arXiv subjects

Urna Basu

Publications and source records attributed to Urna Basu.

At least 55 records · Page 3Linked to original sources

arXiv2019

Symmetric Exclusion Process under Stochastic Resetting

We study the behaviour of a Symmetric Exclusion Process (SEP) in presence of stochastic resetting where the configuration of the system is reset to a step-like profile with a fixed rate $r.$ We show that the presence of resetting affects both the stationary and dynamical properties of SEP strongly. We compute the exact time-dependent density profile and show that the stationary state is characterized by a non-trivial inhomogeneous profile in contrast to the flat one for $r=0.$ We also show that for $r>0$ the average diffusive current grows linearly with time $t,$ in stark contrast to the $\sqrt{t}$ growth for $r=0.$ In addition to the underlying diffusive current, we identify the resetting current in the system which emerges due to the sudden relocation of the particles to the step-like configuration and is strongly correlated to the diffusive current. We show that the average resetting current is negative, but its magnitude also grows linearly with time $t.$ We also compute the probability distributions of the diffusive current, resetting current and the total current (sum of the diffusive and the resetting currents) using the renewal approach. We demonstrate that while the typical fluctuations of both the diffusive and reset currents around the mean are typically Gaussian, the distribution of the total current shows a strong non-Gaussian behaviour.

cond-mat.stat-mech↗

arXiv2019

Long time position distribution of an active Brownian particle in two dimensions

We study the late time dynamics of a single active Brownian particle in two dimensions with speed $v_0$ and rotation diffusion constant $D_R$. We show that at late times $t\gg D_R^{-1}$, while the position probability distribution $P(x,y,t)$ in the $x$-$y$ plane approaches a Gaussian form near its peak describing the typical diffusive fluctuations, it has non-Gaussian tails describing atypical rare fluctuations when $\sqrt{x^2+y^2}\sim v_0 t$. In this regime, the distribution admits a large deviation form, $P(x,y,t) \sim \exp\left[-t\, D_R\, Φ\left(\sqrt{x^2+y^2}/(v_0 t)\right)\right]$, where we compute the rate function $Φ(z)$ analytically and also numerically using an importance sampling method. We show that the rate function $Φ(z)$, encoding the rare fluctuations, still carries the trace of activity even at late times. Another way of detecting activity at late times is to subject the active particle to an external harmonic potential. In this case we show that the stationary distribution $P_\text{stat}(x,y)$ depends explicitly on the activity parameter $D_R^{-1}$ and undergoes a crossover, as $D_R$ increases, from a ring shape in the strongly active limit ($D_R\to 0$) to a Gaussian shape in the strongly passive limit $(D_R\to \infty)$.

cond-mat.stat-mech↗

arXiv2018

Extrapolation to nonequilibrium from coarse grained response theory

Nonlinear response theory, in contrast to linear cases, involves (dynamical) details, and this makes application to many body systems challenging. From the microscopic starting point we obtain an exact response theory for a small number of coarse grained degrees of freedom. With it, an extrapolation scheme uses near-equilibrium measurements to predict far from equilibrium properties (here, second order responses). Because it does not involve system details, this approach can be applied to many body systems. It is illustrated in a four state model and in the near critical Ising model.

cond-mat.stat-mech↗

arXiv2017

Negative Differential Mobility in Interacting Particle Systems

Driven particles in presence of crowded environment, obstacles or kinetic constraints often exhibit negative differential mobility (NDM) due to their decreased dynamical activity. We propose a new mechanism for complex many-particle systems where slowing down of certain {\it non-driven} degrees of freedom by the external field can give rise to NDM. This phenomenon, resulting from inter-particle interactions, is illustrated in a pedagogical example of two interacting random walkers, one of which is biased by an external field while the same field only slows down the other keeping it unbiased. We also introduce and solve exactly the steady state of several driven diffusive systems, including a two species exclusion model, asymmetric misanthrope and zero-range processes, to show explicitly that this mechanism indeed leads to NDM.

cond-mat.stat-mech↗

arXiv2017

On the universal Gaussian behavior of Driven Lattice Gases at short-times

The dynamic and static critical behaviors of driven and equilibrium lattice gas models are studied in two spatial dimensions. We show that in the short-time regime immediately following a critical quench, the dynamics of the transverse order parameters, auto-correlations, and Binder cumulant are consistent with the prediction of a Gaussian, $i.e.,$ non-interacting, effective theory, both for the equilibrium lattice gas and its nonequilibrium counterparts. Such a "super-universal" behavior is observed only at short times after a critical quench, while the various models display their distinct behaviors in the stationary states, described by the corresponding, known universality classes.

