Macroscopically deterministic Markovian thermalization in finite quantum spin systems

Emergence of steady quantum transport in a superconducting processor

Non-equilibrium quantum transport is crucial to technological advances ranging from nanoelectronics to thermal management. In essence, it deals with the coherent transfer of energy and (quasi-)particles through quantum channels between thermodynamic baths. A complete understanding of quantum transport thus requires the ability to simulate and probe macroscopic and microscopic physics on equal footing. Using a superconducting quantum processor, we demonstrate the emergence of non-equilibrium steady quantum transport by emulating the baths with qubit ladders and realising steady particle currents between the baths. We experimentally show that the currents are independent of the microscopic details of bath initialisation, and their temporal fluctuations decrease rapidly with the size of the baths, emulating those predicted by thermodynamic baths. The above characteristics are experimental evidence of pure-state statistical mechanics and prethermalisation in non-equilibrium many-body quantum systems. Furthermore, by utilising precise controls and measurements with single-site resolution, we demonstrate the capability to tune steady currents by manipulating the macroscopic properties of the baths, including filling and spectral properties. Our investigation paves the way for a new generation of experimental exploration of non-equilibrium quantum transport in strongly correlated quantum matter.

Stiffness of probability distributions of work and Jarzynski relation for initial microcanonical and energy eigenstates

We consider closed quantum systems which are driven such that only negligible heating occurs. If driving only affects small parts of the system, it may nonetheless be strong. Our analysis aims at clarifying under which conditions the Jarzynski relation (JR) holds in such setups, if the initial states are microcanonical or even energy eigenstates. We find that the validity of the JR for the microcanonical initial state hinges on an exponential density of states and on stiffness. The latter indicates an independence of the probability density functions (PDFs) of work of the energy of the respective microcanonical initial state. The validity of the JR for initial energy eigenstates is found to additionally require smoothness. The latter indicates an independence of the work PDFs of the specific energy eigenstates within a microcanonical energy shell. As the validity of the JR for pure initial energy eigenstates has no analog in classical systems, we consider it a genuine quantum phenomenon.

Taking snapshots of a quantum thermalization process: Emergent classicality in quantum jump trajectories

We investigate theoretically the emergence of classical statistical physics in a finite quantum system that is either totally isolated or otherwise subjected to a quantum measurement process. We show via a random matrix theory approach to nonintegrable quantum systems that the set of outcomes of the measurement of a macroscopic observable evolve in time like stochastic variables, whose variance satisfies the celebrated Einstein relation for Brownian diffusion. Our results show how to extend the framework of eigenstate thermalization to the prediction of properties of quantum measurements on an otherwise closed quantum system. We show numerically the validity of the random matrix approach in quantum chain models.

Stiffness of probability distributions of work and Jarzynski relation for non-Gibbsian initial states

We consider closed quantum systems (into which baths may be integrated) that are driven, i.e., subject to time-dependent Hamiltonians. Our point of departure is the assumption that if systems start in non-Gibbsian states at some initial energies, the resulting probability distributions of work may be largely independent of the specific initial energies. It is demonstrated that this assumption has some far-reaching consequences, e.g., it implies the validity of the Jarzynski relation for a large class of non-Gibbsian initial states. By performing numerical analysis on integrable and nonintegrable spin systems, we find the above assumption fulfilled for all examples considered. Through an analysis based on Fermi's golden rule, we partially relate these findings to the applicability of the eigenstate thermalization ansatz to the respective driving operators.

Quantum Statistical Ensemble Resilient to Thermalization

The sampling of the wave function within a suitable ensemble is an important tool in the statistical analysis of a molecule interacting with its environment. The uniform statistical distribution of quantum pure states in an active space is often the privileged choice. However, such a distribution with constant average populations of eigenstates is not preserved upon the interaction between quantum systems. This appears as a severe methodological shortcoming, as long as a quantum system can be always considered as the result of interactions among previously isolated subsystems. In the present work we formulate an alternative statistical ensemble of pure states that is robust with respect to interaction, and it is thus preserved when subsystems are merged. It is derived from the condition of invariance of the average populations upon interaction between quantum systems in the same thermal state. These average populations allow a simple identification of the thermodynamic properties of the system. We find that such a statistical distribution is robust with respect to interaction of systems at different temperatures reproducing the thermalization of macroscopic bodies, and for this reason we identify it as the Thermalization Resilient Ensemble.

