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Effective equations of motion for quantum systems. (English) Zbl 1124.82010

Summary: In many situations, one can approximate the behavior of a quantum system, i.e. a wave function subject to a partial differential equation, by effective classical equations which are ordinary differential equations. A general method and geometrical picture are developed and shown to agree with effective action results, commonly derived through path integration, for perturbations around a harmonic oscillator ground state. The same methods are used to describe dynamical coherent states, which in turn provide means to compute quantum corrections to the symplectic structure of an effective system.

MSC:

82C05 Classical dynamic and nonequilibrium statistical mechanics (general)
81Q15 Perturbation theories for operators and differential equations in quantum theory
81Q20 Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory
81S30 Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics

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