Related papers: Quasiclassical approximation for magnetic monopole…
We introduce some discrete analogues of the Dirac magnetic monopole on a unit sphere S^2 and explain how to compute the corresponding spectrum using the representation theory of finite groups. The main examples are certain magnetic…
We derive the semiclassical WKB quantization condition for obtaining the energy band edges of periodic potentials. The derivation is based on an approach which is much simpler than the usual method of interpolating with linear potentials in…
The method of quantization of magnetic monopoles based on the order-disorder duality existing between the monopole operator and the lagrangian fields is applied to the description of the quantum magnetic monopoles of `t Hooft and Polyakov…
Numerical integration and function approximation on compact Riemannian manifolds based on eigenfunctions of the Laplace-Beltrami operator have been widely studied in the recent literature. The standard example in numerical experiments is…
Different analogs of quasiclassical limit for a q-oscillator which result in different (commutative and non-commutative) algebras of ``classical'' observables are derived. In particular, this gives the q-deformed Poisson brackets in terms…
We present an alternative description of magnetic monopoles by lifting quantum mechanics from 3-dimensional space into a one with 2 complex dimensions. Magnetic monopoles are realized as a generalization of the considered states. Usual…
We consider Witten Laplacians associated to some non-Morse potentials. We prove Eyring-Kramers formulas for the bottom of the spectrum of these operators in the semiclassical regime and quantify the spectral gap separating these eigenvalues…
This paper is devoted to the asymptotic analysis of the eigenvalues of the Laplace operator with a strong magnetic field and Robin boundary condition on a smooth planar domain and with a negative boundary parameter. We study the singular…
We consider the semiclassical magnetic Laplacian $\mathcal{L}_h$ on a Riemannian manifold, with a constant-rank and non-vanishing magnetic field $B$. Under the localization assumption that $B$ admits a unique and non-degenerate well, we…
Quasinormal modes describe the ringdown of compact objects deformed by small perturbations. In generic theories of gravity that extend General Relativity, the linearized dynamics of these perturbations is described by a system of coupled…
We present a semiclassical analysis of the quantum propagator of a particle confined on one side by a steeply, monotonically rising potential. The models studied in detail have potentials proportional to $x^{\alpha}$ for $x>0$; the limit…
We introduce an analog of the Dirichlet-to-Neumann map for the Maxwell equation in a bounded domain. We show that it can be approximated by a pseudodifferential operator on the boundary with a matrix-valued symbol and we compute the…
The Dirichlet Laplacian between two parallel hypersurfaces in Euclidean spaces of any dimension in the presence of a magnetic field is considered in the limit when the distance between the hypersurfaces tends to zero. We show that the…
The aim of the paper is to derive spectral estimates into several classes of magnetic systems. They include three-dimensional regions with Dirichlet boundary as well as a particle in $\mathbb{R}^3$ confined by a local change of the magnetic…
Baskakov operators and their inverses can be expressed as linear differential operators on polynomials. Recurrence relations are given for the computation of these coefficients. They allow the construction of the associated Baskakov…
A class of singular integral operators, encompassing two physically relevant cases arising in perturbative QCD and in classical fluid dynamics, is presented and analyzed. It is shown that three special values of the parameters allow for an…
We construct pairs of compact K\"ahler-Einstein manifolds $(M_i,g_i,\omega_i)$ ($i=1,2)$ of complex dimension $n$ with the following properties: The canonical line bundle $L_i=\bigwedge^n T^*M_i$ has Chern class $[\omega_i/2\pi]$, and for…
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…
We study the orbital magnetic moment of Bogoliubov quasiparticles in superconductors with the semiclassical approach. We derive the orbital magnetic moment of a quasiparticle wavepacket by considering the energy correction of the wavepacket…
This paper is devoted to semiclassical estimates of the eigenvalues of the Pauli operator on a bounded open set whose boundary carries Dirichlet conditions. Assuming that the magnetic field is positive and a few generic conditions, we…