cond-mat.stat-mech↗

arXiv2017

Short-time Behaviour and Criticality of Driven Lattice Gases

The nonequilibrium short-time critical behaviors of driven and undriven lattice gases are investigated via Monte Carlo simulations in two spatial dimensions starting from a fully disordered initial configuration. In particular, we study the time evolution of suitably defined order parameters, which account for the strong anisotropy introduced by the homogeneous drive. We demonstrate that, at short times, the dynamics of all these models is unexpectedly described by an effective continuum theory in which transverse fluctuations, i.e., fluctuations averaged along the drive, are Gaussian, irrespective of this being actually the case in the stationary state. Strong numerical evidence is provided, in remarkable agreement with that theory, both for the driven and undriven lattice gases, which therefore turn out to display the same short-time dynamics.

cond-mat.stat-mech↗

arXiv2017

Phase Separation Transition in a Nonconserved Two Species Model

A one dimensional stochastic exclusion process with two species of particles, $+$ and $-$, is studied where density of each species can fluctuate but the total particle density is conserved. From the exact stationary state weights we show that, in the limiting case where density of negative particles vanishes, the system undergoes a phase separation transition where a macroscopic domain of vacancies form in front of a single surviving negative particle. We also show that the phase separated state is associated with a diverging correlation length for any density and the critical exponents characterizing the behaviour in this region are different from those at the transition line. The static and the dynamical critical exponents are obtained from the exact solution and numerical simulations, respectively.

cond-mat.stat-mech↗

arXiv2016

Measurement of second-order response without perturbation

We study the second order response functions of a colloidal particle being subjected to an anharmonic potential. Contrary to typical response measurements which require an external perturbation, here we experimentally confirm a recently developed approach where the system's susceptibilities up to second order are obtained from the particle's equilibrium trajectory [PCCP $\mathrm{\bf 17}$, 6653 (2015)]. The measured susceptibilities are in quantitative agreement with those obtained from the response to an external perturbation.

cond-mat.soft↗

arXiv2016

Driving-induced stability with long-range effects

We give a sufficient condition under which an applied rotation on medium particles stabilizes a slow probe in the rotation center. The symmetric part of the stiffness matrix thus gets a positive Lamb shift with respect to equilibrium. For illustration we take diffusive medium particles with a self-potential in the shape of a Mexican hat, high around the origin. There is a short-range attraction between the medium particles and the heavier probe, all immersed in an equilibrium thermal bath. For no or small rotation force on the medium particles, the origin is an unstable fixed point for the probe and the precise shape of the self-potential at large distances from the origin is irrelevant for the statistical force there. Above a certain rotation threshold, while the medium particles are still repelled from the origin, the probe stabilizes there and more details of the medium-density at large distance start to matter. The effect is robust around the quasi-static limit with rotation threshold only weakly depending on the temperature but the stabilization gets stronger at lower temperatures.

cond-mat.stat-mech↗

arXiv2015

Statistical forces from close--to--equilibrium media

We discuss the physical meaning and significance of statistical forces on quasi-static probes in first order around detailed balance for driven media. Exploiting the quasi-static energetics and the structure of (McLennan) steady nonequilibrium ensembles, we find that the statistical force obtains a nonequilibrium correction deriving from the excess work of driving forces on the medium in its relaxation after probe displacement. This reformulates, within a more general context, the recent result by N. Nakagawa (Phys. Rev. E 90, 022108 (2014)) on thermodynamic aspects of weakly nonequilibrium adiabatic pumping. It also proposes a possible operational tool for accessing some excess quantities in steady state thermodynamics. Furthermore, we show that the point attractors of a (macroscopic) probe coupled to a weakly driven medium realize the predictions of the minimum entropy production principle. Finally, we suggest a method to measure the relative dynamical activity through different transition channels, via the measurement of the statistical force induced by a suitable driving.

cond-mat.stat-mech↗

arXiv2015

Nonequilibrium Response and Frenesy

We present examples of how time-symmetric kinetic factors contribute to the response either in nonlinear order around equilibrium or in linear order around nonequilibrium. The phenomenology we associate to that so called frenetic contribution are negative differential conductivity, changes in the Einstein relation between friction and noise, and population inversion.

cond-mat.stat-mech↗

arXiv2015

How statistical forces depend on thermodynamics and kinetics of driven media

We study the statistical force of a nonequilibrium environment on a quasi-static probe. In the linear regime the isothermal work on the probe equals the excess work for the medium to relax to its new steady condition with displaced probe. Also the relative importance of reaction paths can be measured via statistical forces, and from second order onwards the force on the probe reveals information about nonequilibrium changes in the reactivity of the medium. We also show that statistical forces for nonequilibrium media are generally nonadditive, in contrast with the equilibrium situation. Both the presence of non-thermodynamic corrections to the forces and their nonadditivity put serious constraints on any formulation of nonequilibrium steady state thermodynamics.

