Semiclassical Approximation to Quantum Mechanics

Vladislav G. Bagrov, Владимир Владимирович Белов, M. F. Kondrat’eva

Robert I. Cukier, Manuel Morillo

A Hamiltonian describing the interaction of a two-level system with an oscillator and an external field that induces transitions between the two levels is analyzed using the quantum mechanical (QM) solution and a semiclassical (SC) approximation. The Hamiltonian can describe coherent optical transitions and coherences in electron transfer processes. We focus on strongly driven systems where coherent oscillations of the populations of the two-level system are important and show that in this regime the SC approximation is a good representation of the QM behavior. The results are interpreted by constructing appropriate Landau-Zener-Massey parameters.

Виктор Павлович Маслов, M. V. Fedoriuk

T. F. Kamalov

Abstract The semiclassical approximation of quantum computing and quasi-qubits (s-bits) have been obtained by us as a result of our work over the past few years. This work can be conventionally divided into two parts. The first part, let’s call it the programming model, contains a computer model of quasi-qubits and quantum computing. The second part, let’s call it the microelectronic model, describes the microelectronic realization of qubits in the semiclassical approximation (quasi-qubits) and exists in the form of block diagrams, which are supposed to be easy to manufacture. How did we get the semiclassical approximation? The difficulty in solving such a problem was that microparticles in quantum mechanics are described in an infinite-dimensional Hilbert space. Classical models are much poorer in the number of variables; therefore, it is impossible to describe quantum mechanical objects by classical methods due to the small number of available parameters.

Steven M. Moore

Semiclassical approximations are developed for stochastic mechanics and stochastic field theory at positive temperatures. The tunneling phenomena of Euclidean quantum mechanics is seen to have a statistical interpretation. A semiclassical algorithm for calculating the generating functional of the moments of the positive-temperature process is developed. Positive-temperature fluctuations around a scalar soliton and in the pure SU(2) Yang–Mills theory are also briefly considered.