Results are presented for the dynamics arising due to a sudden quench of a boson interaction parameter with the simultaneous switching on of a commensurate periodic potential, the latter providing a source of non-linearity that can cause inelastic scattering. A quantum kinetic equation is derived perturbatively in the periodic potential and solved within the leading order gradient expansion. A two-particle irreducible formalism is employed to construct the stress-momentum tensor and hence the conserved energy. The dynamics is studied in detail in the phase where the boson spectrum remains gapless. The periodic potential is found to give rise to multi-particle scattering processes that relaxes the boson distribution function. At long times the system is found to thermalize with a thermalization time that depends in a non-monotonic way on the amount of energy injected into the system due to the quantum quench. This non-monotonic behavior arises due to the competing effect of an increase of phase space for scattering on the one hand, and an enhancement of the orthogonality catastrophe on the other hand as the quench amplitude is increased. The approach to equilibrium is found to be purely exponential for large quench amplitudes, and more complex for smaller quench amplitudes.
The steady state structure of an interface in an Ising system on a square lattice placed in a {\em non-uniform} external field, shows a commensurate -incommensurate transition driven by the velocity of the interface. The non-uniform field has a profile with a fixed shape which is designed to stabilize a flat interface, and is translated with velocity $v_{e}$. For small velocities the interface is stuck to the profile and is rippled with a periodicity which may be either commensurate or incommensurate with the lattice parameter of the square lattice. For a general orientation of the profile, th…
We study phase ordering dynamics in the three-dimensional nearest-neighbor Ising model, following rapid quenches from infinite to zero temperature. Results on various aspects, viz., domain growth, persistence, aging and pattern, have been obtained via the Glauber Monte Carlo simulations of the model on simple cubic lattice. These are analyzed via state-of-the-art methods, including the finite-size scaling, and compared with those for quenches to a temperature above the roughening transition. Each of these properties exhibit remarkably different behavior at the above mentioned final temperature…
We investigate by means of Monte Carlo simulations the dynamic phase transition of the two-dimensional kinetic Blume-Capel model under a periodically oscillating magnetic field in the presence of a quenched random crystal-field coupling. We analyze the universality principles of this dynamic transition for various values of the crystal-field coupling at the originally second-order regime of the corresponding equilibrium phase diagram of the model. A detailed finite-size scaling analysis indicates that the observed nonequilibrium phase transition belongs to the universality class of the equilib…
Quantum dynamics of magnetic order in a chiral multiferroic chain is studied. We consider two different scenarios: Ultrashort terahertz (THz) excitations or a sudden electric field quench. Performing analytical and numerical exact diagonalization calculations we trace the pulse induced spin dynamics and extract quantities that are relevant to quantum information processing. In particular, we analyze the dynamics of the system chirality, the von Neumann entropy, the pairwise and the many body entanglement. If the characteristic frequencies of the generated states are non-commensurate then a par…
We consider the effects of a quench to T = 0 on a spin system with axial next-next nearest neighbour Ising interactions, evolving under a conserved 3-spin flip dynamics. Such a model is motivated by the kinetics of stacking layers in polytypes near the 3C-6H transition. We find that the system generically gets arrested in interesting metastable states which have inhomogeneously distributed quiescent and active regions. In such arrested states, the autocorrelation function decays as a stretched exponential $\sim \exp(-(t/τ_{o})^{1 \over 3})$. The latter feature can be understood in terms of a m…
We investigate a kinetic Ising model with several single-spin flip dynamics (including Metropolis and heat-bath) on quenched and annealed random regular graphs. As expected, on the quenched structures all proposed algorithms reproduce the same results since the conditions for the detailed balance and the Boltzmann distribution in an equilibrium are satisfied. However, on the annealed graphs situation is far less clear -- the network annealing disturbs the equilibrium moving the system away from it. Consequently, distinct dynamics lead to different steady states. We show that some algorithms ar…
While a large number of studies have focused on the nonequilibrium dynamics of a system when it is quenched instantaneously from a disordered phase to an ordered phase, such dynamics have been relatively less explored when the quench occurs at a finite rate. Here we study the slow quench dynamics in two paradigmatic models of classical statistical mechanics, {viz.}, one-dimensional kinetic Ising model and mean-field zero-range process, when the system is annealed slowly to the critical point. Starting from the time evolution equations for the spin-spin correlation function in the Ising model a…
We study the dynamics of open quantum many-body systems driven across a critical point by quenching an Hamiltonian parameter at a certain velocity. General scaling laws are derived for the density of excitations and energy produced during the quench as a function of quench velocity and bath temperature. The scaling laws and their regimes of validity are verified for the XY spin chain locally coupled to bosonic baths. A detailed derivation and analysis of the kinetic equation of the problem is presented.
