Related papers: Spectral asymptotics of a broken delta interaction
For a class of non-selfadjoint semiclassical operators in dimension one, we get a complete asymptotic description of all eigenvalues near a critical value of the leading symbol of the operator on the boundary of the pseudospectrum.
We analyze the peculiarities of the interaction of the lambda hyperon with s-shell nuclei. The spectra of bound and scattering states are studied in the hypernuclei $_{\Lambda}^{2}$H, $_{\Lambda}^{3}$H, $_{\Lambda}^{4}$H, $_{\Lambda}^{4}$He…
We consider a waveguide-like domain consisting of two thin straight tubular domains connected through a tiny window. The perpendicular size of this waveguide is of order $\varepsilon$. Under the assumption that the window is appropriately…
We consider an abstract pair-interaction model in quantum field theory with a coupling constant $\lambda\in {\mathbb R}$ and analyze the Hamiltonian $H(\lambda)$ of the model. In the massive case, there exist constants $\lambda_{\rm c}<0$…
We consider operators $-\Delta + X$ where $X$ is a constant vector field, in a bounded domain and show spectral instability when the domain is expanded by scaling. More generally, we consider semiclassical elliptic boundary value problems…
The spectrum of an exactly solvable non-relativistic system of a charged particle interacting with a quantized electromagnetic mode is studied with various polarizations. Quasiparticle dispersion relations can be derived from the…
In this paper, we study the asymptotic behavior of globally minimizing orbits of contact Hamiltonian systems. Under some assumptions, we prove that the $\omega$-limit set of globally minimizing orbits is contained in the set of semi-static…
In this paper, we consider the one-dimensional semirelativistic Schr\"{o}dinger equation for a particle interacting with $N$ Dirac delta potentials. Using the heat kernel techniques, we establish a resolvent formula in terms of an $N \times…
The mechanism of backbending is semi-phenomenologically investigated based on the hybridization of two rotational bands. These bands are defined by treating a model Hamiltonian describing two interacting subsystems: a set of particles…
The quantum dynamics of an electron in a uniform magnetic field is studied for geometries corresponding to integrable cases. We obtain the uniform asymptotic approximation of the WKB energies and wavefunctions for the semi-infinite plane…
The spectral series of the Schr\"odinger operator with a delta-potential on a three-dimensional compact spherically symmetric manifold in the semiclassical limit as $h\to0$ are described.
We give an example of a one-dimensional scalar spin energy with long-range interactions not satisfying standard decay conditions and which admits a continuum approximation defined for functions u in BV((0,L),[-1,1]) taking into account the…
The purpose of this note is to review some recent results concerning the pseudospectra and the eigenvalues asymptotics of non-selfadjoint semiclassical pseudo-differential operators subject to small random perturbations.
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 propose a model for energy-dependent $\delta-\delta^{\prime}$ interactions which yields scattering coefficients exhibiting full transmission for high-energy incident particles, also computing the bound solutions in one-dimension…
The exact elementary excitations in a typical U(1) symmetry broken quantum integrable system, that is the twisted J1-J2 spin chain with nearest-neighbor, next nearest neighbor and chiral three spin interactions, are studied. The main…
The interaction Hamiltonian of an electron and a quasi-monochromatic pulse of a strong quantized electromagnetic field is examined. Canonical transformations of the field variables are found that allow the division of the system's…
We investigate relations between spectral properties of a single-centre point-interaction Hamiltonian describing a particle confined to a bounded domain $\Omega\subset\mathbb{R}^{d},\: d=2,3$, with Dirichlet boundary, and the geometry of…
We study the bound states of a quantum mechanical system consisting of a simple harmonic oscillator with an inverse square interaction, whose interaction strength is governed by a constant $\alpha$. The singular form of this potential has…
In this paper we study the low-lying spectrum of the AKLT model perturbed by small, finite-range potentials and with open boundary conditions imposed at the edges of the chain. Our analysis is based on the \emph{local, iterative Lie…