Linear-response formula for finite-frequency thermal conductance of open systems

Abhishek Dhar, Onuttom Narayan, Anupam Kundu, Keiji Saitou

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

An exact linear-response expression is obtained for the heat current in a classical Hamiltonian system coupled to heat baths with time-dependent temperatures. The expression is equally valid at zero and finite frequencies. We present numerical results on the frequency dependence of the response function for three different one-dimensional models of coupled oscillators connected to Langevin baths with oscillating temperatures. For momentum conserving systems, a low-frequency peak is seen that is higher than the zero-frequency response for large systems. For momentum nonconserving systems, there is no low-frequency peak. The momentum nonconserving system is expected to satisfy Fourier's law; however, at the single bond level, we do not see any clear agreement with the predictions of the diffusion equation even at low frequencies. We also derive an exact analytical expression for the response of a chain of harmonic oscillators to a (not necessarily small) temperature difference; the agreement with the linear-response simulation results for the same system is excellent.

Original languageEnglish
Article number011101
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume83
Issue number1
DOIs
Publication statusPublished - 2011 Jan 3
Externally publishedYes

Fingerprint

Linear Response
Open Systems
Conductance
Low Frequency
low frequencies
momentum
Momentum
baths
Fourier law
heat
Fourier's Law
Heat Bath
harmonic oscillators
frequency response
Zero
Coupled Oscillators
Response Function
temperature gradients
Frequency Response
One-dimensional Model

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Statistical and Nonlinear Physics
  • Statistics and Probability

Cite this

Linear-response formula for finite-frequency thermal conductance of open systems. / Dhar, Abhishek; Narayan, Onuttom; Kundu, Anupam; Saitou, Keiji.

In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, Vol. 83, No. 1, 011101, 03.01.2011.

Research output: Contribution to journalArticle

@article{dd6146b5982a442eb248846e3d36d39b,
title = "Linear-response formula for finite-frequency thermal conductance of open systems",
abstract = "An exact linear-response expression is obtained for the heat current in a classical Hamiltonian system coupled to heat baths with time-dependent temperatures. The expression is equally valid at zero and finite frequencies. We present numerical results on the frequency dependence of the response function for three different one-dimensional models of coupled oscillators connected to Langevin baths with oscillating temperatures. For momentum conserving systems, a low-frequency peak is seen that is higher than the zero-frequency response for large systems. For momentum nonconserving systems, there is no low-frequency peak. The momentum nonconserving system is expected to satisfy Fourier's law; however, at the single bond level, we do not see any clear agreement with the predictions of the diffusion equation even at low frequencies. We also derive an exact analytical expression for the response of a chain of harmonic oscillators to a (not necessarily small) temperature difference; the agreement with the linear-response simulation results for the same system is excellent.",
author = "Abhishek Dhar and Onuttom Narayan and Anupam Kundu and Keiji Saitou",
year = "2011",
month = "1",
day = "3",
doi = "10.1103/PhysRevE.83.011101",
language = "English",
volume = "83",
journal = "Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics",
issn = "1063-651X",
publisher = "American Physical Society",
number = "1",

}

TY - JOUR

T1 - Linear-response formula for finite-frequency thermal conductance of open systems

AU - Dhar, Abhishek

AU - Narayan, Onuttom

AU - Kundu, Anupam

AU - Saitou, Keiji

PY - 2011/1/3

Y1 - 2011/1/3

N2 - An exact linear-response expression is obtained for the heat current in a classical Hamiltonian system coupled to heat baths with time-dependent temperatures. The expression is equally valid at zero and finite frequencies. We present numerical results on the frequency dependence of the response function for three different one-dimensional models of coupled oscillators connected to Langevin baths with oscillating temperatures. For momentum conserving systems, a low-frequency peak is seen that is higher than the zero-frequency response for large systems. For momentum nonconserving systems, there is no low-frequency peak. The momentum nonconserving system is expected to satisfy Fourier's law; however, at the single bond level, we do not see any clear agreement with the predictions of the diffusion equation even at low frequencies. We also derive an exact analytical expression for the response of a chain of harmonic oscillators to a (not necessarily small) temperature difference; the agreement with the linear-response simulation results for the same system is excellent.

AB - An exact linear-response expression is obtained for the heat current in a classical Hamiltonian system coupled to heat baths with time-dependent temperatures. The expression is equally valid at zero and finite frequencies. We present numerical results on the frequency dependence of the response function for three different one-dimensional models of coupled oscillators connected to Langevin baths with oscillating temperatures. For momentum conserving systems, a low-frequency peak is seen that is higher than the zero-frequency response for large systems. For momentum nonconserving systems, there is no low-frequency peak. The momentum nonconserving system is expected to satisfy Fourier's law; however, at the single bond level, we do not see any clear agreement with the predictions of the diffusion equation even at low frequencies. We also derive an exact analytical expression for the response of a chain of harmonic oscillators to a (not necessarily small) temperature difference; the agreement with the linear-response simulation results for the same system is excellent.

UR - http://www.scopus.com/inward/record.url?scp=78651429595&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=78651429595&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.83.011101

DO - 10.1103/PhysRevE.83.011101

M3 - Article

AN - SCOPUS:78651429595

VL - 83

JO - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

JF - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

SN - 1063-651X

IS - 1

M1 - 011101

ER -