We investigate the relaxation dynamics of magnetic vortex lines in type-II superconductors following rapid changes of the external driving current by means of an elastic line model simulated with Langevin molecular dynamics. A system of flux vortices in a sample with randomly distributed point-like defects is subjected to an external current of appropriate strength for a sufficient period of time so as to be in a moving non-equilibrium steady state. The current is then instantaneously lowered to a value that pertains to either the moving or pinned regime. The ensuing relaxation of the flux lin…
We present a comprehensive Monte Carlo study of the ordering kinetics in the $d=2$ ferromagnetic $q$-state clock model with nonconserved Glauber dynamics. In agreement with previous studies we find that $q \geqslant 5$ is characterized by two phase transitions occurring at temperatures $T_{c}^1$ and $T_{c}^2$ ($T_{c}^2<T_{c}^1$). Phase ordering kinetics is then investigated by rapidly quenching the system in two phases, in the quasi-long range ordered phase (QLRO) where $T_{c}^2<T<T_{c}^1$ and in the long-range ordered phase (LRO) where $T<T_{c}^2$; $T$ being the quench temperature. Our numeri…
Large-scale Monte Carlo simulations are used to explore the effect of quenched disorder on one dimensional, non-equilibrium kinetic Ising models with locally broken spin symmetry, at zero temperature (the symmetry is broken through spin-flip rates that differ for '+' and '-' spins). The model is found to exhibit a continuous phase transition to an absorbing state. The associated critical behavior is studied at zero branching rate of kinks, through analysis spreading of '+' and '-' spins and, of the kink density. Impurities exert a strong effect on the critical behavior only for a particular ch…
We study the fate of the 2d kinetic q-state Potts model after a sudden quench to zero temperature. Both ground states and complicated static states are reached with non-zero probabilities. These outcomes resemble those found in the quench of the 2d Ising model; however, the variety of static states in the q-state Potts model (with q>=3) is much richer than in the Ising model, where static states are either ground or stripe states. Another possibility is that the system gets trapped on a set of equal-energy blinker states where a subset of spins can flip ad infinitum; these states are similar t…
After a sudden disruption, weakly interacting quantum systems first relax to a prethermalized state that can be described by perturbation theory and a generalized Gibbs ensemble. Using these properties of the prethermalized state we perturbatively derive a kinetic equation which becomes a quantum Boltzmann equation in the scaling limit of vanishing interaction. Applying this to interaction quenches in the fermionic Hubbard model we find that the momentum distribution relaxes to the thermal prediction of statistical mechanics. For not too large interaction, this two-stage scenario provides a qu…
We study numerically the two-dimensional Ising model with non-conserved dynamics quenched from an initial equilibrium state at the temperature $T_i\ge T_c$ to a final temperature $T_f$ below the critical one. By considering processes initiating both from a disordered state at infinite temperature $T_i=\infty$ and from the critical configurations at $T_i=T_c$ and spanning the range of final temperatures $T_f\in [0,T_c[$ we elucidate the role played by $T_i$ and $T_f$ on the aging properties and, in particular, on the behavior of the autocorrelation $C$ and of the integrated response function $χ…
We study numerically the aging dynamics of the two-dimensional p-state clock model after a quench from an infinite temperature to the ferromagnetic phase or to the Kosterlitz-Thouless phase. The system exhibits the general scaling behavior characteristic of non-disordered coarsening systems. For quenches to the ferromagnetic phase, the value of the dynamical exponents, suggests that the model belongs to the Ising-type universality class. Specifically, for the integrated response function $χ(t,s)\simeq s^{-a_χ}f(t/s)$, we find $a_χ$ consistent with the value $a_χ=0.28$ found in the two-dimensio…
