Nonequilibrium Dynamics Research Articles

Lindbladian route towards thermalization of a Luttinger liquid

We study the nonequilibrium dynamics of a Luttinger liquid after a simultaneous quantum quench of the interaction and dissipative quench to the environment within the realm of the Lindblad equation. When the couplings to the environment satisfy detailed balance, the system is destined to thermalize, which we follow using bosonization. The thermodynamic entropy of the system, which also encodes information about the entanglement with the environment, either exhibits a maximum and minimum or grows monotonically before reaching its thermal value in a universal fashion. The single-particle density matrix reveals interesting features in the spatiotemporal ``phase diagram,'' including thermal, prethermal, and dissipation enhanced sudden quench Luttinger liquid behavior, as well as dissipation, enhanced Fermi liquid response.

Dynamics of photoinduced ferromagnetism in oxides with orbital degeneracy

By using intense coherent electromagnetic radiation, it may be possible to manipulate the properties of quantum materials very quickly, or even induce new and potentially useful phases that are absent in equilibrium. For instance, ultrafast control of magnetic dynamics is crucial for a number of proposed spintronic devices, and it can also shed light on the possible dynamics of correlated phases out of equilibrium. Inspired by recent experiments on spin-orbital ferromagnet ${\mathrm{YTiO}}_{3}$, we consider the nonequilibrium dynamics of a Heisenberg ferromagnetic insulator with low-lying orbital excitations. We model the dynamics of the magnon excitations in this system following an optical pulse that resonantly excites infrared-active phonon modes. As the phonons ring down, they can dynamically couple the orbitals with the low-lying magnons, leading to a dramatically modified effective bath for the magnons. We show that this transient coupling can lead to a dynamical acceleration of the magnetization dynamics, which is otherwise bottlenecked by small anisotropy. Exploring the parameter space more, we find that the magnon dynamics can also even completely reverse, leading to a negative relaxation rate when the pump is blue-detuned with respect to the orbital bath resonance. We therefore show that by using specially targeted optical pulses, one can exert a much greater degree of control over the magnetization dynamics, allowing one to optically steer magnetic order in this system. We conclude by discussing interesting parallels between the magnetization dynamics we find here and recent experiments on photoinduced superconductivity, where it is similarly observed that depending on the initial pump frequency, an apparent metastable superconducting phase emerges.

On a thermodynamic foundation of Eyring rate theory for plastic deformation of polymer solids

ABSTRACTThe plastic deformation of almost all solid polymers can be represented by a thermally activated rate process involving the motion of cooperative mobile elements over potential barriers, based on the Eyring activated rate theory. The present study shows that the governing equations for the Eyring rate theory can be completely derived based on the principle of microscopic reversibility in the framework of non-equilibrium dynamics.

Nonequilibrium dynamics of the Ising model on heterogeneous networks with an arbitrary distribution of threshold noise.

The Ising model on networks plays a fundamental role as a testing ground for understanding cooperative phenomena in complex systems. Here we solve the synchronous dynamics of the Ising model on random graphs with an arbitrary degree distribution in the high-connectivity limit. Depending on the distribution of the threshold noise that governs the microscopic dynamics, the model evolves to nonequilibrium stationary states. We obtain an exact dynamical equation for the distribution of local magnetizations, from which we find the critical line that separates the paramagnetic from the ferromagnetic phase. For random graphs with a negative binomial degree distribution, we demonstrate that the stationary critical behavior as well as the long-time critical dynamics of the first two moments of the local magnetizations depend on the distribution of the threshold noise. In particular, for an algebraic threshold noise, these critical properties are determined by the power-law tails of the distribution of thresholds. We further show that the relaxation time of the average magnetization inside each phase exhibits the standard mean-field critical scaling. The values of all critical exponents considered here are independent of the variance of the negative binomial degree distribution. Our work highlights the importance of certain details of the microscopic dynamics for the critical behavior of nonequilibrium spin systems.

