Urna Basu

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.

Frenetic origin of negative differential response.

The Green-Kubo formula for linear response coefficients is 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 a 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.

Active-absorbing-state phase transition beyond directed percolation: a class of exactly solvable models.

We introduce and solve a model of hardcore particles on a one-dimensional periodic lattice which undergoes an active-absorbing-state phase transition at finite density. In this model, an occupied site is defined to be active if its left neighbor is occupied and the right neighbor is vacant. Particles from such active sites hop stochastically to their right. We show that both the density of active sites and the survival probability vanish as the particle density is decreased below half. The critical exponents and spatial correlations of the model are calculated exactly using the matrix product ansatz. Exact analytical study of several variations of the model reveals that these nonequilibrium phase transitions belong to a new universality class different from the generic active-absorbing-state phase transition, namely, directed percolation.

Modeling wealth distribution in growing markets

Abstract.We introduce an auto-regressive model which captures the growing nature of realistic markets. In our model agents do not trade with other agents, they interact indirectly only through a market. Change of their wealth depends, linearly on how much they invest, and stochastically on how much they gain from the noisy market. The average wealth of the market could be fixed or growing. We show that in a market where investment capacity of agents differ, average wealth of agents generically follow the Pareto-law. In few cases, the individual distribution of wealth of every agentcould also be obtained exactly. We also show that the underlying dynamics of other well studied kinetic models of markets can be mapped to the dynamics of our auto-regressive model.

How Statistical Forces Depend on the Thermodynamics and Kinetics of Driven Media.

We study the statistical force of a nonequilibrium environment on a quasistatic 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 a 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 nonthermodynamic corrections to the forces and their nonadditivity put serious constraints on any formulation of nonequilibrium steady state thermodynamics.

Spatial correlations in exclusion models corresponding to the zero-range process

We show that the steady state weights of all one-dimensional exclusion models which are mapped to the zero-range process (ZRP) can be written in a matrix product form, where the required matrices depend only on the steady state weights of the ZRP. An infinite-dimensional representation of these matrices which works for generic systems has also been provided. This is in contrast to the case for the usual matrix product ansatz which does not always guarantee a solution for the dynamics dependent algebra that the matrices need to satisfy. The formulation helps us study the spatial correlations of these exclusion processes which are unfeasibly difficult to obtain directly from their ZRP correspondence. To illustrate this method we reproduce certain known results, and then investigate unexplored correlations in some other model systems.

Driven k-mers: correlations in space and time

Steady-state properties of hard objects with exclusion interaction and a driven motion along a one-dimensional periodic lattice are investigated. The process is a generalization of the asymmetric simple exclusion process (ASEP) to particles of length k, and is called the k-ASEP. Here, we analyze both static and dynamic properties of the k-ASEP. Density correlations are found to display interesting features, such as pronounced oscillations in both space and time, as a consequence of the extended length of the particles. At long times, the density autocorrelation decays exponentially in time, except at a special k-dependent density when it decays as a power law. In the limit of large k at a finite density of occupied sites, the appropriately scaled system reduces to a nonequilibrium generalization of the Tonks gas describing the motion of hard rods along a continuous line. This allows us to obtain in a simple way the known two-particle distribution for the Tonks gas. For large but finite k, we also obtain the leading-order correction to the Tonks result.

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.

Restricted exclusion processes without particle conservation flows to directed percolation

Absorbing phase transitions in restricted exclusion processes are characterized by simple integer exponents. We show that this critical behaviour flows to the directed percolation (DP) universality class when particle conservation is broken suitably. The same transition, when studied using the average density as the controlling parameter, yields critical exponents quite different from DP; we argue that these exponents are actually related to DP by a scaling factor 1/ β DP . These conclusions also apply to conserved lattice gas in one dimension.

Berry phase and fidelity susceptibility of the three-qubit Lipkin–Meshkov–Glick ground state

Berry phases and quantum fidelities for interacting spins have attracted considerable attention, particularly in relation to entanglement properties of spin systems and quantum phase transitions. These efforts mainly focus either on spin pairs or the thermodynamic infinite spin limit, while studies of the multi-partite case of a finite number of spins are rare. Here we analyze Berry phases and quantum fidelities of the ground state of a Lipkin–Meshkov–Glick model consisting of three spin-1/2 particles (qubits). We find explicit expressions for the Berry phase and fidelity susceptibility of the full system as well as the mixed-state Berry phase and partial-state fidelity susceptibility of its one- and two-qubit subsystems. We demonstrate a realization of a nontrivial magnetic monopole structure associated with local, coordinated rotations of the three-qubit system around the external magnetic field.