Nonequilibrium steady-state Kubo formula: equality of transport coefficients

Abstract

We address the question of whether transport coefficients obtained from a unitary closed system setting, i.e., the standard equilibrium Green-Kubo formula, are the same as the ones obtained from a weakly driven nonequilibrium steady-state calculation. We first derive a nonequilibrium Kubo-like expression for the steady-state diffusion constant expressed as a time-integral of either a current or a conserved density nonequilibrium correlation function. This expression has certain advantages over the equilibrium Green-Kubo formula, but is not clear if it gives the same value of the diffusion constant. We then rigorously show that, if the unitary dynamics is diffusive the nonequilibrium formula indeed gives exactly the same transport coefficient. The form of finite-size correction is also predicted. Theoretical results are verified by an explicit calculation of the diffusion constant in several interacting many-body models.

9 pages, 6 figures

References in corpus (16)

• The density-matrix renormalization group in the age of matrix product states
• Heat Transport in low-dimensional systems
• Open XXZ spin chain: Nonequilibrium steady state and strict bound on ballistic transport
• Spin transport in a one-dimensional anisotropic Heisenberg model
• Modeling heat transport through completely positive maps
• Conservation laws, integrability and transport in one-dimensional quantum systems
• Fermi, Pasta, Ulam and a mysterious lady
• Interaction instability of localization in quasiperiodic systems
• Fourier's Law confirmed for a class of small quantum systems
• Density dynamics in translationally invariant spin-1/2 chains at high temperatures: a current auto-correlation approach to finite time- and length-scales
• Green-Kubo formula for heat conduction in open systems
• Anomalous nonequilibrium current fluctuations in the Heisenberg model
• Heat conductivity in small quantum systems: Kubo formula in Liouville space
• Equivalence of transport coefficients in bath-induced and dynamical scenarios
• Locality Bound for Dissipative Quantum Transport
• Kubo formula for finite size systems

Cited by in corpus (27)

• Finite-temperature transport in one-dimensional quantum lattice models
• Anomalous spin diffusion in one-dimensional antiferromagnets
• Exact localized and ballistic eigenstates in disordered chaotic spin ladders and the Fermi-Hubbard model
• Entanglement Barriers in Dual-Unitary Circuits
• Entanglement Negativity and Mutual Information after a Quantum Quench: Exact Link from Space-Time Duality
• Weak integrability breaking: chaos with integrability signature in coherent diffusion
• Exact description of quantum stochastic models as quantum resistors
• Generic transport formula for a system driven by Markovian reservoirs
• Temporal Entanglement in Chaotic Quantum Circuits
• Diffusive transport in a quasiperiodic Fibonacci chain: absence of many-body localization at small interactions
• Phenomenology of anomalous transport in disordered one-dimensional systems
• Classifying transport behavior via current fluctuations in open quantum systems
• Density and current statistics in boundary-driven monitored fermionic chains
• Response theory for nonequilibrium steady-states of open quantum systems
• Ballistic-to-diffusive transition in spin chains with broken integrability
• Less is more: more scattering leading to less resistance
• Exact dynamical correlations of nonlocal operators in quadratic open Fermion systems: a characteristic function approach
• Read-out of Quasi-periodic Systems using Qubits
• Real-time broadening of bath-induced density profiles from closed-system correlation functions
• Spin-1/2 XXZ chain coupled to two Lindblad baths: Constructing nonequilibrium steady states from equilibrium correlation functions
• Non-equilibrium boundary driven quantum systems: models, methods and properties
• Exact Solution for the Heat Conductance in Harmonic Chains
• Lindblad dynamics from spatio-temporal correlation functions in nonintegrable spin-1/2 chains with different boundary conditions
• Quantum fluctuation theorem for initial near-equilibrium system
• Temperature dependence of energy transport in the ${\mathbb{Z}}_3$ chiral clock model
• Prethermalization, shadowing breakdown, and the absence of Trotterization transition in quantum circuits
• Lindblad quantum dynamics from correlation functions of classical spin chains