Nonequilibrium dynamics of axionlike particles: The quantum master equation

We study the non-equilibrium dynamics of Axion-like particles (ALP) coupled to Standard Model degrees of freedom in thermal equilibrium. The Quantum Master Equation (QME) for the (ALP) reduced density matrix is derived to leading order in the coupling of the (ALP) to the thermal bath, but to \emph{all} orders of the bath couplings to degrees of freedom within or beyond the Standard Model other than the (ALP). The (QME) describes the damped oscillation dynamics of an initial misaligned (ALP) condensate, thermalization with the bath, decoherence and entropy production within a unifying framework. The (ALP) energy density $\mathcal{E}(t)$ features two components: a ``cold'' component from the misaligned condensate and a ``hot'' component from thermalization with the bath, with $\mathcal{E}(t)= \mathcal{E}_{c}\,e^{-\gamma(T)\,t}+\mathcal{E}_{h}(1-e^{-\gamma(T)\,t})$ thus providing a ``mixed dark matter'' scenario. Relaxation of the (ALP) condensate, thermalization, decoherence and entropy production occur on similar time scales. An explicit example with (ALP)-photon coupling, valid post recombination yields a relaxation rate $\gamma(T)$ with a substantial enhancement from thermal emission and absorption. A misaligned condensate is decaying at least since recombination and on the same time scale thermalizing with the cosmic microwave background (CMB). Possible consequences for birefringence of the (CMB) and (ALP) contribution to the effective number of ultrarelativistic species and galaxy formation are discussed.

Investigating Fundamental Principles of Nonequilibrium Assembly Using Temperature-Sensitive Copolymers.

Both natural biomaterials and synthetic materials benefit from complex energy landscapes that provide the foundation for structure-function relationships and environmental sensitivity. Understanding these nonequilibrium dynamics is important for the development of design principles to harness this behavior. Using a model system of poly(ethylene glycol) methacrylate-based thermoresponsive lower critical solution temperature (LCST) copolymers, we explored the impact of composition and stimulus path on nonequilibrium thermal hysteretic behavior. Through turbidimetry analysis of nonsuperimposable heat-cool cycles, we observe that LCST copolymers show clear hysteresis that varies as a function of pendent side chain length and hydrophobicity. Hysteresis is further impacted by the temperature ramp rate, as insoluble states can be kinetically trapped under optimized temperature protocols. This systematic study brings to light fundamental principles that can enable the harnessing of out-of-equilibrium effects in synthetic soft materials.

Dynamics of the spin-boson model: The effect of bath initial conditions.

The dynamics of the (sub-)Ohmic spin-boson model under various bath initial conditions is investigated by employing the Dirac-Frenkel time-dependent variational approach with the multiple Davydov D1 Ansatz in the interaction picture. The validity of our approach is carefully checked by comparing the results with those of the hierarchy equations of motion method. By analyzing the features of nonequilibrium dynamics, we identify the phase diagrams for different bath initial conditions. We find that for the spectral exponent s < sc, there exists a transition from coherent to quasicoherent dynamics with increasing coupling strengths. For sc < s ≤ 1, the coherent to incoherent crossover occurs at a certain coupling strength and the quasicoherent dynamics emerges at much larger couplings. The initial preparation of the bath has a considerable influence on the dynamics.

Nonequilibrium dynamics of fluctuations in an ultracold atomic mixture

The nonequilibrium spin-changing dynamics of an ultracold mixture of lithium and sodium atoms reveals the importance of spin fluctuations for key observables. The authors show that the experimental control of fluctuations can give access to the dynamics of a long-lived metastable state, an instability region with strong growth of fluctuations, and a regime with an early approach to thermal equilibrium.

Dynamic screening of quasiparticles in WS2 monolayers

We unravel the influence of quasiparticle screening in the non-equilibrium exciton dynamics of monolayer WS$_2$. We report pump photon energy-dependent exciton blue and red-shifts from time-resolved-reflectance contrast measurements. Based on a phenomenological model, we isolate the effective impact of excitons and free carriers on the renormalization of the quasi-free particle band gap, exciton binding energy and linewidth broadening. By this, our work does not only provide a comprehensive picture of the competing phenomena governing the exciton dynamics in WS$_2$ upon photoexcitation, but also demonstrates that exciton and carrier contributions to dynamic screening of the Coulomb interaction differ significantly.

Most probable path of active Ornstein-Uhlenbeck particles.

Using the path integral representation of the nonequilibrium dynamics, we compute the most probable path between arbitrary starting and final points that is followed by an active particle driven by persistent noise. We focus our attention on the case of active particles immersed in harmonic potentials, where the trajectory can be computed analytically. Once we consider the extended Markovian dynamics where the self-propulsive drive evolves according to an Ornstein-Uhlenbeck process, we can compute the trajectory analytically with arbitrary conditions on position and self-propulsion velocity. We test the analytical predictions against numerical simulations and we compare the analytical results with those obtained within approximated equilibriumlike dynamics.

