相关论文: Semiclassical analysis of level widths for one-dim…

We consider the two-dimensional advection-diffusion equation on a bounded domain subject to either Dirichlet or von Neumann boundary conditions and study both time-independent and time-periodic cases involving Liouville integrable…

We study how the singular behaviour of classical systems at bifurcations is reflected by their quantum counterpart. The semiclassical contributions of individual periodic orbits to trace formulae of Gutzwiller type are known to diverge when…

Consider a semiclassical Hamiltonian $H := h^{2} \Delta + V - E$ where $\Delta$ is the positive Laplacian on $\mathbb{R}^{d}$, $V \in C^{\infty}_{0}(\mathbb{R}^{d})$ and $E > 0$ is an energy level. We prove that under an appropriate…

We investigate the effects of a trapping space-dependent potential on the low-temperature quasi-long-range order phase of two-dimensional particle systems with a relevant U(1) symmetry, such as quantum atomic gases. We characterize the…

Using the intertwining relation we construct a pseudosuperpartner for a (non-Hermitian) Dirac-like Hamiltonian describing a two-level system interacting in the rotating wave approximation with the electric component of an electromagnetic…

We compute both analytically and numerically the geometry of the parameter space of the anharmonic oscillator employing the quantum metric tensor and its scalar curvature. A novel semiclassical treatment based on a Fourier decomposition…

Contrary to conventional wisdom, level repulsion in semiclassical spectrum is not just a feature of classically chaotic systems, but classically integrable systems as well. While in chaotic systems level repulsion develops on a scale of the…

We study edge and bulk open-orbit electron states in a quasi-one-dimensional (Q1D) metal subject to a magnetic field. For both types of the states, the energy spectrum near the Fermi energy consists of two terms. One term has a continuous…

We establish accurate eigenvalue asymptotics and, as a by-product, sharp estimates of the splitting between two consecutive eigenvalues, for the Dirichlet magnetic Laplacian with a non-uniform magnetic field having a jump discontinuity…

`Hypergeometric states', which are a one-parameter generalization of binomial states of the single-mode quantized radiation field, are introduced and their nonclassical properties are investigated. Their limits to the binomial states and to…

We propose a simple description of the spectrum of edge states in the quantum Hall regime, in terms of semiclassical quantization of skipping orbits along hard wall boundaries, ${\cal A}=2 \pi (n+\gamma) \ell_B^2$, where ${\cal A}$ is the…

Wave equations with energy-dependent potentials appear in many areas of physics, ranging from nuclear physics to black hole perturbation theory. In this work, we use the semi-classical WKB method to first revisit the computation of bound…

The combined effect of finite potential barriers and dielectric mismatch between dot and matrix on excitonic properties of semiconductor quantum dots has been studied. To avoid the unphysical divergence in the self-polarization energy which…

The interaction of a quantum field with a background containing a Dirac delta function with support on a surface of codimension 1 represents a particular kind of matching conditions on that surface for the field. In this article we show…

We extend the application of the techniques developed within the framework of the pseudo-Hermitian quantum mechanics to study a unitary quantum system described by an imaginary PT-symmetric potential v(x) having a continuous real spectrum.…

Matrix configurations define noncommutative spaces endowed with extra structure including a generalized Laplace operator, and hence a metric structure. Made dynamical via matrix models, they describe rich physical systems including…

In the presence of a chemical potential, the physics of level crossings leads to singularities at zero temperature, even when the spatial volume is finite. These singularities are smoothed out at a finite temperature but leave behind…

We discuss the semiclassical limit of the entanglement for the class of closed pure systems. By means of analytical and numerical calculations we obtain two main results: (i) the short-time entanglement does not depend on Planck's constant…

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…

We study bounded, monotone solutions of$\Delta u=W'(u)$ in the whole of$\R^n$, where$W$ is a double-well potential. We prove that under suitable assumptions on the limit interface and on the energy growth, $u$ is $1$D. In particular,…