Eigenstate thermalization hypothesis and quantum Jarzynski relation for pure initial states

Since the first suggestion of the Jarzynski equality many derivations of this equality have been presented in both the classical and the quantum context. While the approaches and settings differ greatly from one another, they all appear to rely on the condition that the initial state is a thermal Gibbs state. Here, we present an investigation of work distributions in driven isolated quantum systems, starting from pure states that are close to energy eigenstates of the initial Hamiltonian. We find that, for the nonintegrable quantum ladder studied, the Jarzynski equality is fulfilled to a good accuracy.

Numerical evidence for approximate consistency and Markovianity of some quantum histories in a class of finite closed spin systems

Closed quantum systems obey the Schrödinger equation, whereas nonequilibrium behavior of many systems is routinely described in terms of classical, Markovian stochastic processes. Evidently, there are fundamental differences between those two types of behavior. We discuss the conditions under which the unitary dynamics may be mapped onto pertinent classical stochastic processes. This is first principally addressed based on the notions of "consistency" and "Markovianity." Numerical data are presented that show that the above conditions are to good approximation fulfilled for Heisenberg-type spin models comprising 12-20 spins. The accuracy to which these conditions are met increases with system size.

Off-diagonal matrix elements of local operators in many-body quantum systems

In the time evolution of isolated quantum systems out of equilibrium, local observables generally relax to a long-time asymptotic value, governed by the expectation values (diagonal matrix elements) of the corresponding operator in the eigenstates of the system. The temporal fluctuations around this value, response to further perturbations, and the relaxation toward this asymptotic value are all determined by the off-diagonal matrix elements. Motivated by this nonequilibrium role, we present generic statistical properties of off-diagonal matrix elements of local observables in two families of interacting many-body systems with local interactions. Since integrability (or lack thereof) is an important ingredient in the relaxation process, we analyze models that can be continuously tuned to integrability. We show that, for generic nonintegrable systems, the distribution of off-diagonal matrix elements is a Gaussian centered at zero. As one approaches integrability, the peak around zero becomes sharper, so the distribution is approximately a combination of two Gaussians. We characterize the proximity to integrability through the deviation of this distribution from a Gaussian shape. We also determine the scaling dependence on system size of the average magnitude of off-diagonal matrix elements.

Pushing the limits of the eigenstate thermalization hypothesis towards mesoscopic quantum systems

In the ongoing discussion on thermalization in closed quantum many-body systems, the eigenstate thermalization hypothesis has recently been proposed as a universal concept and has attracted considerable attention. So far this concept is, as the name states, hypothetical. The majority of attempts to overcome this hypothetical character are based on exact diagonalization, which implies for, e.g., spin systems a limitation of roughly 15 spins. In this Letter we present an approach that pushes this limit up to system sizes of roughly 35 spins, thereby going significantly beyond what is possible with exact diagonalization. A concrete application to a Heisenberg spin ladder which yields conclusive results is demonstrated.

Entropy increase in K-step Markovian and consistent dynamics of closed quantum systems

We consider sequences of measurements implemented by positive operator valued measures (POVMs). Starting from the assumption that these sequences may be described as consistent and Markovian, even and especially for closed quantum systems, we identify properties of the equilibrium state that coincide with the properties of typical pure quantum states. We define a physical entropy that converges against the standard entropies in the approach to equilibrium. Furthermore, strict limits to its possible decrease are derived on the basis of Renyi entropies. It is demonstrated that Landauer's principle follows directly from these limits. Since the above assumptions are rather strong, we exemplify the fact that they may nevertheless apply by checking them numerically for some transition paths in a concrete model.