arXiv subjects

Shamik Gupta

Publications and source records attributed to Shamik Gupta.

At least 73 records · Page 4Linked to original sources

arXiv2017

Dynamical origin of non-thermal states in galactic filaments

Observations strongly suggest that filaments in galactic molecular clouds are in a non-thermal state. As a simple model of a filament we study a two-dimensional system of self-gravitating point particles by means of numerical simulations of the dynamics, with various methods: direct $N$-body integration of the equations of motion, particle-in-cell simulations and a recently developed numerical scheme that includes multiparticle collisions in a particle-in-cell approach. Studying the collapse of Gaussian overdensities we find that after the damping of virial oscillations the system settles in a non-thermal steady state whose radial density profile is similar to the observed ones, thus suggesting a dynamical origin of the non-thermal states observed in real filaments. Moreover, for sufficiently cold collapses the density profiles are anticorrelated with the kinetic temperature, i.e., exhibit temperature inversion, again a feature that has been found in some observations of filaments. The same happens in the state reached after a strong perturbation of an initially isothermal cylinder. Finally, we discuss our results in the light of recent findings in other contexts (including non-astrophysical ones) and argue that the same kind of non-thermal states may be observed in any physical system with long-range interactions.

astro-ph.GA↗

arXiv2017

Non-thermal states in models of filaments: a dynamical study

We study the origin of the non-thermal profiles observed in filamentary structures in galactic molecular clouds by means of numerical dynamical simulations. We find that such profiles are intrinsic features of the end products of dissipationless collapse in cylindrical symmetry. Moreover, for sufficiently cold initial conditions, we obtain end states characterized by markedly anticorrelated radial density and temperature profiles. Gravitational, dissipationless dynamics alone is thus sufficient to reproduce, at least qualitatively, many of the properties of the observed non-thermal structures.

astro-ph.GA↗

arXiv2017

Equilibration in the Nosé-Hoover isokinetic ensemble: Effect of inter-particle interactions

We investigate the stationary and dynamic properties of the celebrated Nosé-Hoover dynamics of many-body interacting Hamiltonian systems, with an emphasis on the effect of inter-particle interactions. To this end, we consider a model system with both short- and long-range interactions. The Nosé-Hoover dynamics aims to generate the canonical equilibrium distribution of a system at a desired temperature by employing a set of time-reversible, deterministic equations of motion. A signature of canonical equilibrium is a single-particle momentum distribution that is Gaussian. We find that the equilibrium properties of the system within the Nosé-Hoover dynamics coincides with that within the canonical ensemble. Moreover, starting from out-of-equilibrium initial conditions, the average kinetic energy of the system relaxes to its target value over a {\it size-independent} timescale. However, quite surprisingly, our results indicate that under the same conditions and with only long-range interactions present in the system, the momentum distribution relaxes to its Gaussian form in equilibrium over a scale that {\it diverges with the system size}. On adding short-range interactions, the relaxation is found to occur over a timescale that has a much weaker dependence on system size. This system-size dependence of the timescale vanishes when only short-range interactions are present in the system. An implication of such an ultra-slow relaxation when only long-range interactions are present in the system is that macroscopic observables other than the average kinetic energy when estimated in the Nosé-Hoover dynamics may take an unusually long time to relax to its canonical equilibrium value. Our work underlines the crucial role that interactions play in deciding the equivalence between Nosé-Hoover and canonical equilibrium.

cond-mat.stat-mech↗

arXiv2017

Spontaneous collective synchronization in the Kuramoto model with additional non-local interactions

In the context of the celebrated Kuramoto model of globally-coupled phase oscillators of distributed natural frequencies, which serves as a paradigm to investigate spontaneous collective synchronization in many-body interacting systems, we report on a very rich phase diagram in presence of thermal noise and an additional non-local interaction on a one-dimensional periodic lattice. Remarkably, the phase diagram involves both equilibrium and non-equilibrium phase transitions. In two contrasting limits of the dynamics, we obtain exact analytical results for the phase transitions. These two limits correspond to (i) the absence of thermal noise, when the dynamics reduces to that of a non-linear dynamical system, and (ii) the oscillators having the same natural frequency, when the dynamics becomes that of a statistical system in contact with a heat bath and relaxing to a statistical equilibrium state. In the former case, our exact analysis is based on the use of the so-called Ott-Antonsen ansatz to derive a reduced set of nonlinear partial differential equations for the macroscopic evolution of the system. Our results for the case of statistical equilibrium are on the other hand obtained by extending the well-known transfer matrix approach for nearest-neighbor Ising model to consider non-local interactions. The work offers a case study of exact analysis in many-body interacting systems. The results obtained underline the crucial role of additional non-local interactions in either destroying or enhancing the possibility of observing synchrony in mean-field systems exhibiting spontaneous synchronization.

