Single molecule junctions are important examples of complex out-of-equilibrium many-body quantum systems. We identify a nontrivial clustering of steady state populations into distinctive subspaces with Boltzmann-like statistics, which persist far from equilibrium. Such Boltzmann subspaces significantly reduce the information needed to describe the steady state, enabling modeling of high-dimensional systems that are otherwise beyond the reach of current computations. The emergence of Boltzmann subspaces is demonstrated analytically and numerically for fermionic transport systems of increasing complexity.
Single molecule junctions are important examples of complex out-of-equilibrium many-body quantum systems. We identify a nontrivial clustering of steady state populations into distinctive subspaces with Boltzmann-like statistics, which persist far from equilibrium. Such Boltzmann subspaces significantly reduce the information needed to describe the steady state, enabling modeling of high-dimensional systems that are otherwise beyond the reach of current computations. The emergence of Boltzmann subspaces is demonstrated analytically and numerically for fermionic transport systems of increasing complexity.
Abstract 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 to complex non-equilibrium states beyond the traditional dogma of statistical mechanics.
Relaxation dynamics of complex quantum systems with strong interactions towards the steady state is a fundamental problem in statistical mechanics. The steady state of subsystems weakly interacting with their environment is described by the canonical ensemble which assumes the probability distribution for energy to be of the Boltzmann form. The emergence of this probability distribution is ensured by the detailed balance of the transitions induced by the interaction with the environment. Here we consider relaxation of an open correlated quantum system brought into contact with a reservoir in the vacuum state. We refer to such a system as emissive since particles irreversibly evaporate into the vacuum. The steady state of the system is a statistical mixture of the stable eigenstates. We found that, despite the absence of the detailed balance, the stationary probability distribution over these eigenstates is of the Boltzmann form in each N-particle sector. A quantum statistical ensemble corresponding to the steady state is characterized by different temperatures in the different sectors, in contrast to the Gibbs ensemble. We investigate the transition rates between the eigenstates to understand the emergence of the Boltzmann distribution and find their exponential dependence on the transition energy. We argue that this property of transition rates is generic for a wide class of emissive quantum many-body systems.
A powerful perspective in understanding nonequilibrium quantum dynamics is through the time evolution of its entanglement content. Yet apart from a few guiding principles for the entanglement entropy, to date, much less is known about the refined characteristics of entanglement propagation. Here, we unveil signatures of the entanglement evolving and information propagating out of equilibrium, from the view of the entanglement Hamiltonian. We investigate quantum quench dynamics of prototypical Bose-Hubbard model using state-of-the-art numerical technique combined with conformal field theory. Before reaching equilibrium, it is found that a current operator emerges in the entanglement Hamiltonian, implying that entanglement spreading is carried by particle flow. In the long-time limit the subsystem enters a steady phase, evidenced by the dynamic convergence of the entanglement Hamiltonian to the expectation of a thermal ensemble. Importantly, the entanglement temperature in steady state is spatially independent, which provides an intuitive trait of equilibrium. These findings not only provide crucial information on how equilibrium statistical mechanics emerges in many-body dynamics, but also add a tool to exploring quantum dynamics from the perspective of the entanglement Hamiltonian.
A numerical approach is presented that allows to compute nonequilibrium steady-state properties of strongly correlated quantum many-body systems. The method is imbedded in the Keldysh Green's function formalism and is based upon the idea of the variational cluster approach as far as the treatment of strong correlations is concerned. It appears that the variational aspect is crucial as it allows for a suitable optimization of a ``reference'' system to the nonequilibrium target state. The approach is neither perturbative in the many-body interaction nor in the field, that drives the system out of equilibrium, and it allows to study strong perturbations and nonlinear responses of systems in which also the correlated region is spatially extended. We apply the presented approach to nonlinear transport across a strongly correlated quantum wire described by the fermionic Hubbard model. We illustrate how the method bridges to cluster dynamical mean-field theory upon coupling two baths containing an increasing number of uncorrelated sites.
Understanding the far-from-equilibrium dynamics of dissipative quantum systems, where dissipation and decoherence coexist with unitary dynamics, is an enormous challenge with immense rewards. Often, the only realistic approach is to forgo a detailed microscopic description and search for signatures of universal behavior shared by collections of many distinct, yet sufficiently similar, complex systems. Quantum chaos provides a powerful statistical framework for addressing this question, relying on symmetries to obtain information not accessible otherwise. This thesis examines how to reconcile chaos with dissipation, proceeding along two complementary lines. In Part I, we apply non-Hermitian random matrix theory to open quantum systems with Markovian dissipation and discuss the relaxation timescales and steady states of three representative examples of increasing physical relevance: single-particle Lindbladians and Kraus maps, open free fermions, and dissipative Sachdev-Ye-Kitaev (SYK) models. In Part II, we investigate the symmetries, correlations, and universality of many-body open quantum systems, classifying several models of dissipative quantum matter. From a theoretical viewpoint, this thesis lays out a generic framework for the study of the universal properties of realistic, chaotic, and dissipative quantum systems. From a practical viewpoint, it provides the concrete building blocks of dynamical dissipative evolution constrained by symmetry, with potential technological impact on the fabrication of complex quantum structures. (Full abstract in the thesis.)
Non-equilibrium quantum dynamics represents an emerging paradigm for condensed matter physics, quantum information science, and statistical mechanics. Strongly interacting Rydberg atoms offer an attractive platform to examine driven-dissipative dynamics of quantum spin models with long-range order. Here, we explore the conditions under which stationary many-body entanglement persists with near-unit fidelity and high scalability. In our approach, coherent many-body dynamics is driven by Rydberg-mediated laser transitions, while atoms at the lattice boundary locally reduce the entropy of the many-body system. Surprisingly, the many-body entanglement is established by continuously evolving a locally dissipative Rydberg system towards the steady state, precisely as with optical pumping. We characterize the dynamics of multipartite entanglement in an one-dimensional lattice by way of quantum uncertainty relations, and demonstrate the long-range behavior of the stationary entanglement with finite-size scaling. Our work opens a route towards dissipative preparation of many-body entanglement with unprecedented scaling behavior.