Related papers: Semi-Classical Quantization of the Many-Anyon Syst…

We derive the semiclassical series for the partition function of a one-dimensional quantum-mechanical system consisting of a particle in a single-well potential. We do this by applying the method of steepest descent to the path-integral…

We consider the stationary solutions for a class of Schroedinger equations with a symmetric double-well potential and a nonlinear perturbation. Here, in the semiclassical limit we prove that the reduction to a finite-mode approximation give…

We develop a method to determine the eigenvalues and eigenfunctions of two-boson Hamiltonians include a wide class of quantum optical models. The quantum Hamiltonians have been transformed in the form of the one variable differential…

A semiclassical analysis based on spin-coherent states is used to establish a classification and formulae for the spectral gap of mean-field spin Hamiltonians. For gapped systems we provide a full description of the low-energy spectra based…

We study a quantum double model whose degrees of freedom are Ising anyons. The terms of the Hamiltonian of this system give rise to a competition between single and double topologies. By studying the energy spectra of the Hamiltonian at…

Bosonic end perturbative calculations for quantum mechanical anyon systems require a regularization. I regularize by adding a specific $\delta$-function potential to the Hamiltonian. The reliability of this regularization procedure is…

We are interested in the homogenization of energy like quantities for electromagnetic waves in the high frequency limit for Maxwell's equations with various boundary conditions. We use a scaled variant of H-measures known as semi classical…

Using the symmetry properties of the three-anyon spectrum, we obtain exactly the multiplicities of states with given energy and angular momentum. The results are shown to be in agreement with the proper quantum mechanical and semiclassical…

We study a class of quantum two-dimensional models with complex potentials of specific form. They can be considered as the generalization of a recently studied model with quadratic interaction not amenable to conventional separation of…

The method of separation of variables is significant, it has been applied to physics, engineering , chemistry and other fields. It allows to reduce the diffculity of problems by separating the variables from partial differential equation…

The problem of quantizing a class of two-dimensional integrable quantum field theories is considered. The classical equations of the theory are the complex $sl(n)$ affine Toda equations which admit soliton solutions with real masses. The…

We prove explicit semiclassical resolvent estimates for an integrable potential on the real line. The proof is a comparatively easy case of the spherical energies method, which has been used to prove similar theorems in higher dimensions…

This paper presents a renormalization approach to many-particle systems. By starting from a bare Hamiltonian ${\cal H}= {\cal H}_0 +{\cal H}_1$ with an unperturbed part ${\cal H}_0$ and a perturbation ${\cal H}_1$,we define an effective…

In quasi-exactly solvable problems partial analytic solution (energy spectrum and associated wavefunctions) are obtained if some potential parameters are assigned specific values. We introduce a new class in which exact solutions are…

The semi-classical spectrum of the Homogeneous sine-Gordon theories associated with an arbitrary compact simple Lie group G is obtained and shown to be entirely given by solitons. These theories describe quantum integrable massive…

In this article we describe the semi-classical spectrum of a Schrodinger operator on $\mathbb{R}$ with a double well potential. We study the shape of spectrum around the local maximum of the potential. In the classification of singularities…

Quantum particle is considered confined in a toy-model potential possessing multiple minima. For the specific choice of the family of potentials (in the form of harmonic oscillator plus several logarithmic infinitely high but penetrable…

We develop a quantitative semiclassical formula for the resonant tunneling current through a quantum well in a tilted magnetic field. It is shown that the current depends only on periodic orbits within the quantum well. The theory explains…

The harmonic oscillator is one of the most studied systems in Physics with a myriad of applications. One of the first problems solved in a Quantum Mechanics course is calculating the energy spectrum of the simple harmonic oscillator with…

We revisit the canonical quantization to assess the spectrum of the modified Emden equation $\ddot{x} + kx\dot{x} + \omega^2 x + \frac{k^2}{9}x^3 = 0$, which is an isochronous case of the Li\'enard-Kukles equation. While its classical…