Properties Of Nonequilibrium Steady States Research Articles

Impact of Optically Pumped Nonequilibrium Steady States on Luminescence Emission of Atomically Thin Semiconductor Excitons.

The interplay of the nonequivalent corners in the Brillouin zone of transition metal dichalcogenides (TMDCs) has been investigated extensively. While experimental and theoretical works contributed to a detailed understanding of the relaxation of selective optical excitations and the related relaxation rates, only limited microscopic descriptions of stationary experiments are available so far. Here we present microscopic calculations for the nonequilibrium steady state properties of excitons during continuous wave pumping exemplary for monolayer MoSe_{2}. We find sharp features in photoluminescence excitation spectra and degree of polarization which result from phonon assisted excitonic transitions dominating over exciton recombination and intervalley exchange coupling.

Nonequilibrium steady-state picture of incoherent light-induced excitation harvesting.

We formulate a comprehensive theoretical description of excitation harvesting in molecular aggregates photoexcited by weak incoherent radiation. An efficient numerical scheme that respects the continuity equation for excitation fluxes is developed to compute the nonequilibrium steady state (NESS) arising from the interplay between excitation generation, excitation relaxation, dephasing, trapping at the load, and recombination. The NESS is most conveniently described in the so-called preferred basis in which the steady-state excitonic density matrix is diagonal. The NESS properties are examined by relating the preferred-basis description to the descriptions in the site or excitonic bases. Focusing on a model photosynthetic dimer, we find that the NESS in the limit of long trapping time is quite similar to the excited-state equilibrium in which the stationary coherences originate from the excitation-environment entanglement. For shorter trapping times, we demonstrate how the properties of the NESS can be extracted from the time-dependent description of an incoherently driven but unloaded dimer. This relation between stationary and time-dependent pictures is valid, provided that the trapping time is longer than the decay time of dynamic coherences accessible in femtosecond spectroscopy experiments.

Floquet states in dissipative open quantum systems

We theoretically investigate basic properties of nonequilibrium steady states of periodically-driven open quantum systems based on the full solution of the Maxwell–Bloch equation. In a resonant driving condition, we find that the transverse relaxation, also known as decoherence, significantly destructs the formation of Floquet states while the longitudinal relaxation does not directly affect it. Furthermore, by evaluating the quasienergy spectrum of the nonequilibrium steady states, we demonstrate that Rabi splitting can be observed as long as the decoherence time is as short as one third of the Rabi-cycle. Moreover, we find that Floquet states can be formed even under significant dissipation when the decoherence time is substantially shorter than the cycle of driving, once the driving field strength becomes strong enough. In an off-resonant condition, we demonstrate that the Floquet states can be realized even in weak field regimes because the system is not excited and the decoherence mechanism is not activated. Once the field strength becomes strong enough, the system can be excited by multi-photon absorption and the decoherence process becomes active. As a result, the Floquet states are significantly disturbed by the environment even in the off-resonant condition. Thus, we show here that the suppression of energy transfer from light to matter is a key condition for the realization of Floquet states in both on- and off-resonant conditions not only because it prevents material damage but also because it contributes to preserving coherence.

Nonequilibrium response of a voltage gated sodium ion channel and biophysical characterization of dynamic hysteresis

Here we have studied the dynamic as well as the non-equilibrium thermodynamic response properties of voltage-gated Na-ion channel. Using sinusoidally oscillating external voltage protocol we have both kinetically and energetically studied the non-equilibrium steady state properties of dynamic hysteresis in details. We have introduced a method of estimating the work done associated with the dynamic memory due to a cycle of oscillating voltage. We have quantitatively characterised the loop area of ionic current which gives information about the work done to sustain the dynamic memory only for ion conduction, while the loop area of total entropy production rate gives the estimate of work done for overall gating dynamics. The maximum dynamic memory of Na-channel not only depends on the frequency and amplitude but it also depends sensitively on the mean of the oscillating voltage and here we have shown how the system optimize the dynamic memory itself in the biophysical range of field parameters. The relation between the average ionic current with increasing frequency corresponds to the nature of the average dissipative work done at steady state. It is also important to understand that the utilization of the energy from the external field can not be directly obtained only from the measurement of ionic current but also requires nonequilibrium thermodynamic study.

