Related papers: Sharp asymptotics of the quasimomentum

Under certain assumptions we derive a complete semiclassical asymptotics of the spectral function $e_{h,\varepsilon}(x,x,\lambda)$ for a scalar operator \begin{equation*} A_\varepsilon (x,hD)= A^0(hD) + \varepsilon B(x,hD), \end{equation*}…

we obtain the asympotics for the counting function of resonances for a matrix valued schrodinger operator in dimension one.

We consider the Schr\"odinger operator $H$ on the half-line with a periodic potential $p$ plus a compactly supported potential $q$. For generic $p$, its essential spectrum has an infinite sequence of open gaps. We determine the asymptotics…

We present an exact expression for the quasinormal modes of scalar, electromagnetic and gravitational perturbations of a near extremal Scwarzschild-de Sitter black hole and we show why a previous approximation holds exactly in this near…

We consider the Bochner Laplacian on high tensor powers of a positive line bundle on a closed symplectic manifold (or, equivalently, the semiclassical magnetic Schr\"odinger operator with the non-degenerate magnetic field). We assume that…

In this work, we are devoted to study the Cauchy problem of the Camassa-Holm (CH) equation with weighted Sobolev initial data in space-time solitonic regions \begin{align*} m_t+2\kappa q_x+3qq_x=2q_xq_{xx}+qq_{xx},~~m=q-q_{xx}+\kappa,\\…

We prove asymptotic formulas of Szeg\H{o} type for the periodic Schr\"odinger operator $H=-\frac{d^2}{dx^2}+V$ in dimension one. Admitting fairly general functions $h$ with $h(0)=0$, we study the trace of the operator…

Below we study theoretically and numerically the asymptotics of the algebraic part of the spectrum for the quasi-exactly solvable sextic potential, its level crossing points, and its monodromy in the complex plane of its parameter. We also…

There exists an analogy between Maxwell equations in a rotating frame and Schr\"odinger equation for a charged particle in the presence of a magnetic field. We exploit this analogy to point out that electromagnetic phenomena in the rotating…

We investigate the thermodynamics of Einstein-Maxwell(-Dilaton) theory for an asymptotically flat spacetime in a quasilocal frame. We firstly define a quasilocal thermodynamic potential via the Euclidean on-shell action and formulate a…

This article gives a simple treatment of the quantum Birkhoff normal form for semiclassical pseudo-differential operators with smooth coefficients. The normal form is applied to describe the discrete spectrum in a generalised non-degenerate…

Motivated by a quantum Zeno dynamics in a cavity quantum electrodynamics setting, we study the asymptotics of a family of symbols corresponding to a truncated momentum operator, in the semiclassical limit of vanishing Planck constant…

We study the quenched long time behaviour of the survival probability up to time $t$, $\mathbf{E}_x\big[e^{-\int_0^t V^{\omega}(X_s){\rm d}s}\big],$ of a symmetric L\'evy process with jumps, under a sufficiently regular Poissonian random…

For Schr\"odinger operators with potentials that are asymptotically homogeneous of degree $-2$, the size of the coupling determines whether it has finite or infinitely many negative eigenvalues. In the latter case the asymptotic…

We prove a sharp Weyl estimate for the number of eigenvalues belonging to a fixed interval of energy of a self-adjoint difference operator acting on $\ell^2(\epsilon\mathbb{Z}^d)$ if the associated symplectic volume of phase space in…

The Bochner-Schr\"odinger operator $H_{p}=\frac 1p\Delta^{L^p}+V$ on high tensor powers $L^p$ of a Hermitian line bundle $L$ on a Riemannian manifold $X$ of bounded geometry is studied under the assumption of non-degeneracy of the curvature…

The spectra of the Schr\"odinger operators with periodic potentials are studied. When the potential is real and periodic, the spectrum consists of at most countably many line segments (energy bands) on the real line, while when the…

This paper is devoted to the asymptotics of eigenvalues for a Schr\"o-dinger operator in the case when the potential V does not tend to infinity at infinity. Such a potential is called degenerate. The point is that the set in the phase…

We analyze semi-classical Schr\"odinger operators with potentials of class $C^{1,1/2}$ and establish commutator estimates for the associated projection operators in Schatten norms. These are then applied to prove quantitative versions of…

We investigate spectral and asymptotic properties of the particular Schr\"odinger operator (also known as the Bloch-Torrey operator), $-\Delta + i g x$, in infinite periodically perforated domains of $\mathbb R^d$. We consider Dirichlet…