Frequency evolutions of hysteresis loop area and hysteresis tools such as remanence and coercivity of a kinetic Ising model in the presence of quenched bond dilution are investigated in detail. The kinetic equation describing the time dependence of the magnetization is derived by means of effective-field theory with single-site correlations. It is found that the frequency dispersions of hysteresis loop area, remanence and coercivity strongly depend on the quenched bond randomness, as well as applied field amplitude and oscillation frequency. In addition, the shape of the hysteresis curves for …
The phenomenology from the time of the quench to the asymptotic behavior in the phase-ordering kinetics of a system with conserved order parameter is investigated in the Bray-Humayun model and in the Cahn-Hilliard-Cook model. From the comparison of the structure factor in the two models the generic pattern of the overall time evolution, based on the sequence ``early linear - intermediate mean field - late asymptotic regime'' is extracted. It is found that the time duration of each of these regimes is strongly dependent on the wave vector and on the parameters of the quench, such as the amplitu…
We studied the non-equilibrium dynamics of the q-state Potts model in the square lattice, after a quench to sub-critical temperatures. By means of a continuous time Monte Carlo algorithm (non-conserved order parameter dynamics) we analyzed the long term behavior of the energy and relaxation time for a wide range of quench temperatures and system sizes. For q>4 we found the existence of different dynamical regimes, according to quench temperature range. At low (but finite) temperatures and very long times the Lifshitz-Allen-Cahn domain growth behavior is interrupted with finite probability when…
We present the first systematic observation of scaling of thermal hysteresis with the temperature scanning rate around an abrupt thermodynamic transition in correlated electron systems. We show that the depth of supercooling and superheating in vanadium sesquioxide (V2O3) shifts with the temperature quench rates. The dynamic scaling exponent is close to the mean field prediction of 2/3. These observations, combined with the purely dissipative continuous ordering seen in "quench-and-hold" experiments, indicate departures from classical nucleation theory toward a barrier-free phase ordering asso…
In this article, we present a Monte Carlo study of phase transition and coarsening dynamics in the non-conserved two-dimensional random-bond $q$-state clock model (RBCM) deriving from a pure clock model [Phys. Rev. E 98, 032109 (2018)]. Akin to the pure clock model, RBCM also passes through two different phases when quenched from a disordered initial configuration representing at infinite temperature. Our investigation of the equilibrium phase transition affirms that both upper ($T_c^1$) and lower ($T_c^2$) phase transition temperatures decrease with bond randomness strength $ε$. Effect of $ε$…
We present a detailed derivation of the renormalization group equations for two dimensional electromagnetic Coulomb gases whose charges lie on a triangular lattice (magnetic charges) and its dual (electric charges). The interactions between the charges involve both angular couplings and a new electromagnetic potential. This motivates the denomination of ``elastic'' Coulomb gas. Such elastic Coulomb gases arise naturally in the study of the continuous melting transition of two dimensional solids coupled to a substrate, either commensurate or with quenched disorder.
We study the low-temperature domain growth kinetics of the two-dimensional Ising model with long-range coupling: $J(r) \sim r^{-(d+σ)}$, where $d=2$ is the dimensionality. According to the Bray-Rutenberg predictions, the exponent $σ$ controls the algebraic growth in time of the characteristic domain size $L(t)$, $L(t) \sim t^{1/z}$, with growth exponent $z=1+σ$ for $σ<1$ and $z=2$ for $σ>1$. These results hold for quenches to a non-zero temperature $T>0$ below the critical temperature $T_c$. We show that, in the case of quenches to $T=0$, due to the long-range interactions, the interfaces expe…
If quenched to zero temperature, the one-dimensional Ising spin chain undergoes coarsening, whereby the density of domain walls decays algebraically in time. We show that this coarsening process can be interrupted by exerting a rapidly oscillating periodic field with enough strength to compete with the spin-spin interaction. By analyzing correlation functions and the distribution of domain lengths both analytically and numerically, we observe nontrivial correlation with more than one length scale at the threshold field strength.
