Finite-size and finite-time effects in large deviation functions near dynamical symmetry breaking transitions

We introduce and study a class of particle hopping models consisting of a single box coupled to a pair of reservoirs. Despite being zero-dimensional, in the limit of large particle number and long observation time, the current and activity large deviation functions of the models can exhibit symmetry-breaking dynamical phase transitions. We characterize exactly the critical properties of these transitions, showing them to be direct analogues of previously studied phase transitions in extended systems. The simplicity of the model allows us to study features of dynamical phase transitions which are not readily accessible for extended systems. In particular, we quantify finite-size and finite-time scaling exponents using both numerical and theoretical arguments. Importantly, we identify an analogue of critical slowing near symmetry breaking transitions and suggest how this can be used in the numerical studies of large deviations. All of our results are also expected to hold for extended systems.Comment: 34 pages, 6 figure

Fluctuation Induced Forces in Non-equilibrium (Diffusive) Dynamics

Thermal fluctuations in non-equilibrium steady states generically lead to power law decay of correlations for conserved quantities. Embedded bodies which constrain fluctuations in turn experience fluctuation induced forces. We compute these forces for the simple case of parallel slabs in a driven diffusive system. The force falls off with slab separation $d$ as $k_B T/d$ (at temperature $T$, and in all spatial dimensions), but can be attractive or repulsive. Unlike the equilibrium Casimir force, the force amplitude is non-universal and explicitly depends on dynamics. The techniques introduced can be generalized to study pressure and fluctuation induced forces in a broad class of non-equilibrium systems.Comment: 5 pages, 2 figure

Dynamical symmetry breaking and phase transitions in driven diffusive systems

We study the probability distribution of a current flowing through a diffusive system connected to a pair of reservoirs at its two ends. Sufficient conditions for the occurrence of a host of possible phase transitions both in and out of equilibrium are derived. These transitions manifest themselves as singularities in the large deviation function, resulting in enhanced current fluctuations. Microscopic models which implement each of the scenarios are presented, with possible experimental realizations. Depending on the model, the singularity is associated either with a particle-hole symmetry breaking, which leads to a continuous transition, or in the absence of the symmetry with a first-order phase transition. An exact Landau theory which captures the different singular behaviors is derived.Comment: 14 pages, 2 figure

Dynamical phase transitions in the current distribution of driven diffusive channels

We study singularities in the large deviation function of the time-averaged current of diffusive systems connected to two reservoirs. A set of conditions for the occurrence of phase transitions, both first and second order, are obtained by deriving Landau theories. First-order transitions occur in the absence of a particle-hole symmetry, while second-order occur in its presence and are associated with a symmetry breaking. The analysis is done in two distinct statistical ensembles, shedding light on previous results. In addition, we also provide an exact solution of a model exhibiting a second-order symmetry-breaking transition.Comment: 44 pages, 6 figure

DNA unzipping and the unbinding of directed polymers in a random media

We consider the unbinding of a directed polymer in a random media from a wall in $d=1+1$ dimensions and a simple one-dimensional model for DNA unzipping. Using the replica trick we show that the restricted partition functions of these problems are {\em identical} up to an overall normalization factor. Our finding gives an example of a generalization of the stochastic matrix form decomposition to disordered systems; a method which effectively allows to reduce dimensionality of the problem. The equivalence between the two problems, for example, allows us to derive the probability distribution for finding the directed polymer a distance $z$ from the wall. We discuss implications of these results for the related Kardar-Parisi-Zhang equation and the asymmetric exclusion process.Comment: 5 pages, 2 figures, minor modifications, added discussion on stochastic matrix form decompositio

Superfluid-insulator transition of disordered bosons in one-dimension

We study the superfluid-insulator transition in a one dimensional system of interacting bosons, modeled as a disordered Josephson array, using a strong randomness real space renormalization group technique. Unlike perturbative methods, this approach does not suffer from run-away flows and allows us to study the complete phase diagram. We show that the superfluid insulator transition is always Kosterlitz- Thouless like in the way that length and time scales diverge at the critical point. Interestingly however, we find that the transition at strong disorder occurs at a non universal value of the Luttinger parameter, which depends on the disorder strength. This result places the transition in a universality class different from the weak disorder transition first analyzed by Giamarchi and Schulz [Europhys. Lett. {\bf 3}, 1287 (1987)]. While the details of the disorder potential are unimportant at the critical point, the type of disorder does influence the properties of the insulating phases. We find three classes of insulators which arise for different classes of disorder potential. For disorder only in the charging energies and Josephson coupling constants, at integer filling we find an incompressible but gapless Mott glass phase. If both integer and half integer filling factors are allowed then the corresponding phase is a random singlet insulator, which has a divergent compressibility. Finally in a generic disorder potential the insulator is a Bose glass with a finite compressibility.Comment: 16 page