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 (NESS) in periodically driven dissipative systems by focusing on the systems under high-frequency drive and time-independent Lindblad-type dissipation with the detailed balance condition. Our formula correctly describes the time-average, fluctuation, and symmetry property of the NESS, and can be computed efficiently in numerical calculations. Our approach will play fundamental roles in Floquet engineering in a broad class of dissipative quantum systems such as atoms and molecules, mesoscopic systems, and condensed matter.
We derive some nonequilibrium identities such as the integral fluctuation theorem and the Jarzynski equality starting from a nonequilibrium state for dissipative classical systems. Thanks to the existence of the integral fluctuation theorem we can naturally introduce an entropy-like quantity for dissipative classical systems in far from equilibrium states. We also derive the generalized Green-Kubo formula as a nonlinear response theory for a steady dynamics around a nonequilibrium state. We numerically verify the validity of the derived formulas for sheared frictionless granular particles.
The problem of response of nonequilibrium systems is currently under intense investigation. We propose a general method of solution of the Liouville Equation for thermostatted particle systems subjected to external forces which retains only the slow degrees of freedom, by projecting out the majority of fast variables. Response formulae, extending the Green-Kubo relations to dissipative dynamics are provided, and comparison with numerical data is presented.
We give a decomposition expression for dissipative heat using the instantaneous diffusion coefficient in a nonequilibrium steady state. The dissipative heat can be expressed using three diffusion coefficients: instantaneous, equilibrium, and drift. An experimental application of the decomposition expression permits us to evaluate the heat dissipation rate from single-trajectory data only. We also numerically demonstrate this method.
Dissipative effects in electromagnetism on macroscopic scales are examined by coarse graining the microscopic Maxwell equations with respect to time. We illustrate a procedure to derive the dissipative effects on the macroscopic scale by using a Green-Kubo type expression in terms of the microscopic fluctuations and the correlations between them. The resulting macroscopic Maxwell equations are formulated within the General Equation for the Non-Equilibrium Reversible-Irreversible Coupling (GENERIC) framework, accounting also for inhomogeneous temperature.
Dissipative preparation of a pure steady state usually involves a commutative action of a coherent and a dissipative dynamics on the target state. Namely, the target pure state is an eigenstate of both the coherent and dissipative parts of the dynamics. We show that working in the Zeno regime, i.e. for infinitely large dissipative coupling, one can generate a pure state by a non commutative action, in the above sense, of the coherent and dissipative dynamics. A corresponding Zeno regime pureness criterion is derived. We illustrate the approach, looking at both its theoretical and applicative a…
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…
The exact large deviation function (ldf) for the fluctuations of the energy density field is computed for a chain of Ising (or more generally Potts) spins driven by a zero-temperature (dissipative) Glauber dynamics and sustained in a non trivial stationary regime by an arbitrary energy injection mechanism at the boundary of the system. It is found that this ldf is independent of the dynamical details of the energy injection, and that the energy fluctuations, unlike conservative systems in a nonequilibrium state, are not spatially correlated in the stationary regime.
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…
Chaos is usually referred to the sensitivity to initial conditions in which the nonlinearity plays a crucial role. Beyond such a mathematical description, the understanding of the underlying physical origin of the chaos is still not very clear. Here we study the dissipative chaos from the perspective of the nonequilibrium dynamics. This was not fully investigated in the traditional chaos theory, despite of the Lorenz's original discovery of chaos from the nonequilibrium atmosphere. We found that the nonequilibriumness as the degree of detailed balance breaking can be quantified by the appearan…
Using the path integral approach to equilibrium statistical physics the effect of dissipation on Landau diamagnetism is calculated. The calculation clarifies the essential role of the boundary of the container in which the electrons move. Further, the derived result for diamagnetization also matches with the expression obtained from a time-dependent quantum Langevin equation in the asymptotic limit, provided a certain order is maintained in taking limits. This identification then unifies equilibrium and nonequilibrium statistical physics for a phenomenon like diamagnetism, which is inherently …
How can we derive the evolution equations of dissipative systems? What is the relation between the different approaches? How much do we understand the fundamental aspects of a second law based framework? Is there a hierarchy of dissipative and ideal theories at all? How far can we reach with the new methods of nonequilibrium thermodynamics?
