Related papers: Semi-classical analysis
In this article we give a panoramic view on semi-classical analysis.
Given a quantum Hamiltonian, we explain how the dynamical properties of the underlying classical system affect the behaviour of quantum eigenstates in the semi-classical limit. We study this problem via the notion of semiclassical measures.…
Some quantal systems require only a small part of the full quantum theory for their analysis in classical terms. In such understanding we review some recent literature on semiclassical treatments. An analysis of it allows one to see that…
Semi-classical approaches approximate fully quantum descriptions with partially classical ones. Here we use a toy model to highlight the failings of the standard mean-field semi-classical approach, and show how including environmental…
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 numerical treatment of quantum mechanics in the semi-classical regime is known to be computationally demanding, due to the highly oscillatory behaviour of the wave function and its large spatial extension. A recently proposed…
Semiclassical methods are essential in analyzing quantum mechanical systems. Although they generally produce approximate results, relatively rare potentials exist for which these methods are exact. Such intriguing potentials serve as…
These lectures are an introduction to formal semiclassical quantization of classical field theory. First we develop the Hamiltonian formalism for classical field theories on space time with boundary. It does not have to be a cylinder as in…
The application of a classical approach to various quantum problems - the secular perturbation approach to quantization of a hydrogen atom in external fields and a helium atom, the adiabatic switching method for calculation of a…
We present several recent results concerning the transition between quantum and classical mechanics, in the situation where the underlying dynamical system has an hyperbolic behaviour. The special role of invariant manifolds will be…
A nonlinear dynamics semi-classical model is used to show that standard quantum spin analysis can be obtained. The model includes a classically driven nonlinear differential equation with dissipation and a semi-classical interpretation of…
We discuss the problem of separating consistently the total correlations in a bipartite quantum state into a quantum and a purely classical part. A measure of classical correlations is proposed and its properties are explored.
We present a detailed study of scattering by an amplitude-modulated potential barrier using three distinct physical frameworks: quantum, classical, and semiclassical. Classical physics gives bounds on the energy and momentum of the…
We study interaction effects on the orbital magnetism of diffusive mesoscopic quantum systems. By combining many-body perturbation theory with semiclassical techniques, we show that the interaction contribution to the ensemble averaged…
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 propose a way to study one-dimensional statistical mechanics models with complex-valued action using transfer operators. The argument consists of two steps. First, the contour of integration is deformed so that the associated transfer…
Starting from the Schr\"odinger-equation of a composite system, we derive unified dynamics of a classical harmonic system coupled to an arbitrary quantized system. The classical subsystem is described by random phase-space coordinates…
We use semi--classical and perturbation methods to establish the quantum theory of the Neumann model, and explain the features observed in previous numerical computations.
Semiclassical methods are extremely valuable in the study of transport and thermodynamical properties of ballistic microstructures. By expressing the conductance in terms of classical trajectories, we demonstrate that quantum interference…
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…