Nonequilibrium distribution functions for quantum transport: Universality and approximation for the steady state regime

We derive a general expression for the electron nonequilibrium (NE) distribution function in the context of steady state quantum transport through a two-terminal nanodevice with interaction. The central idea for the use of NE distributions for open quantum systems is that both the NE and many-body (MB) effects are taken into account in the statistics of the finite size system connected to reservoirs. We develop an alternative scheme to calculate the NE steady state properties of such systems. The method, using NE distribution and spectral functions, presents several advantages, and is equivalent to conventional steady-state NE Green's functions (NEGF) calculations when the same level of approximation for the MB interaction is used. The advantages of our method resides in the fact that the NE distribution and spectral functions have better analytic behaviour for numerical calculations. Furthermore our approach offer the possibility of introducing further approximations, not only at the level of the MB interaction as in NEGF, but also at the level of the functional form used for the NE distributions. For the single level model with electron-phonon coupling we have considered, such approximations provide a good representation of the exact results, for either the NE distributions themselves or the transport properties. We also derive the formal extensions of our method for systems consisting of several electronic levels and several vibration modes.

One-dimensional transport of interacting particles: Currents, density profiles, phase diagrams, and symmetries

Driven lattice gases serve as canonical models for investigating collective transport phenomena and properties of nonequilibrium steady states. Here we study one-dimensional transport with nearest-neighbor interactions both in closed bulk systems and in open channels coupled to two particle reservoirs at the ends of the channel. For the widely employed Glauber rates we derive an exact current-density relation in the bulk for unidirectional hopping. An approach based on time-dependent density functional theory provides a good description of the kinetics. For open systems, the system-reservoir couplings are shown to have a striking influence on boundary-induced phase diagrams. The role of particle-hole symmetry is discussed, and its consequence for the topology of the phase diagrams. It is furthermore demonstrated that systems with weak bias can be mapped onto systems with unidirectional hopping.

Nonequilibrium steady state for strongly correlated many-body systems: Variational cluster approach

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 non-linear 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 and increasing number of uncorrelated sites.

Rotational sandpile models: A finite size scaling study

Nontrivial critical behaviour is observed in equilibrium lattice statistical models under rotational constraint. Effect of rotational constraint on lattice statistical models at out of equilibrium situation is important to study. Critical properties of non-equilibrium steady state of sandpile models are studied under rotational constraint via finite size scaling (FSS) analysis. Not only FSS is found to be valid for a wide range of rotational sandpile models but also they are found to belong to the same universality class.

Generalized Green-Kubo relation and integral fluctuation theorem for driven dissipative systems without microscopic time reversibility

We derive the generalized Green-Kubo relation and an integral form of the fluctuation theorem that apply to driven dissipative systems, in which time-reversal symmetry or local detailed balance is broken. Uniformly sheared granular systems and driven inelastic Lorentz-gas model are considered as examples. It is discussed how statistical mechanical theory dealing with nonequilibrium steady-state properties can be constructed for such systems for which equilibrium state does not exist.

Properties of nonequilibrium steady states: a path integral approach

A number of properties of systems in a nonequilibrium steady state (NESS) areinvestigated by a generalization of the Onsager–Machlup (OM) path integral approach forsystems in an equilibrium state (ES). A thermodynamics formally identical to that in anES can be formulated, but with definitions of work and heat as needed to maintain theNESS. In this approach, the heat plays a crucial role and is directly related to the differentbehavior of a system’s forward and backward paths in time in an appropriate functionspace. However, an ambiguity in the choice of the time-backward path corresponding to agiven time-forward path prevents a unique general formal theory for systems in aNESS. Unique unambiguous physically acceptable physical results for a system in aNESS appear to be obtainable only after specifying the physical nonequilibriumparameters, which define a system in a NESS as part of a larger system. NESSsystems are therefore fundamentally different from those in an ES. Furthermore, anexample is given for a particular system that the fluctuations of a system in aNESS behave in many respects very differently from those in a system in anES.

