Periodic Orbits and Recurrences: An Introduction and Review
The study of periodic classical orbits of quantum systems is a branch of the field called “quantum chaos,” which is the study of quantum-mechanical systems whose classical counterparts exhibit chaotic motion. Many examples have now been examined: a one-electron atom in magnetic field, an atom in an oscillating electric field, any molecule in a high vibrational state, a “quantum billiard,” such as an electron in a stadium-shaped microjunction, and numerous model systems, including the Henon-Heiles oscillator, quantum maps, or geodesic motion of a particle on a surface of constant negative curvature. Always the central issues are: How do we use information about classical orbits to generate information about quantum wave-functions? Can we interpret observations on a quantum system using classical or semiclassical mechanics? How does classically chaotic behavior manifest itself in quantum properties of a system?
KeywordsPeriodic Orbit Quantum Property Maslov Index Conductance Spectrum Geodesic Motion
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