On the microscopic and Boltzmann equation approaches to nonequilibrium superconductors: O. Entin-Wohlman and R. Orbach. Physics Department, University of California, Los Angeles, California 90024

• Publisher: Elsevier Science
• Year: 1979
• Tongue: English
• Weight: 84 KB
• Volume: 121
• Category: Article
• ISSN: 0003-4916
• DOI: 10.1016/0003-4916(79)90107-6

✦ Synopsis

We quantize area-preserving maps M of the phase plane q,p by devising a unitary operator ir transforming states / 4") into 1 $,,+l). The result is a system with one degree of freedom q on which to study the quantum implications of generic classical motion, including stochasticity. We derive exact expressions for the equation iterating wavefunctions g"(q), the propagator for Wigner functions W,,(q,p), the eigenstates of the discrete analog of the quantum harmonic oscillator, and general complex Gaussian wave packets iterated by a 0 derived from a linear M. For I 4.J associated with curves V, in q, p, we derive a semiclassical theory for evolving states and stationary states, analogous to the familiar WKB method. This theory breaks down when Q, gets so complicated as to develop convolutions of area fi or smaller. Such complication is generic; its principal morphologies are "whorls" and "tendrils," associated respectively with elliptic and hyperbolic fixed points of M. Under l?, (Gn(q) eventually transforms into a new sort of wave that no longer perceives the details of em. For all regimes, however, the smoothed j tin( appears semiclassically to be given accurately by the smoothed projection of Q, onto the q axis, both smoothings being over a de Broglie wavelength. The classical, quantum, and semiclassical theory is illustrated by computations on the discrete quartic oscillator map. We display for the first time stochastic wavefunctions, dominated by dense clusters of caustics and characterized by multiple scales of oscillation.