to quasi-one-dimensional (quasi-1D), the heat conductivity κ diverges with the system size L as κ∼lnL (the theoretical prediction for 2D systems) for a short L and shows, in the thermodynamic limit, a tendency to κ∼L^{1/3} like that predicted in 1D fluids. This suggests that the dimensional-crossover effect of heat conduction exists in 2D systems with conserved momentum. In contrast, for the momentum-nonconserving system, as L increases, finite heat conductivity independent of L is observed. These findings are in agreement with the predictions given by hydrodynamic theory and thus further confirm the validity of the theory in 2D gases.
Collapse
Affiliation(s)
- Rongxiang Luo
- Department of Physics, Fuzhou University, Fuzhou 350108, Fujian, China and Fujian Science and Technology Innovation Laboratory for Optoelectronic Information of China, Fuzhou 350108, Fujian, China
| |
Collapse
|
5
|
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.
Collapse
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
| |
Collapse
|
6
|
Miron A, Cividini J, Kundu A, Mukamel D. Derivation of fluctuating hydrodynamics and crossover from diffusive to anomalous transport in a hard-particle gas. Phys Rev E 2019; 99:012124. [PMID: 30780243 DOI: 10.1103/physreve.99.012124] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/13/2018] [Indexed: 06/09/2023]
Abstract
A recently developed nonlinear fluctuating hydrodynamics theory has been quite successful in describing various features of anomalous energy transport. However, the diffusion and the noise terms present in this theory are not derived from microscopic descriptions but rather added phenomenologically. We here derive these hydrodynamic equations with explicit calculation of the diffusion and noise terms in a one-dimensional model. We show that in this model the energy current scales anomalously with system size L as ∼L^{-2/3} in the leading order with a diffusive correction of order ∼L^{-1}. The crossover length ℓ_{c} from diffusive to anomalous transport is expressed in terms of microscopic parameters. Our theoretical predictions are verified numerically.
Collapse
Affiliation(s)
- Asaf Miron
- Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 7610001, Israel
| | - Julien Cividini
- Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 7610001, Israel
| | - Anupam Kundu
- International Center for Theoretical Sciences, TIFR, Bangalore-560012, India
| | - David Mukamel
- Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 7610001, Israel
| |
Collapse
|