Real-time evolution of Anderson impurity models via tensor network influence functionals

In this work we present and analyze two tensor network-based influence functional approaches for simulating the real-time dynamics of quantum impurity models such as the Anderson model. Via comparison with recent numerically exact simulations, we show that such methods accurately capture the long-time non-equilibrium quench dynamics. The two parameters that must be controlled in these tensor network influence functional approaches are a time discretization (Trotter) error and a bond dimension (tensor network truncation) error. We show that the actual numerical uncertainties are controlled by an intricate interplay of these two approximations which we demonstrate in different regimes. Our work opens the door to using these tensor network influence functional methods as general impurity solvers.

NON-EQUILIBRIUM SUPERSONIC FLOW AROUND A BLUNT

The computational model designed for studying the processes of non-equilibrium physicochemical gas dynamics in supersonic rarefied-air flow past a blunt plate of finite dimensions under the laboratory experiment conditions is formulated. The computational model is based on the two-dimensional Navier–Stokes equations, the energy conservation laws for the translational degrees of freedom of atoms and molecules and the vibrational degrees of freedom of diatomic molecules, and the chemical kinetics and diffusion equations for individual components of partially ionized gas flow. The basic gas dynamic and kinetic processes in flow past a blunt plate are analyzed at the Mach numbers M = 10 and 20. It is shown that regions of thermal nonequilibrium are formed.

Scalar potentials for light in a cavity

The nonequilibrium dynamics of light in a coherently driven nonlinear cavity resembles the equilibrium dynamics of a Brownian particle in a scalar potential. This resemblance has been known for decades, but the correspondence between the two systems has never been properly assessed. Here we demonstrate that this correspondence can be exact, be approximate, or break down, depending on the driving conditions. For vanishing nonlinearity and on-resonance driving, the correspondence is exact: The cavity dissipation and driving amplitude define a scalar potential, and light follows the equilibrium Boltzmann distribution with an effective temperature defined by the noise variance and cavity dissipation. The scalar potential pertaining to linear on-resonance dynamics fails dramatically in nonlinear and/or off-resonance regimes. However, we introduce a distinct scalar potential enabling an effective equilibrium description of light. Our potential gives a reasonably accurate description in limited nonlinear regimes of bistability, but fails deep in the bistability where nonconservative forces dominate the dynamics. Consequently, the correspondence to Brownian motion in a scalar potential breaks down. This breakdown is accompanied by a qualitative change in the spectrum of small intracavity field fluctuations, reminiscent of an exceptional point of a non-Hermitian Hamiltonian. Our results lay the foundations for an effective thermodynamic description of coherently driven cavities, and suggest that fundamental results for overdamped Langevin dynamics can help to assess the energetics and information processing of resonant optical technologies.

A framework to identify critical dynamics of water quality for diagnosing river basin ecosystem resilience and management

This study proposed a novel framework to identify critical water quality dynamics as early warning signals for diagnosing changes in the resilience of river basin ecosystems. We established empirical linkages between the theoretical background of three resilience capacities (robustness, adaptability and transformability) and water quality dynamics. Then, the processes of resilience degradation and their risk transfer or accumulation have been identified based on the shifts among different states. The methods of time-domain analysis and frequency-domain analysis were integrated into this framework, aiming to identify gradual and transient responses of water quality and its periodic fluctuation characteristics at multiple temporal scales. The time-domain analysis methods obtained the trend, cumulative periodic fluctuation of water quality by extracting the key characteristic parameters from the time-series data. The wavelet transform methods were introduced into the frequency-domain analysis to reveal the water quality fluctuation patterns at specific temporal scales. We tested the proposed framework in a typical agriculture-intensive watershed in eastern China. The results showed that this framework can be effectively used to identify three resilience states of river basin ecosystems. The degraded resilience regions were mainly distributed in the downstream area, which was influenced by their specific land use/cover and different agricultural soil health conditions. Particularly, urban sewage discharge was the main cause of periodic fluctuation in water quality time series at multiple high-frequency scales. The theoretical background of resilience capacities was elaborated in non-equilibrium dynamics before resilience degradation. Thus, this novel framework could reveal the pollution processes and driving mechanisms in different river reaches, and it also can provide adaptive management suggestions according to resilience dynamics traits.

The connection between dissipative chaos and nonequilibrium

Strong nonequilibrium conditions often give rise to dissipative chaos. However, the underlying connection between dissipative chaos and nonequilibrium remains unclear. Herein, we study this connection from the framework of the nonequilibrium potential-flux landscape. The nonequilibrium system dynamics are determined in part by the potential landscape associated with the steady-state probability distribution. The other part of the driving force for nonequilibrium dynamics comes from the steady-state probability flow, leading to the breaking of detailed balance. We find that dissipative chaos is driven mainly by the nonequilibrium probability flow. Using the Lorenz strange attractor model, we quantitatively demonstrate the close connection between the kinematic measures of the appearance of dissipative chaos and the degree of nonequilibrium. This work reveals the dynamic and thermodynamic origins of dissipative chaos beyond the interpretation based on nonlinearity. This study also provides a new understanding of the phase transitions in nonequilibrium systems.

