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Sun Y, Wang L. Heat transport in an angular-momentum-conserving lattice. Phys Rev E 2024; 109:034118. [PMID: 38632744 DOI: 10.1103/physreve.109.034118] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/04/2024] [Accepted: 02/23/2024] [Indexed: 04/19/2024]
Abstract
It is expected that the energy-diffusion propagator in a one-dimensional nonlinear lattice with three conserved quantities: energy, momentum, and stretch, consists of a central heat mode and two sound modes. The heat mode follows a Lévy distribution. Consequently, the heat diffusion is super, i.e., the second moment of the diffusion propagator diverges as t^{β} with β>1; and the heat conduction is anomalous, i.e., the heat conductivity is size dependent and diverges with size N by N^{α}, with α>0. In this paper, we study a one-dimensional lattice with two-dimensional transverse motions, in which the total angular momentum also conserves. More importantly, the diffusion of this conserved quantity is ballistic. Surprisingly, the above pictures and the values of the mentioned power exponents keep unchanged. The universality of the scalings is then further extended. On the other hand, the detailed strengths of heat transports are largely enhanced. Such a counterintuitive finding can be explained by the change of the phonon mean-free path of the lattices.
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Affiliation(s)
- Yachao Sun
- Department of Physics, Beijing Key Laboratory of Opto-electronic Functional Materials and Micro-nano Devices, and Key Laboratory of Quantum State Construction and Manipulation (Ministry of Education), Renmin University of China, Beijing 100872, People's Republic of China
| | - Lei Wang
- Department of Physics, Beijing Key Laboratory of Opto-electronic Functional Materials and Micro-nano Devices, and Key Laboratory of Quantum State Construction and Manipulation (Ministry of Education), Renmin University of China, Beijing 100872, People's Republic of China
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2
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Guo Y, Sun Y, Wang L. Thermalization process in a one-dimensional lattice with two-dimensional motions: The role of angular momentum conservation. Phys Rev E 2023; 108:014127. [PMID: 37583148 DOI: 10.1103/physreve.108.014127] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/17/2023] [Accepted: 06/27/2023] [Indexed: 08/17/2023]
Abstract
We study the thermalization process in a one-dimensional lattice with two-dimensional motions. The phonon modes in such a lattice consist of two branches. Unlike in general nonlinear Hamiltonian systems, for which the only conserved quantity is the total energy, the total angular momentum J is also conserved in this system. Consequently, the intra- and interbranch energy transports behave significantly differently. For the intrabranch transport, all the existing rules for the one-dimensional systems including the Chirikov overlap criterion apply. As for the interbranch transport, some trivial processes in one-dimensional lattices become nontrivial. During these processes, all the conservation laws can be satisfied exactly; thus the Chirikov criterion does not apply. These processes provide some fast channels for the interbranch transport, although the thermalization cannot be reached through them alone. A system with nonzero-J initial state, however, can never be thermalized to an equipartition state having zero J. Quite counterintuitively, the corresponding asymptotic mode energy distribution greatly concentrates to a few lowest-frequency modes in one branch.
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Affiliation(s)
- Yanjiang Guo
- Department of Physics, Beijing Key Laboratory of Opto-electronic Functional Materials and Micro-nano Devices, and Key Laboratory of Quantum State Construction and Manipulation (Ministry of Education), Renmin University of China, Beijing 100872, People's Republic of China
| | - Yachao Sun
- Department of Physics, Beijing Key Laboratory of Opto-electronic Functional Materials and Micro-nano Devices, and Key Laboratory of Quantum State Construction and Manipulation (Ministry of Education), Renmin University of China, Beijing 100872, People's Republic of China
| | - Lei Wang
- Department of Physics, Beijing Key Laboratory of Opto-electronic Functional Materials and Micro-nano Devices, and Key Laboratory of Quantum State Construction and Manipulation (Ministry of Education), Renmin University of China, Beijing 100872, People's Republic of China
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Guo Y, Sun Y, Wang L. Energy diffusion in two-dimensional momentum-conserving nonlinear lattices: Lévy walk and renormalized phonon. Phys Rev E 2023; 107:014109. [PMID: 36797934 DOI: 10.1103/physreve.107.014109] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/28/2022] [Accepted: 12/21/2022] [Indexed: 01/12/2023]
Abstract
The energy diffusion process in a few two-dimensional Fermi-Pasta-Ulam-type lattices is numerically simulated via the equilibrium local energy spatiotemporal correlation. Just as the nonlinear fluctuating hydrodynamic theory suggested, the diffusion propagator consists of a bell-shaped central heat mode and a sound mode extending with a constant speed. The profiles of the heat and sound modes satisfy the scaling properties from a random-walk-with-velocity-fluctuation process very well. An effective phonon approach is proposed, which expects the frequencies of renormalized phonons as well as the sound speed with quite good accuracy. Since many existing analytical and numerical studies indicate that heat conduction in such two-dimensional momentum-conserving lattices is divergent and the thermal conductivity κ increases logarithmically with lattice length, it is expected that the mean-square displacement of energy diffusion grows as tlnt. Discrepancies, however, are noticeably observed.
