Related papers: Two-point generating function of the free energy f…
The one-point distribution of the height for the continuum Kardar-Parisi-Zhang (KPZ) equation is determined numerically using the mapping to the directed polymer in a random potential at high temperature. Using an importance sampling…
We construct a phenomenological theory of self-localization of directed polymers in d+1 dimensions. In d=1 we show that the polymer is always self-localized, whereas in d=2 there is a phase transition between localized and free states. We…
Long linear polymers in dilute solutions are known to undergo a collapse transition from a random coil (expand itself) to a compact ball (fold itself up) when the temperature is lowered, or the solvent quality deteriorates. A natural model…
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 derive an expression for the free energy of the blends of block copolymers expressed as a functional of the density distribution of the monomer of each block. The expression is a generalization of the Flory-Huggins-de Gennes theory for…
In a recent contribution, Dotsenko establishes a Fredholm determinant formula for the two-point distribution of the KPZ equation in the long time limit and starting from narrow wedge initial conditions. We establish that his expression is…
We consider field theory formulation for directed polymers and interfaces in the presence of quenched disorder. We write a series representation for the averaged free energy, where all the integer moments of the partition function of the…
In this paper, we study the random polynomial $p_n(\rho):=\prod_{j=1}^n (|z_j|-\rho)$, where the points $\{z_j\}_{j=1}^n$ are the eigenvalue moduli of random normal matrices with a radially symmetric potential. We establish precise large…
We have studied the structure and free energy landscape of a semi-flexible lattice-polymer in the presence of a surface. At low temperatures coexistence of two-dimensional integer-folded crystals is observed. As the temperature is increased…
The general one-dimensional ``log-sine'' gas is defined by restricting the positive and negative charges of a two-dimensional Coulomb gas to live on a circle. Depending on charge constraints, this problem is equivalent to different boundary…
We introduce a general class of generating functionals for the calculation of quantum-mechanical expectation values of arbitrary functionals of fluctuating paths with fixed end points in configuration or momentum space. The generating…
We revisit the long standing problem of the geometric free variable approach to computing the generating function for disk amplitudes in the matrix model formulation of the 3-state Potts model coupled to 2D discrete gravity. This method is…
We consider the low-temperature $T<T_c$ disorder-dominated phase of the directed polymer in a random potentiel in dimension 1+1 (where $T_c=\infty$) and 1+3 (where $T_c<\infty$). To characterize the localization properties of the polymer of…
The thermalization process is studied in an expanding parton gas using the Boltzmann equation with two types of collision terms. In the relaxation time approximation we determine the criteria under which a time-dependent relaxation time…
During fast diffusion-influenced polymerization, nonequilibrium behavior of the polymer chains and the surrounding reactive monomers has been reported recently. Based on the laws of thermodynamics, the emerging nonequilibrium structures…
We study the activated motion of adsorbed polymers which are driven over a structured substrate by a localized point force.Our theory applies to experiments with single polymers using, for example, tips of scanning force microscopes to drag…
We consider the one-dimensional Kardar-Parisi-Zhang (KPZ) equation with half Brownian motion initial condition, studied previously through the weakly asymmetric simple exclusion process. We employ the replica Bethe ansatz and show that the…
In terms of the replica method we consider the low temperature limit of (2+1) directed polymers in a random potential. The proposed approach allows to compute the scaling exponent $\theta$ of the free energy fluctuations as well as the left…
Inspired by Gansner's elegant $k$-trace generating function for rectangular plane partitions, we introduce two novel operators, $\varphi_{z}$ and $\psi_{z}$, along with their combinatorial interpretations. Through these operators, we derive…
We study a determinantal Coulomb gas in the complex plane associated with the external potential $$ Q(z)=\frac{1}{1-\tau^2}\big(|z|^2-\tau \text{Re } z^2\big)-2c\log|z-a|, $$ where $\tau\in[0,1)$, $c\ge0$, and $a\ge0$. In the regimes where…