Late-time critical behavior of local stringlike observables under quantum quenches

In recent times it has been observed that signatures of equilibrium quantum criticality surprisingly show up in many-body systems which are manifestly far from equilibrium. We explore such scenarios in interacting spin systems subject to a quench and develop a robust method to systematically probe ground state critical physics through nonequilibrium post-quench dynamics. Analyzing late-time behavior of finite string-like observables, we find emerging sharp signatures of equilibrium criticality. Specifically, these observables accurately detect equilibrium critical points and universal scaling exponents after long times following a quench. This happens despite the fact that the analyzed systems are strongly chaotic/ergodic and is interestingly due to a strong memory of the initial conditions retained by these observables after quench. We find that our results can also be used to explain critical signatures in post-quench domain formation, seen in a recent experiment with trapped ion quantum simulators.

Using (1+1)D quantum cellular automata for exploring collective effects in large-scale quantum neural networks.

Central to the field of quantum machine learning is the design of quantum perceptrons and neural network architectures. A key question in this regard is the impact of quantum effects on the way such models process information. Here, we establish a connection between (1+1)D quantum cellular automata, which implement a discrete nonequilibrium quantum many-body dynamics through successive applications of local quantum gates, and quantum neural networks (QNNs), which process information by feeding it through perceptrons interconnecting adjacent layers. Exploiting this link, we construct a class of QNNs that are highly structured-aiding both interpretability and helping to avoid trainability issues in machine learning tasks-yet can be connected rigorously to continuous-time Lindblad dynamics. We further analyze the universal properties of an example case, identifying a change of critical behavior when quantum effects are varied, showing their potential impact on the collective dynamical behavior underlying information processing in large-scale QNNs.

Entanglement Barrier and its Symmetry Resolution: Theory and Experimental Observation

An efficient method to extract higher-order density-matrix functionals and access operator entanglement is introduced and tested on experimental data, improving the characterization of nonequilibrium dynamics of many-body quantum systems.

Reversible Electrical Control of Interfacial Charge Flow across van der Waals Interfaces.

Bond-free integration of two-dimensional (2D) materials yields van der Waals (vdW) heterostructures with exotic optical and electronic properties. Manipulating the splitting and recombination of photogenerated electron-hole pairs across the vdW interface is essential for optoelectronic applications. Previous studies have unveiled the critical role of defects in trapping photogenerated charge carriers to modulate the photoconductive gain for photodetection. However, the nature and role of defects in tuning interfacial charge carrier dynamics have remained elusive. Here, we investigate the nonequilibrium charge dynamics at the graphene-WS2 vdW interface under electrochemical gating by operando optical-pump terahertz-probe spectroscopy. We report full control over charge separation states and thus photogating field direction by electrically tuning the defect occupancy. Our results show that electron occupancy of the two in-gap states, presumably originating from sulfur vacancies, can account for the observed rich interfacial charge transfer dynamics and electrically tunable photogating fields, providing microscopic insights for optimizing optoelectronic devices.

Tuning nonequilibrium phase transitions with inertia.

In striking contrast to equilibrium systems, inertia can profoundly alter the structure of active systems. Here, we demonstrate that driven systems can exhibit effective equilibrium-like states with increasing particle inertia, despite rigorously violating the fluctuation-dissipation theorem. Increasing inertia progressively eliminates motility-induced phase separation and restores equilibrium crystallization for active Brownian spheres. This effect appears to be general for a wide class of active systems, including those driven by deterministic time-dependent external fields, whose nonequilibrium patterns ultimately disappear with increasing inertia. The path to this effective equilibrium limit can be complex, with finite inertia sometimes acting to accentuate nonequilibrium transitions. The restoration of near equilibrium statistics can be understood through the conversion of active momentum sources to passive-like stresses. Unlike truly equilibrium systems, the effective temperature is now density dependent, the only remnant of the nonequilibrium dynamics. This density-dependent temperature can in principle introduce departures from equilibrium expectations, particularly in response to strong gradients. Our results provide additional insight into the effective temperature ansatz while revealing a mechanism to tune nonequilibrium phase transitions.