Dynamics of a system in general depends on its initial state and how the system is driven, but in many-body systems the memory is usually averaged out during evolution. Here, interacting quantum systems without external relaxations are shown to retain long-time memory effects in steady states. To identify memory effects, we first show quasi-steady-state currents form in finite, isolated Bose- and Fermi-Hubbard models driven by interaction imbalance and they become steady-state currents in the thermodynamic limit. By comparing the steady-state currents from different initial states or ramping rates of the imbalance, long-time memory effects can be quantified. While the memory effects of initial states are more ubiquitous, the memory effects of switching protocols are mostly visible in interaction-induced transport in lattices. Our simulations suggest that the systems enter a regime governed by a generalized Fick's law and memory effects lead to initial-state-dependent diffusion coefficients. We also identify conditions for enhancing memory effects and discuss possible experimental implications.
Dynamics of a system generally depends on its initial state and how the system is driven, but in many-body systems the memory is usually averaged out during evolution. Here, interacting quantum systems without external relaxations are shown to retain long-time memory effects in steady states. To identify memory effects, we first show quasi-steady state currents form in finite, isolated Bose and Fermi Hubbard models driven by interaction imbalance and they become steady-state currents in the thermodynamic limit. By comparing the steady state currents from different initial states or ramping rates of the imbalance, long-time memory effects can be quantified. While the memory effects of initial states are more ubiquitous, the memory effects of switching protocols are mostly visible in interaction-induced transport in lattices. Our simulations suggest the systems enter a regime governed by a generalized Fick's law and memory effects lead to initial-state dependent diffusion coefficients. We also identify conditions for enhancing memory effects and discuss possible experimental implications.
We demonstrate the remnant presence of initial correlations in the steady-state electrical current jS flowing between low-dimensional interacting leads. The leads are described as Luttinger liquids and electrons can tunnel via a quantum point contact. We derive an analytic result for the time-dependent current and show that ground-state correlations have a large impact on the relaxation and long-time behavior. In particular, the I-V characteristic is not reproduced by quenching the interaction in time. We further present a universal formula of jS for an arbitrary sequence of interaction quenches and it is established that jS is history dependent for nonsmooth switching process.
Full understanding of the relaxation mechanisms and far-from-equilibrium transport in modern mesoscopic structures requires that such systems be treated as open. We therefore generalize some of the core elements of the Kadanoff-Baym-Keldysh nonequilibrium Green's function formalism, inherently formulated for closed systems, to treatment of an open system, coupled with its environment. We define the two-time correlation functions and analyze the influence of the memory effects on the open-system transport. In the transient regime, the two-time correlation functions clearly show four distinct terms: a closed-system-like term, an entanglement term, and two memory terms that depend explicitly on the initial state of the environment. We show that it is not possible to completely eliminate the influence of the environment by a fortunate choice of the initial state, and approximating the system as closed is valid only in the limit of negligible system-environment coupling, which is never the case in the transient regime. We derive the transport equations for transients that properly account for the system-environment coupling. On the other hand, we address the important issue of transport in a far-from-equilibrium steady state. We show that, once a steady state is reached, the balance between the driving and relaxation forces implies that the two-time correlation functions regain a closed-system-like form, but with an effective, modified system Hamiltonian, and with the system statistical operator unrelated to that of the initial state. We emphasize that the difference between the transient and the far-from-equilibrium steady-state regimes, crucial for theoretical investigation of nonequilibrium quasiparticle transport, effectively lies within the different relative magnitude of the combined entanglement and memory terms with respect to the closed-system-like term in two-time correlation functions.
We study the dynamics of one- and two-dimensional disordered lattice bosons/fermions initialized to a Fock state with 1 particle on a set of lattice sites (
A) and 0 particles on the rest of the sites (
A). Such states have been considered in recent ultracold atomic experiments to detect many body localization. For noninteracting systems we establish a universal relation between the long time density imbalance between
A and
A sites, $I(\ensuremath{\infty})$, the localization length ${\ensuremath{\xi}}_{l}$, and the geometry of the initial pattern. For the alternating initial pattern of 1 and 0 particles in one dimension, $I(\ensuremath{\infty})=tanh[a/{\ensuremath{\xi}}_{l}]$, where
a is the lattice spacing. For systems with mobility edge, we find analytic relations between $I(\ensuremath{\infty})$, the effective localization length ${\overline{\ensuremath{\xi}}}_{l}$, and the fraction of localized states
fl. The imbalance as a function of disorder shows nonanalytic behavior when the mobility edge passes through a band edge. For interacting bosonic systems, we show that there is a mechanism to retain a finite long-time imbalance in the system even in presence of dissipative and stochastic processes coming from interparticle scattering. The scattering of particles, which lead to a decay of the memory of initial conditions through dissipative processes, also creates excitations in the system. For strong disorder, the excitations act as a local bath, whose noise correlators retain information of the initial pattern. This sustains a finite imbalance at long times in strongly disordered interacting systems.
We study theoretically the memory effects due to different kinds of initial conditions in the transport properties of one-dimensional systems described by the Tomonaga-Luttinger model. We show that in presence of electron–electron interactions the sudden switching of a weak link between two initially uncontacted reservoirs induces a qualitative change in the transient current with respect to the contacted case. In particular the different switching process produces a change in the power-law temporal relaxation of the current towards the steady-state as well as a significant suppression of the transient oscillations. Even more dramatic is the response to a sudden interaction quench, which remarkably leads to a current–voltage characteristic differing from the one displayed if the system was initially interacting.
We study time-dependent quantum transport through a correlated double quantum dot (DQD) model system by means of time propagation of the nonequilibrium many-body Green's function. The theory is an extension of the Kadanoff-Baym approach for finite inhomogeneous systems ( Phys. Rev. Lett. , 98 (2007) 153004) to open inhomogeneous systems and generalizes the Meir-Wingreen formula to include initial correlations and memory effects. Important features of the theory are 1) the possibility to study the ultrafast dynamics of transients and other time-dependent regimes and 2) the inclusion of exchange and correlation effects in a conserving approximation scheme. We calculate time-dependent local currents and densities for different many-body approximations and highlight the role of initial correlations and memory effects on the transient dynamics. Furthermore we show that coherent charge oscillations on the DQD are strongly affected by the confined Coulomb interaction and can be directly related to the local equilibrium spectral density.