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We review exact approaches and recent results related to the relaxation dynamics and description after relaxation of various one-dimensional lattice systems of hard-core bosons after a sudden quench. We first analyze the integrable case,…
Local relaxation after a quench in 1-D quantum many-body systems is a well known and very active problem with rich phenomenology. Except for pathological cases, the local relaxation is accompanied by the local restoration of the symmetries…
We study the stochastic relaxation dynamics of the Ising p-spin model on a random graph, a well-known model with glassy dynamics at low temperatures. We introduce and discuss a new closure scheme for the master equation governing the…
We study a granular gas of viscoelastic particles (kinetic energy loss upon collision is a function of the particles' relative velocities at impact) subject to a stochastic thermostat. We show that the system displays anomalous cooling and…
Understanding relaxation processes is an important unsolved problem in many areas of physics. A key challenge in studying such non-equilibrium dynamics is the scarcity of experimental tools for characterizing their complex transient states.…
We present a thermodynamic theory of the Kovacs effect based on the idea that the configurational degrees of freedom of a glass-forming material are driven out of equilibrium with the heat bath by irreversible thermal contraction and…
The nonequilibrium thermodynamics feature of a Brownian motor operating between two different heat baths is explored as a function of time $t$. Using the Gibbs entropy and Schnakenberg microscopic stochastic approach, we find exact closed…
An irreversible Markov-chain Monte Carlo (MCMC) algorithm with skew detailed balance conditions originally proposed by Turitsyn et al. is extended to general discrete systems on the basis of the Metropolis-Hastings scheme. To evaluate the…
We present a generic reweighting method for nonequilibrium Markov processes. With nonequilibrium Monte Carlo simulations at a single temperature, one calculates the time evolution of physical quantities at different temperatures, which…
We address the question whether observables of an exactly solvable model of electrons coupled to (optical) phonons relax into large time stationary state values and investigate if the asymptotic expectation values can be computed using a…
We introduce an extension of the non-equilibrium dynamical mean field theory to incorporate the effects of static random disorder in the dynamics of a many-particle system by integrating out different disorder configurations resulting in an…
We have studied the relation between the structural relaxation and the frequency dependent thermal response or the specific heat, $c_p(\omega)$, in a supercooled liquid. The Mode Coupling Theory (MCT) results are used to obtain…
Mapping finite-temperature dynamical phase diagrams of quantum many-body models is a necessary step towards establishing a framework of far-from-equilibrium quantum many-body universality. However, this is quite difficult due, in part, to…
The extension of Boltzmann-Gibbs thermostatistics, proposed by Tsallis, introduces an additional parameter $q$ to the inverse temperature $\beta$. Here, we show that a previously introduced generalized Metropolis dynamics to evolve spin…
An exact reduced dynamical map along with its operator sum representation is derived for a central spin interacting with a thermal spin environment. The dynamics of the central spin shows high sustainability of quantum traits such as…
We show that there are two distinct mechanisms that can cause the symmetry-restoration Mpemba effect in spin chains with \textit{weakly broken} integrability, such that the asymptotic equilibration is diffusive, but the lifetime of…
The non-equilibrium physics of many-body quantum systems harbors various unconventional phenomena. In this study, we experimentally investigate one of the most puzzling of these phenomena -- the quantum Mpemba effect, where a tilted…
We establish a link between unitary relaxation dynamics after a quench in closed many-body systems and the entanglement in the energy eigenbasis. We find that even if reduced states equilibrate, they can have memory on the initial…
As recently manifested , the quench dynamics of isolated quantum systems consisting of a finite number of particles, is characterized by an exponential spreading of wave packets in the many-body Hilbert space. This happens when the…
We establish a setting - atoms in optical superlattices with period 2 - in which one can experimentally probe signatures of the process of local relaxation and apparent thermalization in non-equilibrium dynamics without the need of…