Related papers: Directed polymers and the quantum Toda lattice
In a recent paper we constructed an integrable generalization of the Toda law on the square lattice. In this paper we construct other examples of integrable dynamics of Toda-type on the square lattice, as well as on the triangular lattice,…
In this paper, connections between surface roughness and directed polymers in random medium are studied, when the surface is considered as a directed line undergoing stochastic oscillations. This is performed by studying the influence of a…
In the first paper of this series, I investigated whether a wavefunction model of a heavy particle and a collection of light particles might generate "Brownian-Motion-Like" trajectories of the heavy particle. I concluded that it was…
It is well known that the mean field theory of directed polymers in a random medium exhibits replica symmetry breaking with a distribution of overlaps which consists of two delta functions. Here we show that the leading finite size…
In this paper, we consider four integrable models of directed polymers for which the free energy is known to exhibit KPZ fluctuations. A common framework for the analysis of these models was introduced in our recent work on the…
We study the Busemann process and competition interfaces of the planar directed polymer model with i.i.d.\ weights on the vertices of the planar square lattice, in both the general case and the solvable inverse-gamma case. We prove new…
We derive exact matrix integral representations for different sums over partitions. The characteristic feature of all obtained matrix models is the presence of logarithmic (or, vice versa, exponential) terms in the potential. Our derivation…
This study presents a generalized theory for the diffusion of Brownian particles in shear flows. By solving the Langevin equations using stochastic instead of classical calculus, we propose a new mathematical formulation that resolves the…
We investigated three models of Brownian motors which convert rotational diffusion into directed translational motion by switching on and off a potential. In the first model a spatially asymmetric potential generates directed translational…
For directed polymers, the shape function computes the limiting average energy accrued by paths with a given average slope. We prove that, for a large family of directed polymer models in discrete time and continuous space in dimension…
The general covariance of the diffusion equation is exploited in order to explore the curvature effects appearing on brownian motion over a d-dimensional curved manifold. We use the local frame defined by the so called Riemann normal…
We consider random flights of point particles inside $n$-dimensional channels of the form $\mathbb{R}^{k} \times \mathbb{B}^{n-k}$, where $\mathbb{B}^{n-k}$ is a ball of radius $r$ in dimension $n-k$. The particle velocities immediately…
We prove that the values of discrete directed polymer partition functions involving multiple non-intersecting paths remain invariant under replacing the background weights by their images under the geometric RSK correspondence. This result…
In nanoscale space and pico- to nanoseconds enormous physical, chemical and biological processes take place, while the motions of involved particles/molecules under thermal fluctuations are usually analyzed using the conventional theory of…
A simple application of classical density functional theory is derived and applied to a system of polymers grafted to a plane. The system is assumed to have symmetry in directions parallel to the grafting plane hence it being a…
Orthogonal Laurent polynomials in the unit circle and the theory of Toda-like integrable systems are connected using the Gauss--Borel factorization of a Cantero-Moral-Velazquez moment matrix, which is constructed in terms of a complex…
The Langevin equation with multiplicative noise and state-dependent transport coefficient has to be always complemented with the proper interpretation rule of the noise, such as the Ito and Stratonovich conventions. Although the…
An elastic rod model for semi-flexible polymers is presented. Theory for a continuum rod is reviewed, and it is shown that a popular discretised model used in numerical simulations gives the correct continuum limit. Correlation functions…
In this article, we consider two models of directed polymers in random environment: a discrete model and a continuous model. We consider these models in dimension greater or equal to 3 and we suppose that the normalized partition function…
We present a diagrammatic formulation of a theory for the time dependence of density fluctuations in equilibrium systems of interacting Brownian particles. To facilitate derivation of the diagrammatic expansion we introduce a basis that…