Quantum Variance Research Articles

Chaos and a quantum-classical correspondence in the kicked top.

The problem ``what is the quantum signature of a classically chaotic system'' is studied for the periodically kicked top. We find that the quantum variances initially grow exponentially if the corresponding classical description is chaotic. The rate of growth is connected to the corresponding classical Jacobi matrix and, thereby, to the local, classical, transient expansion rate. These connections were recently established in an analysis of the kicked pendulum for the correspondence between quantum Husimi-O'Connell-Wigner distributions and classical Gaussian ensembles. Here, we present closely related results for the kicked top by using generalized coherent states. An explanation is given for why this quantum signature of classical chaos was missed in earlier studies of the kicked top.

Chaos and the quantum-classical correspondence in the kicked pendulum.

The problem of determining the quantum signature of a classically chaotic system is studied for the periodically kicked pendulum. In parallel with the observation that chaos creates exponential growth of intrinsic fluctuations in classical, macroscopic, dissipative systems, we find that the quantum variances initially grow exponentially if the corresponding classical description is chaotic. The rate of growth is connected to the corresponding classical Jacobi matrix and, thereby, to the largest classical Liapunov exponent. These connections are established by examining the correspondence between the quantum Husimi-0 Connell-Wigner distribution and the classical Liouville distribution for an ensemble. Explicit results for the kicked pendulum are presented.

Quantum yield of electron-hole pairs in semiconductors

It is shown that the two existing theories, the "crazy-carpentry" and the probability method, are essentially equivalent in evaluating quantum yield and variance in semiconductors. Quantum yield is determined by an integro-differential equation represented in terms of the density of states, the loss parameter, and the threshold energy. The analytical method used to calculated the relative yield, i.e., the inverse of the average $e\ensuremath{-}h$ pair-creation energy, is developed for the two cases: extended crazy-carpentry and free-particle models. The optical-mode deformation-potential and the polar-mode electrostatic-potential contributions to the phonon loss are taken into account.