We present an approach based upon binary tree tensor network (BTTN) states for computing steady-state current statistics for a many-particle 1D ratchet subject to volume exclusion interactions. The ratcheted particles, which move on a lattice with periodic boundary conditions subject to a time-periodic drive, can be stochastically evolved in time to sample representative trajectories via a Gillespie method. In lieu of generating realizations of trajectories, a BTTN state can variationally approximate a distribution over the vast number of many-body configurations. We apply the density matrix renormalization group (DMRG) algorithm to initialize BTTN states, which are then propagated in time via the time-dependent variational principle (TDVP) algorithm to yield the steady-state behavior, including the effects of both typical and rare trajectories. The application of the methods to ratchet currents is highlighted in a companion letter, but the approach extends naturally to other interacting lattice models with time-dependent driving. Though trajectory sampling is conceptually and computationally simpler, we discuss situations for which the BTTN TDVP strategy could be more favorable.
A system that violates detailed balance evolves asymptotically into a nonequilibrium steady state with non-vanishing currents. Analogously, when detailed balance holds at any instant of time but the system is driven through time-periodic variations of external parameters, it evolves toward a time-periodic state, which can also support non-vanishing currents. In both cases the maintenance of currents throughout the system incurs a cost in terms of entropy production. Here we compare these two scenarios for one dimensional diffusive systems with periodic boundary condition, a framework commonly …
Transport of an inertial particle advected by a two-dimensional steady laminar flow is numerically investigated in the presences of a constant force and a periodic potential. Within particular parameter regimes this system exhibits absolute negative mobility, which means that the particle can travel in a direction opposite to the constant force. It is found that the profile of the periodic potential plays an important role in the nonlinear response regime. Absolute negative mobility can be drastically enhanced by applying appropriate periodic potential, the parameter regime for this phenomenon…
We discuss the effect of dissipation on heating which occurs in periodically driven quantum many body systems. We especially focus on a periodically driven Bose-Hubbard model coupled to an energy and particle reservoir. Without dissipation, this model is known to undergo parametric instabilities which can be considered as an initial stage of heating. By taking the weak on-site interaction limit as well as the weak system-reservoir coupling limit, we find that parametric instabilities are suppressed if the dissipation is stronger than the on-site interaction strength and stable steady states ap…
Steady Periodic Shear Flow is Stable in Two Space Dimensions . Nonequilibrium Molecular Dynamics vs Navier-Stokes-Fourier Stability Theory -- A Comment on two Arxiv Contributions
Laser technology has developed and accelerated photo-induced nonequilibrium physics from both scientific and engineering viewpoints. The Floquet engineering, i.e., controlling material properties and functionalities by time-periodic drives, is a forefront of quantum physics of light-matter interaction, but limited to ideal dissipationless systems. For the Floquet engineering extended to a variety of materials, it is vital to understand the quantum states emerging in a balance of the periodic drive and energy dissipation. Here we derive the general description for nonequilibrium steady states (…
We study the nonequilibrium dynamics of a periodically-driven anisotropic Kondo impurity model. The periodic time dependence is introduced for a local magnetic field which couples to the impurity spin and also for an in-plane exchange interaction. We obtain the exact results on the time evolution for arbitrary periodic time dependence at the special point in the parameter space known as the Toulouse limit. We first consider a specific case where the local magnetic field is periodically switched on and off. When the driving period is much shorter than the inverse of the Kondo temperature, an in…
We consider a harmonic oscillator under periodic driving and coupled to two harmonic-oscillator heat baths at different temperatures. We use the thermofield transformation with chain mapping for this setup, which allows us to study the unitary evolution of the system and the baths up to a time when the periodic steady state emerges in the system. We characterize this periodic steady state, and we show that, by tuning the system and the bath parameters, one can turn this system from an engine to an accelerator or even to a heater. The possibility to study the unitary evolution of the system and…
Does a closed quantum many-body system that is continually driven with a time-dependent Hamiltonian finally reach a steady state? This question has only recently been answered for driving protocols that are periodic in time, where the long time behavior of the local properties synchronize with the drive and can be described by an appropriate periodic ensemble. Here, we explore the consequences of breaking the time-periodic structure of the drive with additional aperiodic noise in a class of integrable systems. We show that the resulting unitary dynamics leads to new emergent steady states in a…
Driven many-body quantum systems where some parameter in the Hamiltonian is varied quasiperiodically in time may exhibit nonequilibrium steady states that are qualitatively different from their periodically driven counterparts. Here we consider a prototypical integrable spin system, the spin-$1/2$ transverse field Ising model in one dimension, in a pulsed magnetic field. The time dependence of the field is taken to be quasiperiodic by choosing the pulses to be of two types that alternate according to a Fibonacci sequence. We show that a novel steady state emerges after an exponentially long ti…
Nonlinear classical dissipative systems present a rich phenomenology in their "route to chaos", including period-doubling, i.e. the system evolves with a period which is twice that of the driving. However, typically the attractor of a periodically driven quantum open system evolves with a period which exactly matches that of the driving. Here we analyze a manybody open quantum system whose classical correspondent presents period-doubling. We show that by analysing the spectrum of the periodic propagator and by studying the dynamical correlations, it is possible to show the occurrence of period…
We investigate a heating phenomenon in periodically driven integrable systems that can be mapped to free-fermion models. We find that heating to the high-temperature state, which is a typical scenario in non-integrable systems, can also appear in integrable time-periodic systems; the amount of energy absorption rises drastically near a frequency threshold where the Floquet-Magnus expansion diverges. As the driving period increases, we also observe that the effective temperatures of the generalized Gibbs ensemble for conserved quantities go to infinity. By the use of the scaling analysis, we re…