We study the stochastic Kardar-Parisi-Zhang equation for kinetic roughening where the time-independent (columnar or spatially quenched) Gaussian random noise $f(t,{\bf x})$ is specified by the pair correlation function $\langle f(t,{\bf x})f(t',{\bf x'}) \rangle \propto δ^{(d)} ({\bf x-x'})$, $d$ being the dimension of space. The field-theoretic renormalization group analysis shows that the effect of turbulent motion of the environment (modelled by the coupling with the velocity field described by the Kazantsev-Kraichnan statistical ensemble for an incompressible fluid) gives rise to a new non…
The exact relation between the response function $R(t,t^{\prime})$ and the two time correlation function $C(t,t^{\prime})$ is derived analytically in the one dimensional kinetic Ising model subjected to a temperature quench. The fluctuation dissipation ratio $X(t,t^{\prime})$ is found to depend on time through $C(t,t^{\prime})$ in the time region where scaling $C(t,t^{\prime}) = f(t/t^{\prime})$ holds. The crossover from the nontrivial form $X(C(t,t^{\prime}))$ to $X(t,t^{\prime}) \equiv 1$ takes place as the waiting time $t_w$ is increased from below to above the equilibration time $t_{eq}$.
We derive equation describing distribution of energy losses of the particle propagating in fractal medium with quenched and dynamic heterogeneities. We show that in the case of the medium with fractal dimension $2<D<3$ the losses $Δ$ are characterized by the sublinear anomalous dependence $Δ\sim x^α$ with power-law dependence on the distance $x$ from the surface and exponent $α=D-2$.
In order to find a measure of the dynamical features of phase separation kinetics during spinodal decomposition of a liquid binary mixture (like water and cyclohexane , water and 2,6 lutidiene or methanol and cyclohexane), we study both the initial fast exponential-like growth (the Cahn-Hilliard regime) and the subsequent cross-over to a much slower, non-exponential long time growth (the so-called scaling regime), by atomistic molecular dynamics (MD) simulation of a structure breaking binary liquid mixture. In particular, we combine our MD simulations with a coarse grained multi scale modellin…
We analyse the spin-flip dynamics in kinetic Ising chains with Kimball-Deker-Haake (KDH) transition rates, and evaluate exactly the evolution of global quantities like magnetisation and its fluctuations, and the two-time susceptibilities and correlations of the global spin and the global three-spin. Information on the ageing behaviour after a quench to zero temperature is extracted.
This is a less technical presentation of the ideas in quant-ph/9804035 [Phys Rev Lett 83 (1999), 1707-1710]. A second order phase transition induced by a rapid quench can lock out topological defects with densities far exceeding their equilibrium expectation values. This phenomenon is a generic prediction of nonequilibrium statistical mechanics, and can appear in a wide range of physical systems. We discuss it qualitatively in the context of trapped dilute Bose-Einstein condensates, outline a simple quantitative theory based on the time-dependent Ginzburg-Landau equation, and briefly compare t…
We investigate the long-time properties of the Ising-Glauber model on a periodic cubic lattice after a quench to zero temperature. In contrast to the conventional picture from phase-ordering kinetics, we find: (i) Domains at long time are highly interpenetrating and topologically complex, with average genus growing algebraically with system size. (ii) The long-time state is almost never static, but rather contains "blinker" spins that can flip ad infinitum with no energy cost. (iii) The energy relaxation has a complex time dependence with multiple characteristic time scales, the longest of whi…
We study the growth kinetics of glassy correlations in a structural glass by monitoring the evolution, within mode-coupling theory, of a suitably defined three-point function $χ_C(t,t_w)$ with time $t$ and waiting time $t_w$. From the complete wave vector-dependent equations of motion for domain growth we pass to a schematic limit to obtain a numerically tractable form. We find that the peak value $χ_C^P$ of $χ_C(t,t_w)$, which can be viewed as a correlation volume, grows as $t_w^{0.5}$, and the relaxation time as $t_w^{0.8}$, following a quench to a point deep in the glassy state. These resul…
The kinetics of chiral transitions in quark matter is studied in a two flavor Nambu-Jona-Lasinio model. We focus on the phase ordering dynamics subsequent to a temperature quench from the massless quark phase to the massive quark phase. We study the dynamics by considering a phenomenological model (Ginzburg-Landau free-energy functional). The morphology of the ordering system is characterized by the scaling of the order-parameter correlation function.
