Perturbative approach to weakly driven many-particle systems in the presence of approximate conservation laws

Abstract

We develop a Liouville perturbation theory for weakly driven and weakly open quantum systems in situations when the unperturbed system has a number of conservations laws. If the perturbation violates the conservation laws, it drives the system to a new steady state which can be approximately but efficiently described by a (generalized) Gibbs ensemble characterized by one Lagrange parameter for each conservation law. The value of those has to be determined from rate equations for conserved quantities. Remarkably, even weak perturbations can lead to large responses of conserved quantities. We present a perturbative expansion of the steady state density matrix; first we give the condition that fixes the zeroth order expression (Lagrange parameters) and then determine the higher order corrections via projections of the Liouvillian. The formalism can be applied to a wide range of problems including two-temperature models for electron-phonon systems, Bose condensates of excitons or photons or weakly perturbed integrable models. We test our formalism by studying interacting fermions coupled to non-thermal reservoirs, approximately described by a Boltzmann equation.

15 pages, 6 figures, published version

References in corpus (29)

• Many body localization and thermalization in quantum statistical mechanics
• Bose-Einstein condensation of photons in an optical microcavity
• Quantum Quench in the Transverse Field Ising Chain
• Experimental Observation of a Generalized Gibbs Ensemble
• Quench dynamics and non equilibrium phase diagram of the Bose-Hubbard model
• Interaction Quench in the Hubbard model
• Exact relaxation in a class of non-equilibrium quantum lattice systems
• Dephasing and the steady state in quantum many-particle systems
• Quenching the Anisotropic Heisenberg Chain: Exact Solution and Generalized Gibbs Ensemble Predictions
• Correlations after quantum quenches in the XXZ spin chain: Failure of the Generalized Gibbs Ensemble
• Quantum Quench in the Transverse Field Ising Chain II: Stationary State Properties
• Dissipative Floquet Topological Systems
• Dynamical Correlations after a Quantum Quench
• Validity of the GGE for quantum quenches from interacting to noninteracting models
• Dissipation induced Tonks-Girardeau gas in an optical lattice
• Charge and spin transport in strongly correlated one-dimensional quantum systems driven far from equilibrium
• Occupation of topological Floquet bands in open systems
• Quenching the XXZ spin chain: quench action approach versus generalized Gibbs ensemble
• Quench action approach for releasing the Néel state into the spin-1/2 XXZ chain
• Condition for emergence of the Floquet-Gibbs state in periodically driven open systems
• Quantum quenches and Generalized Gibbs Ensemble in a Bethe Ansatz solvable lattice model of interacting bosons
• Bose-Einstein condensation of magnons under incoherent pumping
• Lower bounds for the conductivities of correlated quantum systems
• Classification of Floquet Statistical Distribution for Time-Periodic Open Systems
• Prethermalization from a low-density Holstein-Primakoff expansion
• Quantum quenches in the thermodynamic limit. II. Initial ground states
• Exact asymptotics of the current in boundary dissipated quantum chains in large external fields
• Asymptotic Entanglement and Lindblad Dynamics: a Perturbative Approach
• Long time asymptotic state of periodically driven open quantum systems

Cited by in corpus (2)

• The effect of atom losses on the distribution of rapidities in the one-dimensional Bose gas
• Prethermalization of quantum systems interacting with non-equilibrium environments