相关论文: Resonances In a Box

Resonances, or scattering poles, are complex numbers which mathematically describe meta-stable states: the real part of a resonance gives the rest energy, and its imaginary part, the rate of decay of a meta-stable state. This description…

We present a formulation of quantum mechanics based on orthogonal polynomials. The wavefunction is expanded over a complete set of square integrable basis in configuration space where the expansion coefficients are orthogonal polynomials in…

Much experimental effort is invested these days in fabricating nanoelectromechanical systems (NEMS) that are sufficiently small, cold, and clean, so as to approach quantum mechanical behavior as their typical quantum energy scale…

We extend the semiclassical study of the Neumann model down to the deep quantum regime. A detailed study of connection formulae at the turning points allows to get good matching with the exact results for the whole range of parameters.

We derive a semiclassical quantization for a spin, study it for not too small a spin quantum number (S>5), and compute the 2S+1 eigenvalues of a Hamiltonian exhibiting resonant tunnelling as the magnetic field parallel to the anisotropy…

We construct a non-perturbative approach based on quantum averaging combined with resonant transformations to detect the resonances of a given Hamiltonian and to treat them. This approach, that generalizes the rotating-wave approximation,…

Essential properties of semiclassical approximation for quantum mechanics are viewed as axioms of an abstract semiclassical mechanics. Its symmetry properties are discussed. Semiclassical systems being invariant under Lie groups are…

The operational meaning of some measures of noise and disturbance in measurements is analyzed and their limitations are pointed out. The cases of minimal noise and least disturbance are characterized.

We study the solutions to the wave equation in a two-dimensional tube of unit width comprised of two straight regions connected by a region of constant curvature. We introduce a numerical method which permits high accuracy at high…

We provide an overview of a canonical formalism that describes mixed quantum-classical systems in terms of statistical ensembles on configuration space, and discuss applications to measurement theory. It is shown that the formalism allows a…

We review and extend, in a self-contained way, the mathematical foundations of numerical simulation methods that are based on the use of random states. The power and versatility of this simulation technology is illustrated by calculations…

A recently introduced numerical approach to quantum systems is analyzed. The basis of a Fock space is restricted and represented in an algebraic program. Convergence with increasing size of basis is proved and the difference between…

We study semiclassical resonances generated by homoclinic trapped sets. First, under some general assumptions, we prove that there is no resonance in a region below the real axis. Then, we obtain a quantization rule and the asymptotic…

Algebraic approach to the integrability condition called shape invariance is briefly reviewed. Various applications of shape-invariance available in the literature are listed. A class of shape-invariant bound-state problems which represent…

In this paper we review a proposed geometrical formulation of quantum mechanics. We argue that this geometrization makes available mathematical methods from classical mechanics to the quantum frame work. We apply this formulation to the…

Semiclassical techniques have proven to be a very powerful method to extract physical effects from different quantum theories. Therefore, it is expected that in the near future they will play a very prominent role in the context of quantum…

Over the past six years, a detailed framework has been constructed to unravel the quantum nature of the Riemannian geometry of physical space. A review of these developments is presented at a level which should be accessible to graduate…

Analytical and numerical methods are developed to analyze the quantum nature of the big bang in the setting of loop quantum cosmology. They enable one to explore the effects of quantum geometry both on the gravitational and matter sectors…

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 study systems of bosons and fermions in finite periodic boxes and show how the existence and properties of few-body resonances can be extracted from studying the volume dependence of the calculated energy spectra. Using a…