Studying the role of activity parameters and the nature of time-symmetric path-variables constitutes an important part of nonequilibrium physics, so we argue. The relevant variables are residence times and the undirected traffic between different states. Parameters are the reactivities, escape rates and accessibilities and how those possibly depend on the imposed driving. All those count in the frenetic contribution to statistical forces, response and fluctuations, operational even in the stationary distribution when far enough from equilibrium. As these time-symmetric aspects can vary indepen…
The nonequilibrium dynamics of correlated charge transfer along a one-dimensional chain in presence of a phonon environment is investigated within a dissipative Hubbard model. For this generalization of the ubiquitous spin-boson model the crucial role of symmetries is analysed in detail and corresponding invariant subspaces are identified. It is shown that the time evolution typically occurs in each of the disjunct subspaces independently leading e.g. asymptotically to a non-Boltzmann equilibrium state. Based on these findings explicit results are obtained for two interacting electrons by mean…
Theoretical studies of nonequilibrium systems are complicated by the lack of a general framework. In this work we first show that a transformation introduced by Ao recently (J. Phys. A {\bf 37}, L25 (2004)) is related to previous works of Graham (Z. Physik B {\bf 26}, 397 (1977)) and Eyink {\it et al.} (J. Stat. Phys. {\bf 83}, 385 (1996)), which can also be viewed as the generalized application of the Helmholtz theorem in vector calculus. We then show that systems described by ordinary stochastic differential equations with white noise can be mapped to thermostated Hamiltonian systems. A stea…
The emergence of particle irreversibility in periodically driven colloidal suspensions has been interpreted as resulting either from a nonequilibrium phase transition to an absorbing state or from the chaotic nature of particle trajectories. Using a simple model of a driven suspension we show that a nonequilibrium phase transition is accompanied by hyperuniform static density fluctuations in the vicinity of the transition, where we also observe strong dynamic heterogeneities reminiscent of dynamics in glassy materials. We find that single particle dynamics becomes intermittent and strongly non…
The interplay of synchronization and topological band structures with symmetry protected midgap states under the influence of driving and dissipation is largely unexplored. Here we consider a trimer chain of electron shuttles, each consisting of a harmonic oscillator coupled to a quantum dot positioned between two electronic leads. Each shuttle is subject to thermal dissipation and undergoes a bifurcation towards self-oscillation with a stable limit cycle if driven by a bias voltage between the leads. By mechanically coupling the oscillators together, we observe synchronized motion at the ends…
We study an extended system that without noise shows a monostable dynamics, but when submitted to an adequate multiplicative noise, an effective bistable dynamics arise. The stochastic resonance between the attractors of the \textit{noise-sustained dynamics} is investigated theoretically in terms of a two-state approximation. The knowledge of the exact nonequilibrium potential allows us to obtain the output signal-to-noise ratio. Its maximum is predicted in the symmetric case for which both attractors have the same nonequilibrium potential value.
Periodic driving is used to operate machines that go from standard macroscopic engines to small non-equilibrium micro-sized systems. Two classes of such systems are small heat engines driven by periodic temperature variations and molecular pumps driven by external stimuli. Well known results that are valid for nonequilibrium steady states of systems driven by fixed thermodynamic forces, instead of an external periodic driving, have been generalized to periodically driven heat engines only recently. These results include a general expression for entropy production in terms of currents and affin…
Solitons and polarons at nonequilibrium steady states are investigated for the spinless Takayama Lin-Liu Maki model. Polarons are found to be possible {\it only out of equilibrium}. This polaron formation is a genuine nonequilibrium phenomenon, as there is a lower threshold current below which they cannot exist. It is considered to be an example of microscopic dissipative structure.
The physics of critical phenomena in a many-body system far from thermal equilibrium is an interesting and important issue to be addressed both experimentally and theoretically. The trapped cold atoms have been actively used as a clean and versatile simulator for classical and quantum-mechanical systems, deepening understanding of the many-body physics behind. Here we review the nonlinear and collective dynamics in a periodically modulated magneto-optically trapped cold atoms. By temporally modulating the intensity of the trapping lasers with the controlled phases, one can realize two kinds of…
When periodically driven by an external magnetic field, a spin system can enter a phase of steady entrained oscillations with nonequilibrium probability distribution function. We consider an arbitrary magnetic field switching its direction with frequency comparable with the spin-flip rate and show that the resulting nonequilibrium probability distribution can be related to the system equilibrium distribution in the presence of a constant magnetic field of the same magnitude. We derive convenient approximate expressions for this exact relation and discuss their implications.