nlin.AO↗

arXiv2017

Path-integral formalism for stochastic resetting: Exactly solved examples and shortcuts to confinement

We study the dynamics of overdamped Brownian particles diffusing in conservative force fields and undergoing stochastic resetting to a given location with a generic space-dependent rate of resetting. We present a systematic approach involving path integrals and elements of renewal theory that allows to derive analytical expressions for a variety of statistics of the dynamics such as (i) the propagator prior to first reset; (ii) the distribution of the first-reset time, and (iii) the spatial distribution of the particle at long times. We apply our approach to several representative and hitherto unexplored examples of resetting dynamics. A particularly interesting example for which we find analytical expressions for the statistics of resetting is that of a Brownian particle trapped in a harmonic potential with a rate of resetting that depends on the instantaneous energy of the particle. We find that using energy-dependent resetting processes is more effective in achieving spatial confinement of Brownian particles on a faster timescale than by performing quenches of parameters of the harmonic potential.

cond-mat.stat-mech↗

arXiv2017

Importance-sampling computation of statistical properties of coupled oscillators

We introduce and implement an importance-sampling Monte Carlo algorithm to study systems of globally-coupled oscillators. Our computational method efficiently obtains estimates of the tails of the distribution of various measures of dynamical trajectories corresponding to states occurring with (exponentially) small probabilities. We demonstrate the general validity of our results by applying the method to two contrasting cases: the driven-dissipative Kuramoto model, a paradigm in the study of spontaneous synchronization; and the conservative Hamiltonian mean-field model, a prototypical system of long-range interactions. We present results for the distribution of the finite-time Lyapunov exponent and a time-averaged order parameter. Among other features, our results show most notably that the distributions exhibit a vanishing standard deviation but a skewness that is increasing in magnitude with the number of oscillators, implying that non-trivial asymmetries and states yielding rare/atypical values of the observables persist even for a large number of oscillators.

nlin.CD↗

arXiv2017

The world of long-range interactions: A bird's eye view

In recent years, studies of long-range interacting (LRI) systems have taken centre stage in the arena of statistical mechanics and dynamical system studies, due to new theoretical developments involving tools from as diverse a field as kinetic theory, non-equilibrium statistical mechanics, and large deviation theory, but also due to new and exciting experimental realizations of LRI systems. In this invited contribution, we discuss the general features of long-range interactions, emphasizing in particular the main physical phenomenon of non-additivity, which leads to a plethora of distinct effects, both thermodynamic and dynamic, that are not observed with short-range interactions: Ensemble inequivalence, slow relaxation, broken ergodicity. We also discuss several physical systems with long-range interactions: mean-field spin systems, self-gravitating systems, Euler equations in two dimensions, Coulomb systems, one-component electron plasma, dipolar systems, free-electron lasers, atoms trapped in optical cavities.

cond-mat.stat-mech↗

arXiv2016

Dynamics of coupled oscillator systems in presence of a local potential

We consider a long-range model of coupled phase-only oscillators subject to a local potential and evolving in presence of thermal noise. The model is a non-trivial generalization of the celebrated Kuramoto model of collective synchronization. We demonstrate by exact results and numerics a surprisingly rich long-time behavior, in which the system settles into either a stationary state that could be in or out of equilibrium and supports either global synchrony or absence of it, or, in a time-periodic synchronized state. The system shows both continuous and discontinuous phase transitions, as well as an interesting reentrant transition in which the system successively loses and gains synchrony on steady increase of the relevant tuning parameter.

nlin.AO↗

arXiv2016

Surprises from quenches in long-range interacting systems: Temperature inversion and cooling

What happens when one of the parameters governing the dynamics of a long-range interacting system of particles in thermal equilibrium is abruptly changed (quenched) to a different value? While a short-range system, under the same conditions, will relax in time to a new thermal equilibrium with a uniform temperature across the system, a long-range system shows a fast relaxation to a nonequilibrium {\em quasistationary state} (QSS). The lifetime of such an off-equilibrium state diverges with the system size, and the temperature is non-uniform across the system. Quite surprisingly, the density profile in the QSS obtained after the quench is anticorrelated with the temperature profile in space, thus exhibiting the phenomenon of {\em temperature inversion}: denser regions are colder than sparser ones. We illustrate with extensive molecular dynamics simulations the ubiquity of this scenario in a prototypical long-range interacting system subject to a variety of quenching protocols, and in a model that mimics an experimental setup of atoms interacting with light in an optical cavity. We further demonstrate how a procedure of iterative quenching combined with filtering out the high-energy particles in the system may be employed to cool the system. Temperature inversion is observed in nature in some astrophysical settings; our results imply that such a phenomenon should be observable, and could even be exploitable to advantage, also in controlled laboratory experiments.

