Strong Evidence of Normal Heat Conduction in a one-Dimensional Quantum System

Abstract

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 $\sim t^{-1.5}$ 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.

7 pages 6 figures

Cited by in corpus (80)

• Heat Transport in low-dimensional systems
• Open XXZ spin chain: Nonequilibrium steady state and strict bound on ballistic transport
• Third quantization: a general method to solve master equations for quadratic open Fermi systems
• Finite-temperature transport in one-dimensional quantum lattice models
• A note on symmetry reductions of the Lindblad equation: transport in constrained open spin chains
• Exact nonequilibrium steady state of a strongly driven open XXZ chain
• Matrix product simulations of non-equilibrium steady states of quantum spin chains
• Modeling heat transport through completely positive maps
• Nonequilibrium Green's function method for quantum thermal transport
• Zero-frequency transport properties of one dimensional spin-1/2 systems
• Heat conduction in low-dimensional quantum magnets
• Exact solution of Markovian master equations for quadratic fermi systems: thermal baths, open XY spin chains, and non-equilibrium phase transition
• Heat flow in nonlinear molecular junctions
• Real-time and real-space spin- and energy dynamics in one-dimensional spin-1/2 systems induced by local quantum quenches at finite temperatures
• Many-Body Localization in the Age of Classical Computing
• Superdiffusion in spin chains
• Charge and spin transport in strongly correlated one-dimensional quantum systems driven far from equilibrium
• Out of equilibrium open quantum systems: a comparison of approximate Quantum Master Equation approaches with exact results
• A real-time study of diffusive and ballistic transport in spin-1/2 chains using the adaptive time-dependent density matrix renormalization group method
• Controlling and measuring quantum transport of heat in trapped-ion crystals
• Nonequilibrium Green's function method for thermal transport in junctions
• Heat transport through lattices of quantum harmonic oscillators in arbitrary dimensions
• Nonequilibrium thermal transport and its relation to linear response
• Dynamics and thermodynamics of linear quantum open systems
• Quantum transport efficiency and Fourier's law
• Chaos and Complexity of quantum motion
• Transport in open spin chains: A Monte Carlo wave-function approach
• Fourier's Law in a Quantum Spin Chain and the Onset of Quantum Chaos
• Density dynamics in translationally invariant spin-1/2 chains at high temperatures: a current auto-correlation approach to finite time- and length-scales
• Negative differential conductivity in far-from-equilibrium quantum spin chains
• Fourier's Law: insight from a simple derivation
• Harnessing symmetry to control quantum transport
• Reversal of Thermal Rectification in Quantum Systems
• Anomalous heat transport in classical many-body systems: overview and perspectives
• Non-dissipative thermal transport in the massive regimes of the XXZ chain
• Heat flux operator, current conservation and the formal Fourier's law
• Steady state thermal transport in anharmonic systems: Application to molecular junctions
• Heat transport of cuprate-based low-dimensional quantum magnets with strong exchange coupling
• Transport anomaly in the low energy regime of spin chains
• Density dynamics from current auto-correlations at finite time- and length-scales
• Limited validity of the Kubo formula for thermal conduction in modular quantum systems
• Control of heat transport in quantum spin systems
• Heat Transport in Quantum Spin Chains: Stochastic Baths vs Quantum Trajectories
• Quantum transport in d-dimensional lattices
• Thermomagnetic Power and Figure of Merit for Spin-1/2 Heisenberg Chain
• Thermalization in Open Quantum Systems
• Reconstructing Fourier's law from disorder in quantum wires
• Quantum Mechanical Heat Transport in Disordered Harmonic Chains
• Microscopic Quantum Mechanical Foundation of Fourier's Law
• Normal Transport Behavior in Finite One-Dimensional Chaotic Quantum Systems
• Transition from diffusive to ballistic dynamics for a class of finite quantum models
• How can we derive Fourier's Law from quantum mechanics? Exact master equation analysis
• From thermal rectifiers to thermoelectric devices
• Heat transport in quantum spin chains: the relevance of integrability
• Rectification in Nonequilibrium Steady States of Open Many-Body Systems
• Heat conductivity in small quantum systems: Kubo formula in Liouville space
• Equivalence of transport coefficients in bath-induced and dynamical scenarios
• Heat exchange mediated by a quantum system
• Temperature dependence of thermal conductivities of coupled rotator lattice and the momentum diffusion in standard map
• Heat transport in an open transverse-field Ising chain
• Fourier's law on a one-dimensional optical random lattice
• Boundary driven Heisenberg-chain in the long-range interacting regime: Robustness against far from equilibrium effects
• Non-equilibrium thermal transport and vacuum expansion in the Hubbard model
• Quantum transport in chains with noisy off-diagonal couplings
• Temperature-dependent thermal conductivities of one-dimensional nonlinear Klein-Gordon lattices with soft on-site potential
• A perturbative method for nonequilibrium steady state of open quantum systems
• Long-range interaction in an open boundary-driven Heisenberg spin lattice: A far-from-equilibrium transition to ballistic transport
• Stretch diffusion and heat conduction in 1D nonlinear lattices
• Quantum Heat Transport: Perturbation Theory in Liouville Space
• Microscopic energy flows in disordered Ising spin systems
• Quantum-to-Classical Reduction of Quantum Master Equations
• Transport in anisotropic model systems analyzed by a correlated projection superoperator technique
• Transport as a sensitive indicator of quantum criticality
• Stochastic dynamics and control of a driven nonlinear spin chain: the role of Arnold diffusion
• Absence of nontrivial local conserved quantities in the spin-1 bilinear-biquadratic chain and its anisotropic extensions
• Theory of quantum energy transfer in spin chains: From superexchange to ballistic motion
• Energy diffusion in the long-range interacting spin systems
• Proof of the absence of local conserved quantities in general spin-1/2 chains with symmetric nearest-neighbor interaction
• Complete Classification of Integrability and Non-integrability for Spin-1/2 Chain with Symmetric Nearest-Neighbor Interaction
• Energy transport in Z3 chiral clock model