Small nonequilibrium systems in contact with a heat bath can be analyzed with the framework of stochastic thermodynamics. In such systems, fluctuations, which are not negligible, follow universal relations such as the fluctuation theorem. More recently, it has been found that, for nonequilibrium stationary states, the full spectrum of fluctuations of any thermodynamic current is bounded by the average rate of entropy production and the average current. However, this bound does not apply to periodically driven systems, such as heat engines driven by periodic variation of the temperature and art…
Controlling thermodynamic cycles to minimize the dissipated heat is a longstanding goal in thermodynamics, and more recently, a central challenge in stochastic thermodynamics for nanoscale systems. Here, we introduce a theoretical and computational framework for optimizing nonequilibrium control protocols that can transform a system between two distributions in a minimally dissipative fashion. These protocols optimally transport a system along paths through the space of probability distributions that minimize the dissipative cost of a transformation. Furthermore, we show that the thermodynamic…
The nonexponential relaxation and aging inherent to complex dynamics manifested in a wide variety of dissipative systems is analyzed through a model of diffusion in phase space in the presence of a nonconservative force. The action of this force establishes a heat flow which maintains the system away from equilibrium. The inability of the system to find its equilibrium state becomes apparent through the presence of an effective temperature field. This is the temperature of the stationary nonequilibrium state reached by the system satisfying a generalyzed version of the fluctuation-dissipation …
Chemical processes in closed systems are poorly controllable since they always relax to equilibrium. Living systems avoid this fate and give rise to a much richer diversity of phenomena by operating under nonequilibrium conditions. Recent experiments in dissipative self-assembly also demonstrated that by opening reaction vessels and steering certain concentrations, an ocean of opportunities for artificial synthesis and energy storage emerges. To navigate it, thermodynamic notions of energy, work and dissipation must be established for these open chemical systems. Here, we do so by building upo…
We investigate the long-time behavior of quantum N-level systems that are coupled to a Markovian environment and subject to periodic driving. As our main result, we obtain a general algebraic condition ensuring that all solutions of a periodic quantum master equation with Lindblad form approach a unique limit cycle. Quite intuitively, this criterion requires that the dissipative terms of the master equation connect all subspaces of the system Hilbert space during an arbitrarily small fraction of the cycle time. Our results provide a natural extension of Spohn's algebraic condition for the appr…
We examine the question of whether the formal expressions of equilibrium statistical mechanics can be applied to time independent non-dissipative systems that are not in true thermodynamic equilibrium and are nonergodic. By assuming the phase space may be divided into time independent, locally ergodic domains, we argue that within such domains the relative probabilities of microstates are given by the standard Boltzmann weights. In contrast to previous energy landscape treatments, that have been developed specifically for the glass transition, we do not impose an a priori knowledge of the inte…
We study the relaxation of a single colloidal sphere which is periodically driven between two nonequilibrium steady states. Experimentally, this is achieved by driving the particle along a toroidal trap imposed by scanned optical tweezers. We find that the relaxation time after which the probability distributions have been relaxed is identical to that obtained by a steady state measurement. In quantitative agreement with theoretical calculations the relaxation time strongly increases when driving the system further away from thermal equilibrium.
We develop a general framework for the steady-state response of dissipative quantum systems. We concretely derive three different, but equivalent, forms of the quantum response function. We discuss for each of them the role of the noncommutativity of quantum operators and establish links to the Kubo response theory for closed quantum systems. We show in particular that the equilibrium response vanishes for perturbations that commute with the unperturbed Hamiltonian while the steady-state response does not, highlighting the profound difference between the two.
The nonequilibrium dynamics of a small quantum system coupled to a dissipative environment is studied. We show that (1) the oscillatory dynamics close to a coherent-to-incoherent transition is surprisingly different from the one of the classical damped harmonic oscillator and that (2) non-markovian memory plays a prominent role in the time evolution after a quantum quench.
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 …
Fundamental interactions are either fully or nearly symmetric under time reversal. But macroscopic phenomena have a definite arrow of time. Though there is no convergence on the origin of time's preferential direction, many researchers believe that the direction of time is towards increasing entropy. In this paper, we provide an alternate point of view. In driven-dissipative nonequilibrium systems forced at large scale, the energy flows from large scales to dissipative scales. This generic and multiscale process breaks time reversal symmetry and principle of detailed balance, thus can yield an…
Based on the Fokker-Planck and the entropy balance equations we have studied the relaxation of a dissipative dynamical system driven by external Ornstein-Uhlenbeck noise processes in absence and presence of nonequilibrium constraint in terms of the thermodynamically inspired quantities like entropy flux and entropy production. The interplay of nonequilibrium constraint, dissipation and noise reveals some interesting extremal nature in the time dependence of entropy flux and entropy production.
