Related papers: Dirichlet forms and polymer models based on stable…
We use a mixture of a polymer and its dimer to control dynamics in a manner inspired by \emph{pinning} a fraction of the system. In our system of $\alpha$-methyl styrene, where the polymer has a glass transition at higher temperature than…
This paper addresses the asymptotic development of order 2 by the $\Gamma$ -convergence of the Cahn-Hilliard functional with Dirichlet boundary conditions. The Dirichlet data are assumed to be well separated from one of the two wells. In…
Critical dynamics in various glass models including those described by mode coupling theory is described by scale-invariant dynamical equations with a single non-universal quantity, i.e. the so-called parameter exponent that determines all…
We consider a gas of ultracold two-level atoms confined in a cavity, taking into account for atomic center-of-mass motion and cavity mode variations. We use the generalized Dicke model, and analyze separately the cases of a Gaussian, and a…
The mode-coupling theory for ideal glass transitions in simple systems is generalized to a theory for the glassy dynamics of molecular liquids using the density fluctuations of the sites of the molecule's constituent atoms as the basic…
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…
We study a liquid of zigzagging two-dimensional directed polymers with bending rigidity, i.e., polymers whose conformations follow checkerboard paths. In the continuum limit the statistics of such polymers obey the Dirac equation for…
We study the ground-state properties of a system of dimers. Each dimer consists in a pair of equivalent charges at a fixed distance, immersed in a neutralizing homogeneous background. All charges interact pairwisely by Coulomb potential.…
The distribution $g_{cl}$ of a Gibbs cluster point process in $X=\mathbb{R}^{d}$ (with i.i.d. random clusters attached to points of a Gibbs configuration with distribution $g$) is studied via the projection of an auxiliary Gibbs measure…
In this paper, we consider a long-time behavior of stable-like processes. A stable-like process is a Feller process given by the symbol $p(x,\xi)=-i\beta(x)\xi+\gamma(x)|\xi|^{\alpha(x)},$ where $\alpha(x)\in(0,2)$, $\beta(x)\in\R$ and…
I investigate the Kazakov-Migdal (KM) model -- the Hermitean gauge-invariant matrix model on a D-dimensional lattice. I utilize an exact large-N solution of the KM model with a logarithmic potential to examine its critical behavior. I find…
We define a generalized Golomb--Dickman constant $\lambda_{\theta}$ as the limiting expected proportion of the longest cycle in random permutations under the Ewens measure with parameter $\theta > 0$. Exploiting the independence properties…
We investigate dilaton-gravity models whose solutions contain a large portion of the static patch of dS$_2$. The thermodynamic properties of these theories are considered both in the presence of a finite Dirichlet wall, as well as for…
We derive a moment formula for generalized fractional polynomial processes, i.e., for polynomial-preserving Markov processes time-changed by an inverse L\'evy-subordinator. If the time change is inverse $\alpha$-stable, the time-derivative…
We consider the two-dimensional two-component plasma, or Coulomb gas, consisting of $N$ positive and $N$ negative charges with logarithmic interaction. We introduce a suitable regularization of the interaction by smearing the charges over a…
Two-level atoms interacting with a one mode cavity field at zero temperature have order parameters which reflect the presence of a quantum phase transition at a critical value of the atom-cavity coupling strength. Two popular examples are…
We consider a polymer with configuration modeled by the path of a Markov chain, interacting with a potential $u+V_n$ which the chain encounters when it visits a special state 0 at time $n$. The disorder $(V_n)$ is a fixed realization of an…
We consider a model for a directed polymer in a random environment defined on a hierarchical diamond lattice in which i.i.d. random variables are attached to the lattice bonds. Our focus is on scaling schemes in which a size parameter $n$,…
Motivated by the discrete dipole approximation (DDA) for the scattering of electromagnetic waves by a dielectric obstacle that can be considered as a simple discretization of a Lippmann-Schwinger style volume integral equation for…
We introduce and study the disordered Dicke model in which the spin-boson couplings are drawn from a random distribution with some finite width. Regarding the quantum phase transition we show that when the standard deviation $\sigma$ of the…