cond-mat.stat-mech↗

arXiv2015

Frenetic aspects of second order response

Starting from second order around thermal equilibrium, the response of a statistical mechanical system to an external stimulus is not only governed by dissipation and depends explicitly on dynamical details of the system. The so called frenetic contribution in second order around equilibrium is illustrated in different physical examples, such as for non-thermodynamic aspects in the coupling between system and reservoir, for the dependence on disorder in dielectric response and for the nonlinear correction to the Sutherland--Einstein relation. More generally, the way in which a system's dynamical activity changes by the pertubation is visible (only) from nonlinear response.

cond-mat.stat-mech↗

arXiv2014

Thermal response in driven diffusive systems

Evaluating the linear response of a driven system to a change in environment temperature(s) is essential for understanding thermal properties of nonequilibrium systems. The system is kept in weak contact with possibly different fast relaxing mechanical, chemical or thermal equilibrium reservoirs. Modifying one of the temperatures creates both entropy fluxes and changes in dynamical activity. That is not unlike mechanical response of nonequilibrium systems but the extra difficulty for perturbation theory via path-integration is that for a Langevin dynamics temperature also affects the noise amplitude and not only the drift part. Using a discrete-time mesh adapted to the numerical integration one avoids that ultraviolet problem and we arrive at a fluctuation expression for its thermal susceptibility. The algorithm appears stable under taking even finer resolution.

cond-mat.stat-mech↗

arXiv2014

Mobility transition in a dynamic environment

Depending on how the dynamical activity of a particle in a random environment is influenced by an external field $E$, its differential mobility at intermediate $E$ can turn negative. We discuss the case where for slowly changing random environment the driven particle shows negative differential mobility while that mobility turns positive for faster environment changes. We illustrate this transition using a 2D-lattice Lorentz model where a particle moves in a background of simple exclusion walkers. The effective escape rate of the particle (or minus its collision frequency) which is essential for its mobility-behavior depends both on $E$ and on the kinetic rate $γ$ of the exclusion walkers. Large $γ$, i.e., fast obstacle motion, amounts to merely rescaling the particle's free motion with the obstacle density, while slow obstacle dynamics results in particle motion that is more singularly related to its free motion and preserves the negative differential mobility already seen at $γ=0$. In more general terms that we also illustrate using one-dimensional random walkers, the mobility transition is between the time-scales of the quasi-stationary regime and that of the fluid limit.

cond-mat.stat-mech↗

arXiv2013

The frenetic origin of negative differential response

The Green-Kubo formula for linear response coefficients gets modified when dealing with nonequilibrium dynamics. In particular negative differential conductivities are allowed to exist away from equilibrium. We give a unifying framework for such negative differential response in terms of the frenetic contribution in the nonequilibrium formula. It corresponds to a negative dependence of the escape rates and reactivities on the driving forces. Partial caging in state space and reduction of dynamical activity with increased driving cause the current to drop. These are time-symmetric kinetic effects that are believed to play a major role in the study of nonequilibria. We give various simple examples treating particle and energy transport, which all follow the same pattern in the dependence of the dynamical activity on the nonequilibrium driving, made visible from recently derived nonequilibrium response theory.

cond-mat.stat-mech↗

arXiv2013

Revisiting Absorbing Phase Transition in Energy Exchange Models

A recent study of conserved Manna model, with both discrete and continuous variable, indicates that absorbing phase transitions therein belong to the directed percolation (DP) universality class. In this context we revisit critical behaviour in energy exchange models with a threshold. Contrary to the previous claims [PRE 83, 061130 (2011), arXiv:1102.1631], our results indicate that both the maximal and minimal versions of this model belong to the DP class.

cond-mat.stat-mech↗

arXiv2012

Fixed-Energy Sandpiles Belong Generically to Directed Percolation

Fixed-energy sandpiles with stochastic update rules are known to exhibit a nonequilibrium phase transition from an active phase into infinitely many absorbing states. Examples include the conserved Manna model, the conserved lattice gas, and the conserved threshold transfer process. It is believed that the transitions in these models belong to an autonomous universality class of nonequilibrium phase transitions, the so-called Manna class. Contrarily, the present numerical study of selected (1+1)-dimensional models in this class suggests that their critical behavior converges to directed percolation after very long time, questioning the existence of an independent Manna class.

cond-mat.stat-mech↗