Steklov Mathematical Institute

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...

Smooth Dependence of Characteristic Trajectories on the Vector Field

Abstract Given a vector field on a two-dimensional manifold, the smooth dependence of the characteristic trajectories of singular points of preset order on the field is proved. In particular, a strengthened version of the classical Hadamard–Perron theorem is obtained, which impli...

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...

On Sidon sets with squares, cubes and quartics in short intervals

Abstract Representative examples of our results are as follows. For any positive integer $$N$$ N the equation $$x^3+y^3=z^3+t^3, \quad x,y,z,t\in \mathbb{N}, \quad \{x,y\}\not=\{z,t\}$$ x 3 + y 3 = z 3 + t 3 , x , y , z , t ∈ N , { x , y } ≠ { z , t } has no solutions satisfying...

Unified framework for efficiently computable quantum circuits

Quantum circuits consisting of Clifford and matchgates are two classes of circuits that are known to be efficiently simulatable on a classical computer. We introduce a unified framework that shows in a transparent way the special structure that allows these circuits to be efficie...