Quantum computers are a leading platform for the simulation of many-body physics. This task has been recently facilitated by the possibility to program directly the time-dependent pulses sent to the computer. Here, we use this feature to simulate quantum lattice models with long-range hopping. Our approach is based on an exact mapping between periodically driven quantum systems and one-dimensional lattices in the synthetic Floquet direction. By engineering a periodic drive with a power-law spectrum, we simulate a lattice with long-range hopping, whose decay exponent is freely tunable. We propo…
A defining feature of living matter is the ability to harness energy to self-organize multiscale structures whose functions are facilitated by irreversible nonequilibrium dynamics. While progress has been made in elucidating the underlying principles, what remains unclear is the role that thermodynamics plays in shaping these structures and their ensuing functions. Here, we unravel how a fundamental thermodynamic connection between the physical energy dissipation sustaining a nonequilibrium system and a measure of statistical irreversibility (arrow of time), can provide quantitative insight in…
We consider an open quantum system, with dissipation applied only to a part of its degrees of freedom, evolving via a quantum Markov dynamics. We demonstrate that, in the Zeno regime of large dissipation, the relaxation of the quantum system towards a pure quantum state is linked to the evolution of a classical Markov process towards a single absorbing state. The rates of the associated classical Markov process are determined by the original quantum dynamics. Extension of this correspondence to absorbing states with internal structure allows us to establish a general criterion for having a Zen…
Extending notions of phase transitions to nonequilibrium realm is a fundamental problem for statistical mechanics. While it was discovered that critical transitions occur even for transient states before relaxation as the singularity of a dynamical version of free energy, their nature is yet to be elusive. Here, we show that spontaneous symmetry breaking can occur at a short-time regime and causes universal dynamical quantum phase transitions in periodically driven unitary dynamics. Unlike conventional phase transitions, the relevant symmetry is antiunitary: its breaking is accompanied by a ma…
The separation of substances into different phases is ubiquitous in nature and important scientifically and technologically. This phenomenon may become drastically different if the species involved, whether molecules or supramolecular assemblies, interconvert. In the presence of an external force large enough to overcome energetic differences between the interconvertible species (forced interconversion), the two alternative species will be present in equal amounts, and the striking phenomenon of steady-state, restricted phase separation into mesoscales is observed. Such microphase separation i…
By assuming that a particle of energy hbar.omega is actually a dissipative system maintained in a nonequilibrium steady state by a constant throughput of energy (heat flow), the exact Schroedinger equation is derived, both for conservative and nonconservative systems. Thereby, only universal properties of oscillators and nonequilibrium thermostatting are used, such that a maximal model independence of the hypothesised sub-quantum physics is guaranteed. It is claimed that this represents the shortest derivation of the Schroedinger equation from (modern) classical physics in the literature, and …
A new type of quantum transfer matrix, arising as a Cholesky factor for the steady state density matrix of a dissipative Markovian process associated with the boundary-driven Lindblad equation for the isotropic spin-1/2 Heisenberg (XXX) chain, is presented. The transfer matrix forms a commuting family of non-Hermitian operators depending on the spectral parameter which is essentially the strength of dissipative coupling at the boundaries. The intertwining of the corresponding Lax and monodromy matrices is performed by an infinitely dimensional Yang-Baxter R-matrix which we construct explicitly…
We prove the existence of non-equilibrium phases of matter in the prethermal regime of periodically-driven, long-range interacting systems, with power-law exponent $α> d$, where $d$ is the dimensionality of the system. In this context, we predict the existence of a disorder-free, prethermal discrete time crystal in one dimension -- a phase strictly forbidden in the absence of long-range interactions. Finally, using a combination of analytic and numerical methods, we highlight key experimentally observable differences between such a prethermal time crystal and its many-body localized counterpar…
For open quantum systems, the Gaussian environmental dissipative effect can be represented by statistical quasi-particles, namely, dissipatons. We exploit this fact to establish the dissipaton thermofield theory. The resulting generalized Langevin dynamics of absorptive and emissive thermofield operators are effectively noise-resolved. The system-bath entanglement theorem is then readily followed between an important class of nonequilibrium steady-state correlation functions. All these relations are validated numerically. A simple corollary is the transport current expression, which exactly re…
We investigate a dissipatively driven XYZ spin-1/2 chain in the Zeno limit of strong dissipation, described by Lindblad master equation. The nonequilibrium steady state is expressed in terms of a matrix product ansatz using novel site-dependent Lax operators. The components of Lax operators satisfy a simple set of linear recurrence equations that generalize the defining algebraic relations of the quantum group $U_q(sl_2)$. We reveal connection between the nonequilibrium steady state of the nonunitary dynamics and the respective integrable model with edge magnetic fields, described by coherent …
