Related papers: Attempted Bethe ansatz solution for one-dimensiona…
In this work we study the transport properties of non-interacting overdamped particles, moving on tilted disordered potentials, subjected to Gaussian white noise. We give exact formulas for the drift and diffusion coefficients for the case…
We consider a stochastic model of N evolving particles studied by Brunet and Derrida. This model can be seen as a directed polymer in random medium with N sites in the transverse direction. Cook and Derrida, use heuristic arguments to…
We study the elastic (1+1)-dimensional string subject to a random gaussian potential on scales smaller than the correlation radius of the disorder potential (Larkin problem). We present an exact calculation of the probability function…
We consider a model system in which anomalous diffusion is generated by superposition of underlying linear modes with a broad range of relaxation times. In the language of Gaussian polymers, our model corresponds to Rouse (Fourier) modes…
Dynamics of a discrete polymer in time-dependent external potentials is studied with the master equation approach. We consider both stochastic and deterministic switching mechanisms for the potential states and give the essential equations…
The probability distribution for the free energy of directed polymers in random media (DPRM) with uncorrelated noise in $d=1+1$ dimensions satisfies the Tracy-Widom distribution. We inquire if and how this universal distribution is modified…
This paper investigates the combinatorics that gives rise to the Boltzmann probability distribution. Despite being one of the most important distributions in physics and other fields of science, the mathematics of the underlying model of…
The problem to express a natural number N as a product of natural numbers without regard to order corresponds to a thermally isolated non-interacting Bose gas in a one-dimensional potential with logarithmic energy eigenvalues. This…
In this paper, we study the localization length of the $1+1$ continuum directed polymer, defined as the distance between the endpoints of two paths sampled independently from the quenched polymer measure. We show that the localization…
We study directed polymers subject to a quenched random potential in d transversal dimensions. This system is closely related to the Kardar-Parisi-Zhang equation of nonlinear stochastic growth. By a careful analysis of the perturbation…
We demonstrate how an iterative method for potential inversion from distribution functions developed for simple liquid systems can be generalized to polymer systems. It uses the differences in the potentials of mean force between the…
In the theory of Bethe-ansatz integrable quantum systems, rapidities play an important role as they are used to specify many-body states, apart from phases. The physical interpretation of rapidities going back to Sutherland is that they are…
Interacting one-dimensional quantum systems play a pivotal role in physics. Exact solutions can be obtained for the homogeneous case using the Bethe ansatz and bosonisation techniques. However, these approaches are not applicable when…
This study analyzes thermoelectric properties of a one-dimensional random conductor which shows localization effects and simultaneously includes resonant scatterers yielding sharp conductance resonances. These sharp features give rise to a…
We study a one dimensional directed polymer model in an inverse-gamma random environment, known as the log-gamma polymer, in three different geometries: point-to-line, point-to-half line and when the polymer is restricted to a half space…
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 study a one-dimensional system of two-component fermions in the limit of strong attractive particle-particle interactions. First, we analyze scattering in the corresponding few-body problem, which is analytically solvable via Bethe…
The directed polymer in a 1+3 dimensional random medium is known to present a disorder-induced phase transition. For a polymer of length $L$, the high temperature phase is characterized by a diffusive behavior for the end-point displacement…
The analytical probability distribution of finite systems obeying Bose-Einstein statistics in one, two, and three dimensions are investigated by using a canonical ensemble approach. Starting from the canonical partition function of the…
The excluded volume effects of randomly branched polymers are investigated. To approach this problem we assume the Gaussian distribution of segments around the center of gravity. Once this approximation is introduced, we can make use of the…