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Affiliation(s)
- Yanjiang Guo
- 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
| | - Yachao Sun
- 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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Li N, Liu J. Accessing general relations for temperature coefficients of Raman shifts in 2D materials. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2020; 32:285402. [PMID: 32160604 DOI: 10.1088/1361-648x/ab7f07] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
The temperature coefficient of Raman shifts, which regulates the linear-in-temperature dependence of Raman shifts, plays a vital role in the experimental determinations of thermal conductivities in two-dimensional (2D) materials. Originating from anharmonic phonon effects, however, its connection to the underlying phonon structure remains poorly understood. Here, we explore the possibility of a simple albeit general relation that relates temperature coefficients to frequencies of the associated phonon modes in 2D materials. Remarkably, by resorting to a renormalized phonon picture, we explicitly show that the ratio between the temperature coefficient of Raman shifts and the associated phonon frequency is almost a constant that is varied only among materials. Our general relation fits well to experimental results for typical 2D materials and may have implications for addressing the impact of anharmonic phonon effects on thermal conductivities in 2D materials.
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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, People's Republic of China
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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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Renormalized vibrations and normal energy transport in 1d FPU-like discrete nonlinear Schrödinger equations. Sci Rep 2018; 8:5329. [PMID: 29593230 PMCID: PMC5871775 DOI: 10.1038/s41598-018-23719-2] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/05/2018] [Accepted: 03/20/2018] [Indexed: 11/08/2022] Open
Abstract
For one-dimensional (1d) nonlinear atomic lattices, the models with on-site nonlinearities such as the Frenkel-Kontorova (FK) and ϕ4 lattices have normal energy transport while the models with inter-site nonlinearities such as the Fermi-Pasta-Ulam-β (FPU-β) lattice exhibit anomalous energy transport. The 1d Discrete Nonlinear Schrödinger (DNLS) equations with on-site nonlinearities has been previously studied and normal energy transport has also been found. Here, we investigate the energy transport of 1d FPU-like DNLS equations with inter-site nonlinearities. Extended from the FPU-β lattice, the renormalized vibration theory is developed for the FPU-like DNLS models and the predicted renormalized vibrations are verified by direct numerical simulations same as the FPU-β lattice. However, the energy diffusion processes are explored and normal energy transport is observed for the 1d FPU-like DNLS models, which is different from their atomic lattice counterpart of FPU-β lattice. The reason might be that, unlike nonlinear atomic lattices where models with on-site nonlinearities have one less conserved quantities than the models with inter-site nonlinearities, the DNLS models with on-site or inter-site nonlinearities have the same number of conserved quantities as the result of gauge transformation.
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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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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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Bojahr A, Gohlke M, Leitenberger W, Pudell J, Reinhardt M, von Reppert A, Roessle M, Sander M, Gaal P, Bargheer M. Second Harmonic Generation of Nanoscale Phonon Wave Packets. PHYSICAL REVIEW LETTERS 2015; 115:195502. [PMID: 26588396 DOI: 10.1103/physrevlett.115.195502] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/01/2015] [Indexed: 05/06/2023]
Abstract
Phonons are often regarded as delocalized quasiparticles with certain energy and momentum. The anharmonic interaction of phonons determines macroscopic properties of the solid, such as thermal expansion or thermal conductivity, and a detailed understanding becomes increasingly important for functional nanostructures. Although phonon-phonon scattering processes depicted in simple wave-vector diagrams are the basis of theories describing these macroscopic phenomena, experiments directly accessing these coupling channels are scarce. We synthesize monochromatic acoustic phonon wave packets with only a few cycles to introduce nonlinear phononics as the acoustic counterpart to nonlinear optics. Control of the wave vector, bandwidth, and consequently spatial extent of the phonon wave packets allows us to observe nonlinear phonon interaction, in particular, second harmonic generation, in real time by wave-vector-sensitive Brillouin scattering with x-rays and optical photons.
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Affiliation(s)
- A Bojahr
- Institut für Physik and Astronomie, Universität Potsdam, Karl-Liebknecht-Strasse 24-25, 14476 Potsdam, Germany
| | - M Gohlke
- Institut für Physik and Astronomie, Universität Potsdam, Karl-Liebknecht-Strasse 24-25, 14476 Potsdam, Germany
| | - W Leitenberger
- Institut für Physik and Astronomie, Universität Potsdam, Karl-Liebknecht-Strasse 24-25, 14476 Potsdam, Germany
| | - J Pudell
- Institut für Physik and Astronomie, Universität Potsdam, Karl-Liebknecht-Strasse 24-25, 14476 Potsdam, Germany
| | - M Reinhardt
- Helmholtz Zentrum Berlin, Albert-Einstein-Strasse 15, 12489 Berlin, Germany
| | - A von Reppert
- Institut für Physik and Astronomie, Universität Potsdam, Karl-Liebknecht-Strasse 24-25, 14476 Potsdam, Germany
| | - M Roessle
- Institut für Physik and Astronomie, Universität Potsdam, Karl-Liebknecht-Strasse 24-25, 14476 Potsdam, Germany
| | - M Sander
- Institut für Physik and Astronomie, Universität Potsdam, Karl-Liebknecht-Strasse 24-25, 14476 Potsdam, Germany
| | - P Gaal
- Helmholtz Zentrum Berlin, Albert-Einstein-Strasse 15, 12489 Berlin, Germany
| | - M Bargheer
- Institut für Physik and Astronomie, Universität Potsdam, Karl-Liebknecht-Strasse 24-25, 14476 Potsdam, Germany
- Helmholtz Zentrum Berlin, Albert-Einstein-Strasse 15, 12489 Berlin, Germany
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