Related papers: Fluctuation exponents for directed polymers in the…
We define a stochastic lattice model for a fluctuating directed polymer in $d\geq 2$ dimensions. This model can be alternatively interpreted as a fluctuating random path in 2 dimensions, or a one-dimensional asymmetric simple exclusion…
We argue that while fluctuating fronts propagating into an unstable state should be in the standard KPZ universality class when they are {\em pushed}, they should not when they are {\em pulled}: The universal $1/t$ velocity relaxation of…
We obtain an exact result for the midpoint probability distribution function (pdf) of the stationary continuum directed polymer, when averaged over the disorder. It is obtained by relating that pdf to the linear response of the stochastic…
We study random copolymers consisted of two kinds of monomers with attraction between similar kinds. The mean field analysis of this system indicates a continuous phase transition into a phase with periodic microdomain structure. It is…
We prove the scaling relation chi = 2 xi - 1 between the transversal exponent xi and the fluctuation exponent chi for directed polymers in a random environment in d dimensions. The definition of these exponents is similar to that proposed…
We demonstrate that measurements of number fluctuations within finite cells provide a direct means to study fluctuation scaling in a trapped two-component condensate. This quantum system supports a second-order phase transition between…
We study the fluctuations of discretized versions of the stochastic heat equation (SHE) and the Kardar-Parisi-Zhang (KPZ) equation in spatial dimensions $d\geq 3$ in the weak disorder regime. The discretization is defined using the directed…
In this paper in terms of the replica method we consider the high temperature limit of (2+1) directed polymers in a random potential and propose an approach which allows to compute the scaling exponent $\theta$ of the free energy…
We study numerically the geometrical and free-energy fluctuations of a static one-dimensional (1D) interface with a short-range elasticity, submitted to a quenched random-bond Gaussian disorder of finite correlation length $\xi>0$, and at…
We study the directed polymer model in a bounded environment in weak disorder but without $L^2$-boundedness, specifically the speed of homogenization for the field $(W_n^{0,x})_{x\in\mathbb Z^d}$, where $W_n^{0,x}$ denotes the associated…
We introduce the notion of energy solutions of the KPZ equation. Under minimal assumptions, we prove that the density fluctuations of one-dimensional, weakly asymmetric, conservative particle systems with respect to the stationary states…
We use a version of the Skorokhod integral to give a simple and rigorous formulation of the Wick-ordered (stochastic) heat equation with planar white noise, representing the free energy of an undirected random polymer. The solution for all…
A modification of the optimal fluctuation approach is applied to study the tails of the free energy distribution function P(F) for an elastic string in quenched disorder both in the regions of the universal behavior of P(F) and in the…
We prove a central limit theorem for the winding number of a directed polymer on a cylinder, which is equivalent with proving the Gaussian fluctuations of the endpoint of the directed polymer in a spatial periodic environment.
In the context of an exactly soluble out of equilibrium (quenched) model, we study an extension of the fluctuation-dissipation relation. This involves a modified differential form of this relation, with an effective temperature which may…
Using results from Schramm Loewner evolution (SLE), we give the expression of the fluctuation-induced force exerted by a polymer on a small impenetrable disk, in various 2-dimensional domain geometries. We generalize to two polymers and…
We study the directed polymer model in dimension ${1+1}$ when the environment is heavy-tailed, with a decay exponent $\alpha\in(0,2)$. We give all possible scaling limits of the model in the weak-coupling regime, i.e., when the inverse…
We study experimentally the thermal fluctuations of energy input and dissipation in a harmonic oscillator driven out of equilibrium, and search for Fluctuation Relations. We study transient evolution from the equilibrium state, together…
A microscopic model of interacting oscillators, which admits two conserved quantities, volume, and energy, is investigated. We begin with a system driven by a general nonlinear potential under high-temperature regime by taking the inverse…
We consider the discrete directed polymer model with i.i.d. environment and we study the fluctuations of the tail $n^{(d-2)/4}(W_\infty - W_n)$ of the normalized partition function. It was proven by Comets and Liu, that for sufficiently…