Related papers: Semiclassical analysis of level widths for one-dim…
We consider the problem of a semiclassical description of quantum chaotic transport, when a tunnel barrier is present in one of the leads. Using a semiclassical approach formulated in terms of a matrix model, we obtain transport moments as…
This is the third paper in a series analyzing the asymptotic distribution of the phase shifts in the semiclassical limit. We analyze the distribution of phase shifts, or equivalently, eigenvalues of the scattering matrix, $S_h(E)$, for…
Semiclassical methods provide important tools for approximating solutions in quantum mechanics. In several cases these methods are intriguingly exact rather than approximate, as has been shown by direct calculations on particular systems.…
This article is devoted to the spectral analysis of the electro-magnetic Schr\"odinger operator on the Euclidean plane. In the semiclassical limit, we derive a pseudo-differential effective operator that allows us to describe the spectrum…
Consider the semiclassical limit, as the Planck constant $\hbar\ri 0$, of bound states of a one-dimensional quantum particle in multiple potential wells separated by barriers. We show that, for each eigenvalue of the Schr\"odinger operator,…
We study self-oscillations of an optomechanical system, where coherent mechanical oscillations are induced by a driven optical or microwave cavity, for the case of an anharmonic mechanical oscillator potential. A semiclassical analytical…
We present a general semiclassical theory of the orbital magnetic response of noninteracting electrons confined in two-dimensional potentials. We calculate the magnetic susceptibility of singly-connected and the persistent currents of…
We adapt the semiclassical technique, as used in the context of instanton transitions in quantum field theory, to the description of tunneling transmissions at finite energies through potential barriers by complex quantum mechanical…
Experimental results from literature show equidistant energy levels in thin Bi films on surfaces, suggesting a harmonic oscillator description. Yet this conclusion is by no means imperative, especially considering that any measurement only…
Using semi-classical formalism and asymptotic proliferation law of periodic orbits, we obtain an analytical expressions for the two-level cluster function, spectral form factor, level spacing distribution and the number variance for…
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…
We study the low-lying eigenvalues of the semiclassical Robin Laplacian in a smooth planar domain symmetric with respect to an axis. In the case when the curvature of the boundary of the domain attains its maximum at exactly two points away…
We consider one dimensional scattering and show how the presence of a mild positive barrier separating the interaction region from infinity implies that the bound and antibound states are symmetric modulo exponentially small errors in 1/h.…
Highly excited vibrational states of an isolated molecule encode the vibrational energy flow pathways in the molecule. Recent studies have had spectacular success in understanding the nature of the excited states mainly due to the extensive…
We study the energy spectrum of a two-dimensional electron in the presence of both a perpendicular magnetic field and a potential. In the limit where the potential is small compared to the Landau level spacing, we show that the broadening…
A giant level shift, resulted from the interaction of an electron in a spherical quantum dot with zero--point oscillations of confined modes of the electric field, is divulged. The energy correction depends on the dot radius. This size…
The idealized theory of quantum vacuum energy density is a beautiful application of the spectral theory of differential operators with boundary conditions, but its conclusions are physically unacceptable. A more plausible model of a…
The eigenvalue bounds obtained earlier [J. Phys. A: Math. Gen. 31 (1998) 963] for smooth transformations of the form V(x) = g(x^2) + f(1/x^2) are extended to N-dimensions. In particular a simple formula is derived which bounds the…
Following the semiclassical formalism of Strutinsky et al., we have obtained the complete eigenvalue spectrum for a particle enclosed in an infinitely high spheroidal cavity. Our spheroidal trace formula also reproduces the results of a…
We consider the semiclassical limit of systems of autonomous PDE's in 1+1 space-time dimensions in a scattering regime. We assume the matrix valued coefficients are analytic in the space variable and we further suppose that the…