St. Petersburg Department of Steklov Institute of Mathematics

Eigenvalue Falls in Thin Broken Quantum Strips

Abstract. We are interested in the spectrum of the Dirichlet Laplacian in thin broken strips with angle [Formula: see text]. Playing with symmetries, this leads us to investigate spectral problems for the Laplace operator with mixed boundary conditions in trapezoids of thickness...

Last-Passage Percolation and Product-Matrix Ensembles

Abstract We introduce and study a model of directed last-passage percolation in planar layered environment. This environment is represented by an array of random exponential clocks arranged in blocks, for each block the average waiting times depend only on the local coordinates w...

Relatively Undistorted Solutions to the Wave Equation: A Review

A review of simple solutions to the linear wave equation in three spatial variables, involving arbitrary functions, is given. Physicists’ interest in these solutions is primarily motivated by the need for a convenient description of spatiotemporally localized wave beams and packe...

On background fields and a cutoff in sigma models

Abstract In this paper, using the example of a two-dimensional nonlinear sigma model with the Heisenberg group, we compare two variants of chiral field decomposition into a background part and a fluctuation. It is shown that only one of these methods is consistent with the constr...