Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics

Thermal conduction in a quantum system

Keiji Saito, Shinji Takesue, Seiji Miyashita

Published Sep 1, 1996• 79 citations
Publisher

Abstract

We numerically investigate thermal conduction in quantum dynamics. A one-dimensional quantum spin system is used as a model, which we can make integrable or nonintegrable by controlling parameter values. A different method to simulate heat reservoirs is introduced. Using this method, we perform numerical simulations of the spin chain in contact with two heat reservoirs at different temperatures. As a consequence, a flat temperature profile is observed in the integrable case, while a finite temperature gradient is found in a nonintegrable system. This result suggests that the Fourier heat law may be realized in nonintegrable systems and is consistent with the classical case reported in the literature. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physreve.54.2404

Related papers

Heat conduction in one-dimensional aperiodic quantum Ising chains

Wenjuan Li, Peiqing Tong

The heat conductivity of nonperiodic quantum Ising chains whose ends are connected with heat baths at different temperatures are studied numerically by solving the Lindblad master equation. The chains are subjected to a uniform transverse field h, while the exchange coupling J{m} between the nearest-neighbor spins takes the two values J{A} and J{B} arranged in Fibonacci, generalized Fibonacci, Thue-Morse, and period-doubling sequences. We calculate the energy-density profile and energy current of the resulting nonequilibrium steady states to study the heat-conducting behavior of finite but large systems. Although these nonperiodic quantum Ising chains are integrable, it is clearly found that energy gradients exist in all chains and the energy currents appear to scale as the system size ~N{α}. By increasing the ratio of couplings, the exponent α can be modulated from α > -1 to α < -1 corresponding to the nontrivial transition from the abnormal heat transport to the heat insulator. The influences of the temperature gradient and the magnetic field to heat conduction have also been discussed.

Physical Review E•Mar 23, 2011•7 citations

Thermally driven classical Heisenberg model in one dimension

Debarshee Bagchi, P. K. Mohanty

We study thermal transport in a classical one-dimensional Heisenberg model employing a discrete-time odd-even precessional update scheme. This dynamics equilibrates a spin chain for any arbitrary temperature and finite value of the integration time step $\ensuremath{\Delta}t$. We rigorously show that in presence of driving, the system attains local thermal equilibrium, which is a strict requirement of Fourier law. In the thermodynamic limit, heat current for such a system obeys Fourier law for all temperatures, as has been recently shown [A. V. Savin, G. P. Tsironis, and X. Zotos, Phys. Rev. B 72, 140402(R) (2005)]. Finite systems, however, show an apparent ballistic transport which crosses over to a diffusive one as the system size is increased. We provide exact results for current and energy profiles in zero- and infinite-temperature limits.

arXiv:1206.2827•Physical Review B•Dec 14, 2012•8 citations

Evidence for ideal insulating or conducting state in a one-dimensional integrable system

X. Zotos, Peter Prelovšek

Using numerical diagonalization techniques we analyze the finite temperature/frequency conductance of a one-dimensional model of interacting spinless fermions. Depending on the interaction, the observed finite temperature charge stiffness and low-frequency conductance indicate a fundamental difference between integrable and nonintegrable cases. The integrable systems behave as ideal conductors in the metallic regime and as ideal insulators in the insulating one. The nonintegrable systems are, as expected, generic conductors in the metallic regime and activated ones in the insulating regime. \textcopyright{} 1996 The American Physical Society.

arXiv:cond-mat/9508078•Physical review. B, Condensed matter•Jan 15, 1996•148 citations

Thermal transport in one-dimensional spin heterostructures

Liliana Arrachea, Gustavo Sergio Lozano, Armando A. Aligia

We study heat transport in a one-dimensional inhomogeneous quantum spin-1/2 system. It consists of a finite-size $XX$ spin chain coupled at its ends to semi-infinite $XX$ and $XY$ chains at different temperatures, which play the role of heat and spin reservoirs. After using the Jordan-Wigner transformation we map the original spin Hamiltonian into a fermionic Hamiltonian, which contains normal and pairing terms. We find the expressions for the heat currents and solve the problem with a nonequilibrium Green's-function formalism. We analyze the behavior of the heat currents as functions of the model parameters. When finite magnetic fields are applied at the two reservoirs, the system exhibits rectifying effects in the heat flow.

arXiv:0903.3671•Physical Review B•Jul 23, 2009•47 citations

Nonballistic heat conduction in an integrable random-exchange Ising chain studied with quantum master equations

Yonghong Yan, Chang-Qin Wu, Giulio Casati +2 more

We numerically investigate the heat conduction in a random-exchange Ising spin chain by using the quantum master equation. The chain is subject to a uniform transverse field $h$, while the exchange couplings ${{Q}_{n}}$ between the nearest neighbor spins are random; the largest size we simulate is up to 10. This model is integrable; i.e., the nearest neighbor level spacing distribution is Poissonian. However, we find clear evidence of nonballistic transport. In the small coupling regime $({Q}_{n}\ensuremath{\ll}h)$, an energy and/or temperature gradient in the bulk of the system is observed and the energy current appears to be proportional to the inverse of the system size. Moreover, we find that in the low and high temperature regimes, the thermal conductivity $\ensuremath{\kappa}$ and the specific heat ${C}_{v}$ have the same dependence on temperature. The large coupling case $({Q}_{n}\ensuremath{\sim}h)$ is also discussed.

