Related papers: Semiclassical Approximation with two small paramet…
Experimentally, certain degrees of freedom may appear classical because their quantum fluctuations are smaller than the experimental error associated with measuring them. An approximation to a fully quantum theory is described in which the…
A semiclassical Bohr-Sommerfeld approximation is derived for an N-particle, two-mode Bose-Hubbard system modeling a Bose-Einstein condensate in a double-well potential. This semiclassical description is based on the `classical' dynamics of…
We discuss the fluctuation properties of diagonal matrix elements in the semiclassical limit in chaotic systems. For extended observables, covering a phase space area of many times Planck's constant, both classical and quantal distributions…
A new pseudoclassical supersymmetrical model of a spinning particle in 2+1 dimensions is proposed. Different ways of its quantization are discussed. They all reproduce the minimal quantum theory of the particle.
Bifurcations of classical orbits introduce divergences into semiclassical spectra which have to be smoothed with the help of uniform approximations. We develop a technique to extract individual energy levels from semiclassical spectra…
In this short paper we discuss the precise relationship between the semiclassical and standard pseudodifferential algebras and explore implications such as for large spectral parameter elliptic estimates, even in the case of…
Semiclassical mechanics of systems with first-class constraints is developed. Starting from the quantum theory, one investigates such objects as semiclassical states and observables, semiclassical inner product, semiclassical gauge…
We derive explicit semiclassical quantisation conditions for the Dirac and Pauli equations. We show that the spin degree of freedom yields a contribution which is of the same order of magnitude as the Maslov correction in…
The exactness of the semiclassical method for three-dimensional problems in quantum mechanics is analyzed. The wave equation appropriate in the quasiclassical region is derived. It is shown that application of the standard leading-order WKB…
Higher-order WKB methods are used to investigate the border between the solvable and insolvable portions of the spectrum of quasi-exactly solvable quantum-mechanical potentials. The analysis reveals scaling and factorization properties that…
Harmonic inversion techniques have been shown to be a powerful tool for the semiclassical quantization and analysis of quantum spectra of both classically integrable and chaotic dynamical systems. Various computational procedures have been…
The fidelity amplitude is a quantity of paramount importance in echo type experiments. We use semiclassical theory to study the average fidelity amplitude for quantum chaotic systems under external perturbation. We explain analytically two…
Reviewing the semiclassical theory for the parametric level density fluctuations, we show that for large parametric changes the density correlation function, after rescaling, becomes universal and coincides with the leading asymptotic term…
We introduce a semiclassical quantization method which is based on a stroboscopic description of the classical and the quantum flows. We show that this approach emerges naturally when one is interested in extracting the energy spectrum…
The purpose of this paper is to use semiclassical analysis to unify and generalize Lp estimates on high energy eigenfunctions and spectral clusters. In our approach these estimates do not depend on ellipticity and order, and apply to…
Quantile-based classifiers can classify high-dimensional observations by minimising a discrepancy of an observation to a class based on suitable quantiles of the within-class distributions, corresponding to a unique percentage for all…
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…
In this article, we propose a penalized high dimensional semiparametric model average quantile prediction approach that is robust for forecasting the conditional quantile of the response. We consider a two-step estimation procedure. In the…
A semiclassical approach is used to obtain Lorentz covariant expressions for the form factors between the kink states of a quantum field theory with degenerate vacua. Implemented on a cylinder geometry it provides an estimate of the…
We prove dispersive estimates for the wave and Schrodinger groups associated to a second-order elliptic self-adjoint operator depending on a semi-classical parameter. Applications are made to non-trapping metric perturbations and to…