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Journal of the Physical Society of Japan

Anomalous Heat Conduction in One-Dimensional Quantum Fermi–Pasta–Ulam Lattice: Semiquantal Approach

Tao Hu, Yi Ping Tang

Published May 25, 2010• 3 citations
Publisher

Abstract

We investigate the mechanism of heat conduction in one-dimensional (1D) quantum FPU chain with quantum fluctuation in the framework of semiquantal molecular dynamics. In the semiquantal many-body simulations, a Hartree-type many-body wave function is adopted for a whole chain and a single-particle state of a particle is represented by a trial wave function with Jackiw–Kerman (JK) form. With the help of the Dirac's time-dependent variational principle (TDVP), a set of equations of the variational parameters contained in the JK wave packet is obtained, and it describes the quantum dynamics of the nonlinear lattices approximately. These equations not only prove highly efficient in recovering dynamics of classical heat conduction, but also allow exploring the case with quantum mechanical characteristics. As a consequence, we find the thermal conductivity diverges with system size as well as in the classical version when considering quantum fluctuation. Furthermore, in three different temperature regions it is observed that the enhancement of the quantum fluctuation increases the heat flux through the 1D quantum FPU chain.

DOI
10.1143/jpsj.79.064601

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We investigate the mechanism of heat conduction in one-dimensional (1D) quantum FPU chain with quantum fluctuation in the framework of semiquantal molecular dynamics. In the semiquantal many-body simulations, a Hartree-type many-body wave function is adopted for a whole chain and a single-particle state of a particle is represented by a trial wave function with Jackiw–Kerman (JK) form. With the help of the Dirac's time-dependent variational principle (TDVP), a set of equations of the variational parameters contained in the JK wave packet is obtained, and it describes the quantum dynamics of the nonlinear lattices approximately. These equations not only prove highly efficient in recovering dynamics of classical heat conduction, but also allow exploring the case with quantum mechanical characteristics. As a consequence, we find the thermal conductivity diverges with system size as well as in the classical version when considering quantum fluctuation. Furthermore, in three different temperature regions it is observed that the enhancement of the quantum fluctuation increases the heat flux through the 1D quantum FPU chain.
In this paper,the time-dependent variational principle(TDVP) is applied to study the one-dimensional Fermi-Pasta-Ulam(FPU) model,and the dynamic equation of particles in the chain is obtained by TDVP.In the semi-quantal study,the considered quantum effect is quantum fluctuation.The Jackiw-Kerman wave function is used for the single particle.The research results show that quantum fluctuation can disperse,blur and even destroy the nonlinear excitation of FPU model,envelope soliton.The effect of quantum fluctuation has the quasi-exponentional relationship with the effective Plank constant.Furthermore,it is found that coupling the effective Plank constant the anharmonic coupling strength has the joint effect on quantum dissipation.The uniquely joint effect may be induced by the unique Hamiltonian of the FPU chain.
We study the statistics and short-time dynamics of the classical and the quantum Fermi-Pasta-Ulam chain in the thermal equilibrium. We analyze the distributions of single-particle configurations by integrating out the rest of the system. At low temperatures, we observe a systematic increase in the mobility of the chain when transitioning from classical to quantum mechanics due to zero-point energy effects. We analyze the consequences of quantum dispersion on the dynamics at short times of configurational correlation functions.
Digital Quantum Simulation of the quantum βββ-FPUT Lattice: Formulation and Resource Estimation
Heat conduction in low-dimensional systems exhibits strong deviations from Fourier behavior due to anharmonicity and long-lived vibrational correlations, challenging conventional computational approaches. The βββ-Fermi--Pasta--Ulam--Tsingou (βββ-FPUT) chain provides a minimal nonlinear lattice model for studying anomalous transport, yet its quantum real-time dynamics remain difficult to access with classical methods. We develop a first-quantized digital quantum-simulation framework for the quantum βββ-FPUT lattice, targeting fault-tolerant quantum computers. By working directly with discretized lattice displacements rather than truncated phonon occupation spaces, the approach captures anharmonic interactions while avoiding bosonic encoding overheads. We construct Trotterized circuit blocks for real-time evolution and introduce a Hermitian quadrature decomposition of Fourier-mode displacement operators that enables shallow quantum circuits for mode-resolved displacement correlators. We analyze the quantum resources required for the full simulation and measurement workflow, providing qubit counts, gate complexity, circuit-depth and resource estimates as functions of system size and resolution within a fault-tolerant workflow. These results establish a concrete algorithmic blueprint for simulating quantum transport dynamics in nonlinear low-dimensional lattice models on fault-tolerant quantum hardware.
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.
We propose an experimental scheme for studying the emergence of effectively classical nonlinear revivals—the Fermi–Pasta–Ulam (FPU) phenomenon—in interacting quantum many-body systems, e.g. ultracold atoms. Specifically, we suggest and analyze a setup of one-dimensional Bose gases confined into an optical lattice. The strength of quantum fluctuations is controlled by tuning the number of atoms per lattice sites (filling factor). By simulating the real-time dynamics of the Bose–Hubbard model by means of the exact numerical method of time-evolving block decimation, we investigate the effects of quantum fluctuations on the FPU recurrence and show that strong quantum fluctuations cause significant damping of the FPU oscillation.
The phonon dispersion relation of the quantum FPU model is studied by means of the time-dependent variational approach combined with a Hartree-type many-body trial wavefunction.The single-particle state is taken to be a frozen Jackiw-Kerman wavefunction.Under the condition of minimum uncertainty relation,equations of motion for the particle expectation values are derived to obtain the phonon dispersion relation.It is shown that the harmonically coupling strength is strengthened and the width of the phonon band is broadened due to the quantum fluctuations in comparison with those of the classical FPU model.In addition,the harmonically coupling strength and the width of the phonon band increase with increasing the quantum fluctuations and quartic coupling strength.