Physical Review B•May 23, 2008•22 citations

Strong evidence of normal heat conduction in a one-dimensional quantum system

K Saito

We investigate how the normal energy transport is realized in one-dimensional quantum systems using a quantum spin system. The direct investigation of local energy distribution under thermal gradient is made using the quantum master equation, and the mixing properties and the convergence of the Green-Kubo formula are investigated when the number of spin increases. We find that the autocorrelation function in the Green-Kubo formula decays as ∼ t −1.5 to a finite value which vanishes rapidly with the increase of the system size. As a result, the Green-Kubo formula converges to a finite value in the thermodynamic limit. These facts strongly support the realization of Fourier heat law in a quantum system.

arXiv:nlin/0212027•Europhysics Letters (EPL)•Jan 1, 2003•116 citations
We numerically investigate thermal conduction in quantum dynamics. A one-dimensional quantum spin system is used as a model, which we can make integrable or nonintegrable by controlling parameter values. A different method to simulate heat reservoirs is introduced. Using this method, we perform numerical simulations of the spin chain in contact with two heat reservoirs at different temperatures. As a consequence, a flat temperature profile is observed in the integrable case, while a finite temperature gradient is found in a nonintegrable system. This result suggests that the Fourier heat law may be realized in nonintegrable systems and is consistent with the classical case reported in the literature. \textcopyright{} 1996 The American Physical Society.
The heat conductivity of nonperiodic quantum Ising chains whose ends are connected with heat baths at different temperatures are studied numerically by solving the Lindblad master equation. The chains are subjected to a uniform transverse field h, while the exchange coupling J{m} between the nearest-neighbor spins takes the two values J{A} and J{B} arranged in Fibonacci, generalized Fibonacci, Thue-Morse, and period-doubling sequences. We calculate the energy-density profile and energy current of the resulting nonequilibrium steady states to study the heat-conducting behavior of finite but large systems. Although these nonperiodic quantum Ising chains are integrable, it is clearly found that energy gradients exist in all chains and the energy currents appear to scale as the system size ~N{α}. By increasing the ratio of couplings, the exponent α can be modulated from α > -1 to α < -1 corresponding to the nontrivial transition from the abnormal heat transport to the heat insulator. The influences of the temperature gradient and the magnetic field to heat conduction have also been discussed.
We study thermal transport in a classical one-dimensional Heisenberg model employing a discrete-time odd-even precessional update scheme. This dynamics equilibrates a spin chain for any arbitrary temperature and finite value of the integration time step $\ensuremath{\Delta}t$. We rigorously show that in presence of driving, the system attains local thermal equilibrium, which is a strict requirement of Fourier law. In the thermodynamic limit, heat current for such a system obeys Fourier law for all temperatures, as has been recently shown [A. V. Savin, G. P. Tsironis, and X. Zotos, Phys. Rev. B 72, 140402(R) (2005)]. Finite systems, however, show an apparent ballistic transport which crosses over to a diffusive one as the system size is increased. We provide exact results for current and energy profiles in zero- and infinite-temperature limits.
Using numerical diagonalization techniques we analyze the finite temperature/frequency conductance of a one-dimensional model of interacting spinless fermions. Depending on the interaction, the observed finite temperature charge stiffness and low-frequency conductance indicate a fundamental difference between integrable and nonintegrable cases. The integrable systems behave as ideal conductors in the metallic regime and as ideal insulators in the insulating one. The nonintegrable systems are, as expected, generic conductors in the metallic regime and activated ones in the insulating regime. \textcopyright{} 1996 The American Physical Society.
We study heat transport in a one-dimensional inhomogeneous quantum spin-1/2 system. It consists of a finite-size XXXXXX spin chain coupled at its ends to semi-infinite XXXXXX and XYXYXY chains at different temperatures, which play the role of heat and spin reservoirs. After using the Jordan-Wigner transformation we map the original spin Hamiltonian into a fermionic Hamiltonian, which contains normal and pairing terms. We find the expressions for the heat currents and solve the problem with a nonequilibrium Green's-function formalism. We analyze the behavior of the heat currents as functions of the model parameters. When finite magnetic fields are applied at the two reservoirs, the system exhibits rectifying effects in the heat flow.
We numerically investigate the heat conduction in a random-exchange Ising spin chain by using the quantum master equation. The chain is subject to a uniform transverse field hhh, while the exchange couplings Qn{{Q}_{n}}Qn​ between the nearest neighbor spins are random; the largest size we simulate is up to 10. This model is integrable; i.e., the nearest neighbor level spacing distribution is Poissonian. However, we find clear evidence of nonballistic transport. In the small coupling regime $({Q}_{n}\ensuremath{\ll}h)$, an energy and/or temperature gradient in the bulk of the system is observed and the energy current appears to be proportional to the inverse of the system size. Moreover, we find that in the low and high temperature regimes, the thermal conductivity $\ensuremath{\kappa}$ and the specific heat Cv{C}_{v}Cv​ have the same dependence on temperature. The large coupling case $({Q}_{n}\ensuremath{\sim}h)$ is also discussed.
We investigate how the normal energy transport is realized in one-dimensional quantum systems using a quantum spin system. The direct investigation of local energy distribution under thermal gradient is made using the quantum master equation, and the mixing properties and the convergence of the Green-Kubo formula are investigated when the number of spin increases. We find that the autocorrelation function in the Green-Kubo formula decays as ∼ t −1.5 to a finite value which vanishes rapidly with the increase of the system size. As a result, the Green-Kubo formula converges to a finite value in the thermodynamic limit. These facts strongly support the realization of Fourier heat law in a quantum system.