cond-mat.stat-mech↗

arXiv2016

Diffusion with stochastic resetting at power-law times

What happens when a continuously evolving stochastic process is interrupted with large changes at random intervals $τ$ distributed as a power-law $\sim τ^{-(1+α)};α>0$? Modeling the stochastic process by diffusion and the large changes as abrupt resets to the initial condition, we obtain {\em exact} closed-form expressions for both static and dynamic quantities, while accounting for strong correlations implied by a power-law. Our results show that the resulting dynamics exhibits a spectrum of rich long-time behavior, from an ever-spreading spatial distribution for $α< 1$, to one that is time independent for $α> 1$. The dynamics has strong consequences on the time to reach a distant target for the first time; we specifically show that there exists an optimal $α$ that minimizes the mean time to reach the target, thereby offering a step towards a viable strategy to locate targets in a crowded environment.

cond-mat.stat-mech↗

arXiv2016

Resetting of fluctuating interfaces at power-law times

What happens when the time evolution of a fluctuating interface is interrupted with resetting to a given initial configuration after random time intervals $τ$ distributed as a power-law $\sim τ^{-(1+α)};~α> 0$? For an interface of length $L$ in one dimension, and an initial flat configuration, we show that depending on $α$, the dynamics as $L \to \infty$ exhibits a rich long-time behavior. Without resetting, the interface width grows unbounded with time as $t^β$, where $β$ is the so-called growth exponent. We show that introducing resetting induces for $α>1$ and at long times fluctuations that are bounded in time. Corresponding to such a stationary state is a distribution of fluctuations that is strongly non-Gaussian, with tails decaying as a power-law. The distribution exhibits a cusp for small argument, implying that the stationary state is out of equilibrium. For $α<1$, resetting is unable to counter the otherwise unbounded growth of fluctuations in time, so that the distribution of fluctuations remains time dependent with an ever-increasing width even at long times. Although stationary for $α>1$, the width of the interface grows forever with time as a power-law for $1<α< α^{({\rm w})}$, and converges to a finite constant only for larger $α$, thereby exhibiting a crossover at $α^{({\rm w})}=1+2β$. The time-dependent distribution of fluctuations for $α<1$ exhibits for small argument another interesting crossover behavior, from cusp to divergence, across $α^{({\rm d})}=1-β$. We demonstrate these results by exact analytical results for the paradigmatic Edwards-Wilkinson (EW) dynamical evolution of the interface, and further corroborate our findings by extensive numerical simulations of interface models in the EW and the Kardar-Parisi-Zhang universality class.

cond-mat.stat-mech↗

arXiv2016

Out-of-equilibrium fluctuations in stochastic long-range interacting systems

For a many-particle system with long-range interactions and evolving under stochastic dynamics, we study for the first time the out-of-equilibrium fluctuations of the work done on the system by a time-dependent external force. For equilibrium initial conditions, the work distributions for a given protocol of variation of the force in time and the corresponding time-reversed protocol exhibit a remarkable scaling and a symmetry when expressed in terms of the average and the standard deviation of the work. The distributions of the work per particle predict, by virtue of the Crooks fluctuation theorem, the equilibrium free-energy density of the system. For a large number $N$ of particles, the latter is in excellent agreement with the value computed by considering the Langevin dynamics of a single particle in a self-consistent mean field generated by its interaction with other particles. The agreement highlights the effective mean-field nature of the original many-particle dynamics for large $N$. For initial conditions in non-equilibrium steady states (NESSs), we study the distribution of a quantity similar to dissipated work that satisfies the non-equilibrium generalization of the Clausius inequality, namely, the Hatano-Sasa equality, for transitions between NESSs. Besides illustrating the validity of the equality, we show that the distribution has exponential tails that decay differently on the left and on the right.

cond-mat.stat-mech↗

arXiv2015

Stochastic Quantum Zeno by Large Deviation Theory

Quantum measurements are crucial to observe the properties of a quantum system, which however unavoidably perturb its state and dynamics in an irreversible way. Here we study the dynamics of a quantum system while being subject to a sequence of projective measurements applied at random times. In the case of independent and identically distributed intervals of time between consecutive measurements, we analytically demonstrate that the survival probability of the system to remain in the projected state assumes a large-deviation (exponentially decaying) form in the limit of an infinite number of measurements. This allows us to estimate the typical value of the survival probability, which can therefore be tuned by controlling the probability distribution of the random time intervals. Our analytical results are numerically tested for Zeno-protected entangled states, which also demonstrates that the presence of disorder in the measurement sequence further enhances the survival probability when the Zeno limit is not reached (as it happens in experiments). Our studies provide a new tool for protecting and controlling the amount of quantum coherence in open complex quantum systems by means of tunable stochastic measurements.

