Microscopic Quantum Mechanical Foundation of Fourier's Law
arXiv:cond-mat/0611612 · doi:10.1142/S0217979206035849
Abstract
Besides the growing interest in old concepts like temperature and entropy at the nanoscale, theories of relaxation and transport have recently regained a lot of attention. With the electronic circuits and computer chips getting smaller and smaller, a fresh look should be appropriate on the equilibrium and nonequilibrium thermodynamics at small length scales far below the thermodynamic limit, i.e. on the theoretical understanding of original macroscopic processes, e.g. transport of energy, heat, charge, mass, magnetization etc. Only from the foundations of a theory its limits of applicability may be inferred. This review tries to give an overview of the background and recent developments in the field of nonequilibrium quantum thermodynamics focusing on the transport of heat in small quantum systems.
arXiv comment30 pages, 10 figures, review article
References in corpus (45)
- Thermal conduction in classical low-dimensional lattices
- Transport and conservation laws
- A spin-boson thermal rectifier
- Thermal conductance through molecular wires
- Heat conduction in one dimensional chains
- Real-time dynamics in spin-1/2 chains with adaptive time-dependent DMRG
- On the anomalous thermal conductivity of one-dimensional lattices
- Transport in the XX chain at zero temperature: Emergence of flat magnetization profiles
- Magnon Heat Transport in (Sr,La)_14Cu_24O_41
- Ballistic Phonon Thermal Transport in Multi-Walled Carbon Nanotubes
- Zero-frequency transport properties of one dimensional spin-1/2 systems
- Heat conduction in the disordered harmonic chain revisited
- The thermal conductivity of the spin-1/2 XXZ chain at arbitrary temperature
- Evidence for ideal insulating/conducting state in a 1D integrable system
- Thermal conductivity and specific heat of the linear chain cuprate SrCuO: Evidence for thermal transport via spinons
- Time evolution of a quantum many-body system: transition from integrability to ergodicity in thermodynamic limit
- A simple one-dimensional model of heat conduction which obeys Fourier's law
- Thermodynamics of the Spin-1/2 Antiferromagnetic Uniform Heisenberg Chain
- Transport in Almost Integrable Models: Perturbed Heisenberg Chains
- Fourier's Law from Schroedinger Dynamics
- Strong Evidence of Normal Heat Conduction in a one-Dimensional Quantum System
- Thermal conductivity of anisotropic and frustrated spin-1/2 chains
- Distribution of local entropy in the Hilbert space of bi-partite quantum systems: Origin of Jaynes' principle
- Fourier law in the alternate mass hard-core potential chain
- Fourier's Law confirmed for a class of small quantum systems
- Nonequilibrium Steady State in a Quantum System: One-dimensional Transverse Ising Model with Energy Current
- Fourier's Law in a Quantum Spin Chain and the Onset of Quantum Chaos
- Magnon-Hole Scattering and Charge Order in
- Superoperator Representation of Nonlinear Response; Unifying Quantum Field and Mode Coupling Theories
- Thermalization of quantum systems by finite baths
- Pure Stationary States of Open Quantum Systems
- Explicit product ensembles for separable quantum states
- Limited validity of the Kubo formula for thermal conduction in modular quantum systems
- Magnetization distribution in the transverse Ising chain with energy flux
- Diffusive energy transport in the S=1 Haldane chain compound AgVP2S6
- Enhancement of the Thermal Conductivity in gapped Quantum Spin Chains
- Normal Transport Behavior in Finite One-Dimensional Chaotic Quantum Systems
- Relaxation into equilibrium under pure Schrödinger dynamics
- Heat conductivity in small quantum systems: Kubo formula in Liouville space
- Stationary States of Dissipative Quantum Systems
- From Pure Schroedingerian to Statistical Dynamics
- Application of the Hilbert Space Average Method on Heat Conduction Models
- Transport in dimerized and frustrated spin systems
- Thermal conductivity of one-dimensional spin-1/2 systems
- Quantum Heat Transport: Perturbation Theory in Liouville Space
Cited by in corpus (24)
- Quantum thermal transport in nanostructures
- Third quantization: a general method to solve master equations for quadratic open Fermi systems
- Modeling heat transport through completely positive maps
- Nonequilibrium Green's function method for thermal transport in junctions
- Transport in open spin chains: A Monte Carlo wave-function approach
- Nonlinear quantum heat transfer in hybrid structures: Sufficient conditions for thermal rectification
- Fourier's Law: insight from a simple derivation
- Heat flux operator, current conservation and the formal Fourier's law
- Transport and Control in One-Dimensional Systems
- Heat Transport in Quantum Spin Chains: Stochastic Baths vs Quantum Trajectories
- Thermalization in Open Quantum Systems
- Reconstructing Fourier's law from disorder in quantum wires
- Crossover behavior of the thermal conductance and Kramers' transition rate theory
- How can we derive Fourier's Law from quantum mechanics? Exact master equation analysis
- From thermal rectifiers to thermoelectric devices
- Transport Control in Low-Dimensional Spin-1/2 Heisenberg Systems
- Heat exchange mediated by a quantum system
- Geometry of system-bath coupling and gauge fields in bosonic ladders: manipulating currents and driving phase transitions
- Understanding probability and irreversibility in the Mori-Zwanzig projection operator formalism
- Size effects in the long-time quasi-static heat transport
- Entropy Production and Thermal Conductivity of A Dilute Gas
- Quantized Thermal Hall Conductance and the Topological Phase Diagram of a Superconducting Bismuth Bilayer
- Length scale dependent diffusion in the Anderson model at high temperatures
- Fourier's Law for Quasi One--Dimensional Chaotic Quantum Systems