Related papers: Asymptotics of eigenvalues of the Schroedinger ope…

We consider operators of the form H+V where H is the one-dimensional harmonic oscillator and V is a zero-order pseudo-differential operator which is quasi-periodic in an appropriate sense (one can take V to be multiplication by a periodic…

We prove an asymptotic expansion for the eigenvalues and eigenfunctions of Schr\"{o}dinger-type operator with a confining potential and with principle part a periodic elliptic operator in divergence form. We compare the spectrum to the…

This paper is a continuation of research started in [7] devoted to explicit asymptotic formulas for standing coastal-trapped waves. Our main goal is to construct formal asymptotic eigenfunctions of the wave operator $\langle \nabla,…

A family $\BA_\a$ of differential operators depending on a real parameter $\a$ is considered. The problem can be formulated in the language of perturbation theory of quadratic forms. The perturbation is only relatively bounded but not…

In this work we obtain the integrated density of states for the Schr\"{o}dinger operators with decaying random potentials acting on $\ell^2(\mathbb{Z}^d)$. We also study the asymptotic of the largest and smallest eigenvalues of its finite…

Let $\sum_{\beta\in\nats^d} F_\beta x^\beta$ be a multivariate power series. For example $\sum F_\beta x^\beta$ could be a generating function for a combinatorial class. Assume that in a neighbourhood of the origin this series represents a…

In the limit $\hbar\to 0$, we analyze a class of Schr\"odinger operators $H_\hbar = \hbar^2 L + \hbar W + V\cdot \mathrm{id}$ acting on sections of a vector bundle $\mathcal{Eh}$ over a Riemannian manifold $M$ where $L$ is a Laplace type…

The previous attempts of reconstructing the Gell-Mann-Low function \beta(g) of the \phi^4 theory by summing perturbation series give the asymptotic behavior \beta(g) = \beta_\infty g^\alpha in the limit g\to \infty, where \alpha \approx 1…

In this paper we prove that the Dirac operator $A_\eta$ with an electrostatic $\delta$-shell interaction of critical strength $\eta = \pm 2$ supported on a $C^2$-smooth compact surface $\Sigma$ is self-adjoint in…

We consider a non-selfadjoint $h$-differential model operator $P_h$ in the semiclassical limit ($h\rightarrow 0$) subject to small random perturbations. Furthermore, we let the coupling constant $\delta$ be $\exp\{-\frac{1}{Ch}\}\leq \delta…

We study the three-loop gauge $\beta$-functions in general $\mathcal{N}=1$ supersymmetric gauge theories regularized by higher covariant derivatives (HCD) supplemented with Pauli--Villars subtraction. The all-structure three-loop form of…

Reconstruction of the \beta-function for \phi^4 theory, attempted previously by summation of perturbation series, leads to asymptotics \beta(g)=\beta_\infty g^\alpha at g\to\infty, where \alpha\approx 1 for space dimensions d=2,3,4. The…

In this report we construct a family of holomorphic functions $\beta_{\lambda,\mu} (s)$ which behave asymptotically like iterated exponentials as $|s| \to \infty$ in the right half plane. Each $\beta_{\lambda,\mu}$ satisfies a convenient…

Let -Delta+V be the Schrodinger operator acting on L^2(R^d,C) with d>2 odd. Here V is a bounded real or complex function vanishing outside the closed ball of center 0 and of radius a. We show for generic potentials V that the number of…

In this note we sharpen the lower bound from [LLP10] on the spectrum of the 2D Schroedinger operator with a delta-interaction supported on a planar angle. Using the same method we obtain the lower bound on the spectrum of the 2D…

In this paper we obtain asymptotic formulas of arbitrary order for the Bloch eigenvalues and Bloch functions of the Schrodinger operator of arbitrary dimension, with periodic, with respect to arbitrary lattice, potential. Moreover, we…

In this paper, we describe the leftmost eigenvalue of the non-selfadjoint operator $\mathcal{A}_h = -h^2\Delta+iV(x)$ with Dirichlet boundary conditions on a smooth bounded domain $\Omega\subset\mathbb{R}^n\,$, as $h\rightarrow0\,$. $V$ is…

Let \Omega be a bounded connected, open set of \R^n with Lipschitz boundary. Let F be a suitable norm in \R^n and let \Delta_F u be the so-colled Finsler Laplacian. In this paper we prove two inequalities for the first eigenvalue of…

The behaviour of the spectral edges (embedded eigenvalues and resonances) is discussed at the two ends of the continuous spectrum of non-local discrete Schr\"odinger operators with a $\delta$-potential. These operators arise by replacing…

In this paper we study the self-adjointness and spectral properties of two-dimensional Dirac operators with electrostatic, Lorentz scalar, and anomalous magnetic $\delta$-shell interactions with constant weights that are supported on a…