quant-ph↗

arXiv2015

Condensate formation in a zero-range process with random site capacities

We study the effect of quenched disorder on the zero-range process (ZRP), a system of interacting particles undergoing biased hopping on a one-dimensional periodic lattice, with the disorder entering through random capacities of sites. In the usual ZRP, sites can accommodate an arbitrary number of particles, and for a class of hopping rates and high enough density, the steady state exhibits a condensate which holds a finite fraction of the total number of particles. The sites of the disordered zero-range process considered here have finite capacities chosen randomly from the Pareto distribution. From the exact steady state measure of the model, we identify the conditions for condensate formation, in terms of parameters that involve both interactions (through the hop rates) and randomness (through the distribution of the site capacities). Our predictions are supported by results obtained from a direct numerical sampling of the steady state and from Monte Carlo simulations. Our study reveals that for a given realization of disorder, the condensate can relocate on the subset of sites with largest capacities. We also study sample-to-sample variation of the critical density required to observe condensation, and show that the corresponding distribution obeys scaling, and has a Gaussian or a Levy-stable form depending on the values of the relevant parameters.

cond-mat.stat-mech↗

arXiv2015

Temperature inversion in long-range interacting systems

Temperature inversions occur in nature, e.g., in the solar corona and in interstellar molecular clouds: somewhat counterintuitively, denser parts of the system are colder than dilute ones. We propose a simple and appealing way to spontaneously generate temperature inversions in systems with long-range interactions, by preparing them in inhomogeneous thermal equilibrium states and then applying an impulsive perturbation. In similar situations, short-range systems would typically relax to another thermal equilibrium, with uniform temperature profile. By contrast, in long-range systems, the interplay between wave-particle interaction and spatial inhomogeneity drives the system to nonequilibrium stationary states that generically exhibit temperature inversion. We demonstrate this mechanism in a simple mean-field model and in a two-dimensional self-gravitating system. Our work underlines the crucial role the range of interparticle interaction plays in determining the nature of steady states out of thermal equilibrium.

cond-mat.stat-mech↗

arXiv2015

Nonequilibrium inhomogeneous steady state distribution in disordered, mean-field rotator systems

We present a novel method to compute the phase space distribution in the nonequilibrium stationary state of a wide class of mean-field systems involving rotators subject to quenched disordered external drive and dissipation. The method involves a series expansion of the stationary distribution in inverse of the damping coefficient; the expansion coefficients satisfy recursion relations whose solution requires computing a sparse matrix, making numerical evaluation simple and efficient. We illustrate our method for the paradigmatic Kuramoto model of spontaneous collective synchronization and for its two mode generalization, in presence of noise and inertia, and demonstrate an excellent agreement between simulations and theory for the phase space distribution.

cond-mat.stat-mech↗

arXiv2014

Ensemble inequivalence in a mean-field XY model with ferromagnetic and nematic couplings

We explore ensemble inequivalence in long-range interacting systems by studying an XY model of classical spins with ferromagnetic and nematic coupling. We demonstrate the inequivalence by mapping the microcanonical phase diagram onto the canonical one, and also by doing the inverse mapping. We show that the equilibrium phase diagrams within the two ensembles strongly disagree within the regions of first-order transitions, exhibiting interesting features like temperature jumps. In particular, we discuss the coexistence and forbidden regions of different macroscopic states in both the phase diagrams.

cond-mat.stat-mech↗

arXiv2014

Diffusion in periodic, correlated random forcing landscapes

We study the dynamics of a Brownian particle in a strongly correlated quenched random potential defined as a periodically-extended (with period $L$) finite trajectory of a fractional Brownian motion with arbitrary Hurst exponent $H \in (0,1)$. While the periodicity ensures that the ultimate long-time behavior is diffusive, the generalised Sinai potential considered here leads to a strong logarithmic confinement of particle trajectories at intermediate times. These two competing trends lead to dynamical frustration and result in a rich statistical behavior of the diffusion coefficient $D_L$: Although one has the typical value $D^{\rm typ}_L \sim \exp(-βL^H)$, we show via an exact analytical approach that the positive moments ($k>0$) scale like $\langle D^k_L \rangle \sim \exp{[-c' (k βL^{H})^{1/(1+H)}]}$, and the negative ones as $\langle D^{-k}_L \rangle \sim \exp(a' (k βL^{H})^2)$, $c'$ and $a'$ being numerical constants and $β$ the inverse temperature. These results demonstrate that $D_L$ is strongly non-self-averaging. We further show that the probability distribution of $D_L$ has a log-normal left tail and a highly singular, one-sided log-stable right tail reminiscent of a Lifshitz singularity.

cond-mat.stat-mech↗