Related papers: Self-localization of directed polymers and oppress…
In the presented work we study, by means of numerical simulations, the behaviour of a suspension of active ring polymers in the bulk and under lateral confinement. When changing the separation between the confining planes and the polymers'…
We study the directed polymer model in a bounded environment with bond disorder and show that, in the interior of the weak disorder phase, weak disorder continues to hold upon perturbation by a small bias. Using this stability result, we…
In these proceedings, we first summarize some general properties of phase transitions in the presence of quenched disorder, with emphasis on the following points: the need to distinguish typical and averaged correlations, the possible…
We consider a directed random walk model of a random heterogeneous polymer in the proximity of an interface separating two selective solvents. This model exhibits a localization/delocalization transition. A positive value of the free energy…
Pressure-driven flow of a dilute polymer solution has been numerically observed to possess a form of elastic turbulence which is organised around the interactions of localised versions of 2-dimensional `arrowhead' travelling waves (Page et…
The time evolution of spatial fluctuations in inhomogeneous d-dimensional biological systems is analyzed. A single species continuous growth model, in which the population disperses via diffusion and convection is considered.…
We investigate the transition induced by disorder in a periodically-driven one-dimensional model displaying quantized topological transport. We show that, while instantaneous eigenstates are necessarily Anderson localized, the periodic…
In this paper we consider in detail the connection between the problem of a polymer in a random medium and that of a quantum particle in a random potential. We are interested in a system of finite volume where the polymer is known to be…
Motivated by previous investigations on the radiative effects of the electric dipoles embedded in structured cavities, localization of electromagnetic waves in two dimensions is studied {\it ab initio} for a system consisting of many…
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…
We study the local eigenvalue statistics (LES) associated with one-dimensional lattice models of random polymers. We consider models constructed from two polymers. Each polymer is a finite interval of lattice points with a finite potential.…
A random polymer model is a one-dimensional Jacobi matrix randomly composed of two finite building blocks. If the two associated transfer matrices commute, the corresponding energy is called critical. Such critical energies appear in…
For a directed polymer model in random environment, a characterization of the weak disorder phase in terms of the moment of the renormalized partition function has been proved in [S. Junk: Communications in Mathematical Physics 389,…
We propose and compare different strategies to construct dynamic density functional theories (DDFTs) for inhomogeneous polymer systems close to equilibrium from microscopic simulation trajectories. We focus on the systematic construction of…
We consider models of directed random polymers interacting with a defect line, which are known to undergo a pinning/depinning (or localization/delocalization) phase transition. We are interested in critical properties and we prove, in…
We discuss various aspects of the randomly interacting directed polymers with emphasis on the phases and phase transition. We also discuss the behaviour of overlaps of directed paths in a random medium.
Certain polymer models are known to exhibit path localization in the sense that at low temperatures, the average fractional overlap of two independent samples from the Gibbs measure is bounded away from $0$. Nevertheless, the question of…
We study quantum diffusion of wavepackets in one-dimensional random binary subject to an applied electric field. We consider three different cases: Periodic, random, and random dimer (paired) lattices. We analyze the spatial extent of…
We investigate the motion of two overlapping polymers with self-avoidance confined in a narrow 2d box. A statistical model is constructed using blob free-energy arguments. We find spontaneous segregation under the condition: $L > R_{//}$,…
This review is devoted to the detailed consideration of the universal statistical properties of one-dimensional directed polymers in a random potential. In terms of the replica Bethe ansatz technique we derive several exact results for…