Theory of thermostatted inhomogeneous granular fluids: A self-consistent density functional description

The authors present a study of the nonequilibrium statistical properties of a one dimensional hard-rod fluid dissipating energy via inelastic collisions and subject to the action of a Gaussian heat bath, simulating an external driving mechanism. They show that the description of the fluid based on the one-particle phase-space reduced distribution function, in principle necessary because of the presence of velocity dependent collisional dissipation, can be contracted to a simpler description in configurational space. Indeed, by means of a multiple-time-scale method the authors derive a self-consistent governing equation for the particle density distribution function. This equation is similar to the dynamic density functional equation employed in the study of colloids, but contains additional terms taking into account the inelastic nature of the fluid. Such terms cannot be derived from a Liapunov generating functional and contribute not only to the relaxational properties, but also to the nonequilibrium steady state properties. A validation of the theory against molecular dynamics simulations is presented in a series of cases, and good agreement is found.

Heat Transport in Harmonic Lattices

We work out the non-equilibrium steady state properties of a harmonic lattice which is connected to heat reservoirs at different temperatures. The heat reservoirs are themselves modeled as harmonic systems. Our approach is to write quantum Langevin equations for the system and solve these to obtain steady state properties such as currents and other second moments involving the position and momentum operators. The resulting expressions will be seen to be similar in form to results obtained for electronic transport using the non-equilibrium Green's function formalism. As an application of the formalism we discuss heat conduction in a harmonic chain connected to self-consistent reservoirs. We obtain a temperature dependent thermal conductivity which, in the high-temperature classical limit, reproduces the exact result on this model obtained recently by Bonetto, Lebowitz and Lukkarinen.

The Green-Kubo Formula and the Onsager Reciprocity Relations in Quantum Statistical Mechanics

We study linear response theory in the general framework of algebraic quantum statistical mechanics and prove the Green-Kubo formula and the Onsager reciprocity relations for heat fluxes generated by temperature differentials. Our derivation is axiomatic and the key assumptions concern ergodic properties of non-equilibrium steady states.

Nonequilibrium Steady State in Vibrating Granular Gases

Statistical properties of nonequilibrium steady states in vibrating granular gases in an slightly tilted container are investigated in terms of the discrete-element method. It is found that the steady behavior of this granular flow is difficult to be described by the steady Fokker-Planck equation with Coulomb friction.

Synchronous asymmetric exclusion processes

For a fully synchronous asymmetric exclusion process with open or closed boundaries only partial analytic results are known owing to the appearance of strong-short range correlations, which invalidate simple mean-field approximations. Here we present a new method for calculating basic properties of nonequilibrium steady states, and calculate densities, fluxes, travel times, spatial and temporal correlation functions, phase diagrams, profiles and widths of boundary layers and interfaces between phases in coexistence, as well as their microstructures. This paper is based on two new elements: (i) a microscopic characterization of order parameters and local configurations in the relevant phases, based on the microdynamics of the model, and (ii) an improved mean-field approximation, which neglects certain four-point - and higher-order correlation functions. It is conjectured that the density profiles, obtained here, are exact up to terms that are exponentially small in the system size.

Unstable periodic orbits and transport properties of nonequilibrium steady states.

Nonequilibrium steady-state flows governed by time-reversible equations of motion are described in terms of unstable periodic orbits. Important properties, such as transport coefficients and the multifractal spectrum, are related to the difference in probability of observing periodic orbits and their time reverses. We apply the theory to the periodic Lorentz gas driven by a constant external field and numerically calculate the conductivity.

Fluctuation expressions for the derived properties of nonequilibrium steady states.

Fluctuation expressions are developed for the derived properties of steady states. We give expressions for the compressibility and the specific heats at constant volume and pressure. In contrast to the compressibility, the specific-heat fluctuation formulas are not simple generalizations of the corresponding equilibrium expressions.

Nonequilibrium phase transitions in stochastic lattice systems: Influence of the hopping rates

Two-dimensional lattice-gas models with attractive interactions and particle-conserving hopping dynamics under the influence of a very large external electric field ⇀E along a principal axis are studied in the case of different ratiosγ between the jump rates in the field direction and perpendicular to it using different transition probabilities. We investigate the dependence of the non-equilibrium steady-state properties on the transition mechanism. We find self-similarity with respect to (T, γ) and a coexistence curve critical exponent which, for smallγ, seems independent ofγ. There is some evidence that this exponent might be halfway between the equilibrium mean field and Onsager's values. A crossover toward mean-field behavior for largeγ seems also identified.