99 research outputs found
Thermal response in driven diffusive systems
No full textEvaluating 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
Coarse-grained second-order response theory
No full textWhile linear response theory, manifested by the fluctuation dissipation theorem, can be applied at any level of coarse-graining, nonlinear response theory is fundamentally of a microscopic nature. For perturbations of equilibrium systems, we develop an exact theoretical framework for analyzing the nonlinear (second-order) response of coarse-grained observables to time-dependent perturbations, using a path-integral formalism. The resulting expressions involve correlations of the observable with coarse-grained path weights. The time-symmetric part of these weights depends on the paths and perturbation protocol in a complex manner; in addition, the absence of Markovianity prevents slicing of the coarse-grained path integral. We show that these difficulties can be overcome and the response function can be expressed in terms of path weights corresponding to a single-step perturbation. This formalism thus leads to an extrapolation scheme where measuring linear responses of coarse-grained variables suffices to determine their second-order response. We illustrate the validity of the formalism with an exactly solvable four-state model and the near-critical Ising model
Universal Gaussian behavior of driven lattice gases at short times
No full textThe 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 anisotropic order parameter, its autocorrelation, and Binder cumulant are consistent with the prediction of a Gaussian, i.e., noninteracting, effective theory, both for the nonequilibrium lattice gases and, to some extent, their equilibrium counterpart. Such a superuniversal 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
Short-Time Behavior and Criticality of Driven Lattice Gases
No full textThe 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
Symmetric Exclusion Process under Stochastic Power-law Resetting
No full textWe study the behaviour of a symmetric exclusion process in the presence of
non-Markovian stochastic resetting, where the configuration of the system is
reset to a step-like profile at power-law waiting times with an exponent
. We find that the power-law resetting leads to a rich behaviour for
the currents, as well as density profile. We show that, for any finite system,
for , the density profile eventually becomes uniform while for
, an eventual non-trivial stationary profile is reached. We also
find that, in the limit of thermodynamic system size, at late times, the
average diffusive current grows with for , for and for . We also analytically characterize the distribution of the diffusive
current in the short-time regime using a trajectory-based perturbative
approach. Using numerical simulations, we show that in the long-time regime,
the diffusive current distribution follows a scaling form with an
dependent scaling function. We also characterise the behaviour of the
total current using renewal approach. We find that the average total current
also grows algebraically where for ,
for the
average total current reaches a stationary value, which we compute exactly. The
variance of the total current also shows an algebraic growth with an exponent
for , and for ,
whereas it approaches a constant value for . The total current
distribution remains non-stationary for , it
reaches a non-trivial and strongly non-Gaussian stationary distribution, which
we also compute using the renewal approach.Comment: 26 pages, 10 figure
Identifying universality classes of absorbing phase transitions by block renormalization
No full textActivity driven transport in harmonic chains
No full textHow the transport properties of an extended system is affected by coupling to
active reservoirs is a significant, yet virtually unexplored question. Here we
address this issue in the context of energy transport between two active
reservoirs connected by a chain of harmonic oscillators. The couplings to the
reservoirs, which exert correlated stochastic forces on the boundary
oscillators, lead to fascinating behavior of the energy current and kinetic
temperature profile, which we compute exactly in the thermodynamic limit. We
show that the stationary active current (i) changes non-monotonically as the
activity of the reservoirs are changed, leading to a negative differential
conductivity (NDC), and (ii) exhibits an unexpected direction reversal at some
finite value of the activity drive. For the example of a dichotomous active
force, we find the physical origin of the NDC using nonequilibrium response
formalism. It turns out that the kinetic temperature profile remains uniform at
the bulk, and can be expressed in a form similar to the thermally driven case.
We show that despite this apparent similarity, no effective thermal picture can
be consistently built in general. However, such a picture emerges in the small
activity limit, where many of the well-known results are recovered.Comment: Accepted for Publication in SciPost Physic
Mobility transition in a dynamic environment
No full text© 2014 IOP Publishing Ltd. 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 two-dimensional-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.status: Publishe
Chirality Reversing Active Brownian Motion in Two Dimensions
No full textWe study the dynamics of a chirality reversing active Brownian particle,
which models the chirality reversing active motion common in many
microorganisms and microswimmers. We show that, for such a motion, the presence
of the two time-scales set by the chirality reversing rate and
rotational diffusion constant gives rise to four dynamical regimes,
namely, (I) , (II) , (III) and (IV) , each showing different behaviour. The
short-time regime (I) is characterized by a strongly anisotropic and
non-Gaussian position distribution, which crosses over to a diffusive Gaussian
behaviour in the long-time regime (IV) via an intermediate regime (II) or
(III), depending on the relative strength of and . In regime
(II), the chirality reversing active Brownian motion reduces to that of an
ordinary active Brownian particle, with an effective rotation diffusion
coefficient which depends on the angular velocity. Finally, we find that, the
regime (III) is characterized by an effective chiral active Brownian motion.Comment: 13 pages, 7 figure
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