相关论文: Crossing Probabilities and Modular Forms

Semiclassical transition probabilities characterize transfer of energy between "hard" and "soft" modes in various physical systems. We establish the boundary problem for singular euclidean solutions used to calculate such probabilities.…

Evaluating accessible conformational space is computationally expensive and thermal motions are partly neglected in computer models of molecular interactions. This produces error into the estimates of binding strength. We introduce a method…

We derive a microscopic theory for the structural dynamics in the vicinity of the glass transition for a liquid exposed to a one-dimensional periodic potential. The periodic potential breaks translational invariance, in particular, the…

In this paper, we study the critical behavior of percolation on a configuration model with degree distribution satisfying an infinite second-moment condition, which includes power-law degrees with exponent $\tau \in (2,3)$. It is well known…

A system with equal number of positive and negative charges confined in a box with a small but finite thickness is modeled as a function of temperature using mesoscale numerical simulations, for various values of the charges. The Coulomb…

Percolation theory allows simple description of the phase transition based on the scaling properties of the network clusters with respect to a single parameter - site or bond occupation probability. How to design a network exhibiting the…

Colloidal systems offer unique opportunities for the study of phase formation and structure since their characteristic length scales are accessible to visible light. As a model system the two dimensional assembly of colloidal magnetic and…

We analyze the many-particle correlations that affect the optical properties of two-dimensional semiconductors. These correlations manifest themselves through the specific optical resonances such as excitons, trions, etc. Starting from the…

During the past two decades, percolation has long served as a basic paradigm for network resilience, community formation and so on in complex systems. While the percolation transition is known as one of the most robust continuous…

We use a previously introduced mapping between the continuum percolation model and the Potts fluid (a system of interacting s-states spins which are free to move in the continuum) to derive the low density expansion of the pair…

We investigate the critical properties of the four-state commutative random permutation glassy Potts model in three and four dimensions by means of Monte Carlo simulation and of a finite size scaling analysis. Thanks to the use of a field…

A known general class of superintegrable systems on 2D spaces of constant curvature can be defined by potentials separating in (geodesic) polar coordinates. The radial parts of these potentials correspond either to an isotropic harmonic…

We study the conformational freedom of a protein made by two rigid domains connected by a flexible linker. The conformational freedom is represented as an unknown probability distribution on the space of allowed states. A new algorithm for…

Compact stars above a critical stellar mass develop large scalar fields in some scalar-tensor theories. This scenario, called spontaneous scalarization, has been an intense topic of study since it passes weak-field gravity tests naturally…

Some examples of translation invariant site percolation processes on the $\Z^2$ lattice are constructed, the most far-reaching example being one that satisfies uniform finite energy (meaning that the probability that a site is open given…

In this paper we study the macroscopic conduction properties of large but finite binary networks with conducting bonds. By taking a combination of a spectral and an averaging based approach we derive asymptotic formulae for the conduction…

The properties of the similarity transformation in percolation theory in the complex plane of the percolation probability are studied. It is shown that the percolation problem on a two-dimensional square lattice reduces to the Mandelbrot…

In this review paper, we first discuss some open problems related to two-dimensional self-avoiding paths and critical percolation. We then review some closely related results (joint work with Greg Lawler and Oded Schramm) on critical…

We find a class of four dimensional deformed conformal field theories which appear extra dimensional when their gauge symmetries are spontaneously broken. The theories are supersymmetric moose models which flow to interacting conformal…

We introduce a systematic low-energy approach to strongly correlated electron systems in infinite dimensions, and apply it to the problem of the correlation-induced metal-insulator transition in the half-filled Hubbard model. We determine…