The phase ordering kinetics of the two-dimensional uniaxial nematic has been studied using a Cell Dynamic Scheme. The system after quench from T=infinity was found to scale dynamically with an asymptotic growth law similar to that of two-dimensional O(2) model (quenched from above the Kosterlitz - Thouless transition temperature), i.e. L(t) ~ t/ln(t/t0 ^{1/2} (with nonuniversal time scale t0). We obtained the true asymptotic limit of the growth law by performing our simulation for sufficiently long time. The presence of topologically stable 1/2-disclination points is reflected in the observed …
In this work we tackle a kinetic-like model of opinions dynamics in a networked population endued with a quenched plurality and polarization. Additionally, we consider pairwise interactions that are restrictive, which is modeled with a smooth bounded confidence. Our results show the interesting emergence of nonequilibrium hysteresis and heterogeneity-assisted ordering. Such counterintuitive phenomena are robust to different types of network architectures such as random, small-world and scale-free.
Universal scaling behavior in the relaxation dynamics of an isolated two-dimensional Bose gas is studied by means of semi-classical stochastic simulations of the Gross-Pitaevskii model. The system is quenched far out of equilibrium by imprinting vortex defects into an otherwise phase-coherent condensate. A strongly anomalous non-thermal fixed point is identified, associated with a slowed decay of the defects in the case that the dissipative coupling to the thermal background noise is suppressed. At this fixed point, a large anomalous exponent $η\simeq -3$ and, related to this, a large dynamica…
The long-time kinetics of the spherical model in an external magnetic field and below the equilibrium critical temperature is studied. The solution of the associated stochastic Langevin equation is reduced exactly to a single non-linear Volterra equation. For a sufficiently small external field, the kinetics of the magnetization-reversal transition from the metastable to the ground state is compared to the ageing behaviour of coarsening systems quenched into the low-temperature phase. For an oscillating magnetic field and below the critical temperature, we find evidence for the absence of the …
Understanding the non-equilibrium behavior of quantum systems is a major goal of contemporary physics. Much research is currently focused on the dynamics of many-body systems in low-dimensional lattices following a quench, i.e., a sudden change of parameters. Already such a simple setting poses substantial theoretical challenges for the investigation of the real-time post-quench quantum dynamics. In classical many-body systems the Kolmogorov-Mehl-Johnson-Avrami model describes the phase transformation kinetics of a system that is quenched across a first order phase transition. Here we show tha…
We analyze an ideal gas like model of a trading market with quenched random saving factors for its agents and show that the steady state income ($m$) distribution $P(m)$ in the model has a power law tail with Pareto index $ν$ exactly equal to unity, confirming the earlier numerical studies on this model. The analysis starts with the development of a master equation for the time development of $P(m)$. Precise solutions are then obtained in some special cases.
The long-time behaviour of spin-spin correlators in the slow relaxation of systems undergoing phase-ordering kinetics is studied in geometries of finite size. A phenomenological finite-size scaling ansatz is formulated and tested through the exact solution of the kinetic spherical model, quenched to below the critical temperature, in $2<d<4$ dimensions.
