Двумерные электроны низкой плотности в магнитном поле

The photoluminescence spectrum from the two-dimensional low density electrons with the localized valence-band holes in magnetic field is studied. The ground state is considered as Wigner crystal ore the strongly correlated electron system. For the quantum Wigner crystal the Landau levels for vacancions (quasiholes appearing in the process of photoluminescence) are calculated in the quasiclassical approximation. The spectrum of single-particle excitations for a triangular lattice in the nearest-neighbor approximation is used. It is found that Landau levels for vacancions depend unusually on magnetic field. For the electron system with strong Coulomb interaction the Mahan exciton effect in the photoluminescence for the two-dimensional electrons in magnetic field is considered.

The breakthrough of a quantum chemist by classical dynamics: Martin Karplus and the birth of computer simulations of chemical reactions

Abstract1964–1965 was an early, crucial period in Martin Karplus’ research—a time when, rather unexpectedly, he approached the problem of reactive collisions using a quasiclassical approximation with the aid of computer technologies. This marked a substantial departure from the quantum-chemical studies of nuclear magnetic resonance that had, until then, dominated his work. The historical perspective outlined by George Schatz, as well Karplus’ own biography, partly frames the contours of this remarkable period in the history of theoretical chemistry. Yet, the available historical literature is not sufficiently complete to allow us to understand Karplus’ transition from nuclear magnetic resonance to reaction dynamics. In this article, we discuss the intellectual ground on which Karplus operated around 1964, further commenting on the relevance of his quantum and quasiclassical studies and pondering how Karplus’ approach eventually led to his interest in the simulation of complex biomolecules.

Consistent Theory of Alpha-Decay

In the framework of the Goldberger–Watson decay theory, we consider the a-decay of nuclei as a transition between the initial bound state of the nucleus and scattering states of the continuum spectrum with a-particle. The scattering wave functions for the a-decay with arbitrary orbital angular momentum are derived in the quasiclassical approximation. The a-particle is described by the square-integrable wave packet formed by these functions, whose amplitude exponentially grows outside the nucleus up to the wave front. The Moshinsky’s distortions of the a-wave front are analyzed. The derived general expression for the decay rate is approximated by the quasiclassical formula.

Non-coherent diffusion of a vacancy in a one-dimensional lattice in the quasiclassical approximation

A vacancy in a one-dimensional lattice is considered as a vacant site in a one-dimensional chain of atoms. The energy model of this system is a double potential well with two levels. Based on the relations of nonequilibrium statistical mechanics, including the Kubo formula for the transport coefficient, the frequency of vacancy jumps is calculated. In this case, two factors of the system perturbation are taken into account: lattice deformation associated with the formation of an empty site, and phonon scattering by mass fluctuations in the chain. An analysis of two high-temperature jumps is given. First, the classical limit of vacancy motion under weak coupling conditions is considered for small values of the gradient of the interaction potential of the defect with the chain. In the classical case, the transition of an atom adjacent to a vacancy occurs through a quasy-stationary excited state. Secondly, a jump under tight binding conditions, when the motion of a neighboring atom occurs through a quasistationary state of finite width, and therefore having a finite lifetime.

Properties of Non-Instant and Nonlocal Corrections

The derived nonlocal and non-instant shifts are discussed with respect to various symmetries and gauges. The classical counterparts are derived and found in agreement with the expected phenomenological ones from chapter 3. The explicit forms of the hard-sphere like offsets and the delay time in terms of the scattering phase shifts are calculated and discussed on the example of nuclear collision. The numerical results reveal an interesting inside into the microscopic correlations developed in dependence on the scattering angle and scattering energy. The just-accomplished derivation of the nonlocal scattering integrals is far from being intuitive. We have reached our task, the kinetic equation, being guided by nothing but systematic implementation of the quasiclassical approximation and the limit of small scattering rates.