Based on the formalism of thermo field dynamics we propose a concept of nonequilibrium Fock space and nonequilibrium quasiparticles for quantum many-body system in nonequilibrium steady state. We develop a general theory as well as demonstrate the utility of the approach on the example of electron transport through the interacting region. The proposed approach is compatible with advanced methods of electronic structure calculations such as coupled cluster theory and configuration interaction.
Nonequilibrium thermodynamics of interacting tunneling transport: variational grand potential, density-functional formulation, and nature of steady-state forces
We obtain hydrodynamic descriptions of a broad class of conserved-mass transport processes on a ring. These processes are governed by chipping, diffusion and coalescence of masses, where microscopic probability weights in their nonequilibrium steady states, having nontrivial correlations, are not known. In these processes, we analytically calculate two transport coefficients, the bulk-diffusion coefficient and the conductivity. We, remarkably, find that the two transport coefficients obey an equilibriumlike Einstein relation, although the microscopic dynamics does not satisfy detailed balance …
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 cons…
Near equilibrium, Green-Kubo relations provide microscopic expressions for macroscopic transport coefficients in terms of equilibrium correlation functions. At their core, they are based on the intimate relationship between response and fluctuations as embodied by the equilibrium fluctuation-dissipation theorem, a connection generically broken far from equilibrium. In this work, we identify a class of perturbations whose response around far-from-equilibrium steady states is linked to steady-state correlation functions via an equilibrium-like fluctuation-response equality. We then utilize this …
We propose a nonequilibrium variational polaron transformation, based on an ansatz for nonequilibrium steady state (NESS) with an effective temperature, to study quantum heat transport at the nanoscale. By combining the variational polaron transformed master equation with the full counting statistics, we have extended the applicability of the polaron-based framework to study nonequilibrium process beyond the super-Ohmic bath models. Previously, the polaron-based framework for quantum heat transport reduces exactly to the non-interacting blip approximation (NIBA) formalism for Ohmic bath models…
It is known that each single typical pure state in an energy shell of a large isolated quantum system well represents a thermal equilibrium state of the system. We show that such typicality holds also for nonequilibrium steady states (NESS's). We consider a small quantum system coupled to multiple infinite reservoirs. In the long run, the total system reaches a unique NESS. We identify a large Hilbert space from which pure states of the system are to be sampled randomly and show that the typical pure states well describe the NESS. We also point out that the irreversible relaxation to the uniqu…
We analyze the equilibration process between two either fermionic or bosonic reservoirs containing ultracold atoms with a fixed total number of particles that are weakly connected via a few-level quantum system. We allow for both the temperatures and particle densities of the reservoirs to evolve in time. Subsequently, linearizing the resulting equations enables us to characterize the equilibration process and its time scales in terms of equilibrium reservoir properties and linear-response transport coefficients. Additionally, we investigate the use of such a device as particle transistor or p…
We explore the effects of quantum mechanical squeezing on the nonequilibrium fluctuations of bosonic transport between two squeezed harmonic reservoirs and a two level system. A standard full counting statistics technique based on a quantum master equation is employed. We derive a nonzero thermodynamic affinity under equal temperature setting of the two squeezed reservoirs. The odd cumulants are shown to be independent of squeezing under symmetric conditions, whereas the even cumulants depend nonlinearly on the squeezing parameters. The odd and even cumulants saturate at two different but uniq…
We present a hierarchical equations of motion approach, which allows a numerically exact simulation of nonequilibrium transport in general open quantum systems involving multiple macroscopic bosonic and fermionic environments. The performance of the method is demonstrated for a model of a nanosystem, which involves interacting electronic and vibrational degrees of freedom and is coupled to fermionic and bosonic baths. The results show the intricate interplay of electronic and vibrational degrees of freedom in this nonequilibrium transport scenario for both voltage and thermally driven transpor…
This Chapter contains an overview of the effects of nonlinear interactions in selected problems of non-equilibrium statistical mechanics. Most of the emphasis is put on open setups, where energy is exchanged with the environment. With reference to a few models of classical coupled anharmonic oscillators, we review anomalous but general properties such as extremely slow relaxation processes, or non-Fourier heat transport.
The local equilibrium approach previously developed by the Authors [J. Mabillard and P. Gaspard, J. Stat. Mech. (2020) 103203] for matter with broken symmetries is applied to crystalline solids. The macroscopic hydrodynamics of crystals and their local thermodynamic and transport properties are deduced from the microscopic Hamiltonian dynamics. In particular, the Green-Kubo formulas are obtained for all the transport coefficients. The eight hydrodynamic modes and their dispersion relation are studied for general and cubic crystals. In the same twenty crystallographic classes as those compatibl…
We provide a quantitative description of the nonequilibriumness based on the model of coupled oscillators interacting with multiple energy sources. This can be applied to the study of vibrational energy transport in molecules. The curl quantum flux quantifying the nonequilibriumness and time-irreversibility is quantified in the coherent representation and we find the geometric description of the shape and polarization of the flux which provides the connection between the microscopic description of quantum nonequilibriumness and the macroscopic observables, i.e., correlation function. We use th…
The standard equilibrium Green-Kubo and nonequilibrium molecular dynamics (MD) methods for computing thermal transport coefficients in solids typically require relatively long simulation times and large system sizes. To this end, we revisit here the homogeneous nonequilibrium MD method by Evans [Phys. Lett. A \textbf{91}, 457 (1982)] and generalize it to many-body potentials that are required for more realistic materials modeling. We also propose a method for obtaining spectral conductivity and phonon mean free path from the simulation data. This spectral decomposition method does not require …
Computing Nonequilibrium Transport from Short-Time Transients: From Lorentz Gas to Heat Conduction in One Dimensional Chains
Laboratoire de Physique de l’Ecole Normale Supérieure, ENS Université PSL, CNRS, Sorbonne Université, Université de Paris（巴黎高等师范学院物理实验室，ENS巴黎文理研究大学，法国国家科学研究中心，索邦大学，巴黎大学）；Politecnico di Milano（米兰理工大学）；Fondazione Istituto Italiano di Tecnologia（意大利技术研究院基金会）；Consiglio Nazionale delle Ricerche, Istituto dei Sistemi Complessi（国家研究委员会，复杂系统研究所）；INFN, Sezione di Firenze（意大利国家核物理研究所，佛罗伦萨分部）；INFN, Sezione di Torino（意大利国家核物理研究所，都灵分部）；Politecnico di Torino（都灵理工大学）
We review the non-equilibrium dynamics of many-body quantum systems after a quantum quench with spatial inhomogeneities, either in the Hamiltonian or in the initial state. We focus on integrable and many-body localized systems that fail to self-thermalize in isolation and for which the standard hydrodynamical picture breaks down. The emphasis is on universal dynamics, non-equilibrium steady states and new dynamical phases of matter, and on phase transitions far from thermal equilibrium. We describe how the infinite number of conservation laws of integrable and many-body localized systems lead …
We propose a unified framework to study the turbulent transport problem from the perspective of nonequilibrium statistical mechanics. By combining Krarichnan's turbulence thermalization assumption and Ruelle's recent work on nonequilibrium statistical mechanics settings for fluids, we show that the equation for viscous fluid can be viewed as the non-canonical Hamiltonian system perturbed by different thermostats. This allows an analogy between the viscous fluid and the nonequilibrium heat conduction model where the Fourier modes can be regarded as the ''particles''. With this framework, we ref…
