Quantum ergodicity: fundamentals and applications
نویسنده
چکیده
III. Quantum dynamics in phase space. Ergodicity near the classical limit. 19 A. Quick summary of classical Hamiltonian dynamics in phase-space. 19 1. Exercises 22 B. Quantum systems in first and second quantized forms. Coherent states. 22 C. Wigner-Weyl quantization 24 1. Coordinate-Momentum representation 24 D. Coherent state representation. 29 E. Coordinate-momentum versus coherent state representations. 33 F. Spin systems. 34 1. Exercises 36 G. Quantum dynamics in phase space. Truncated Wigner approximation (Liouvillian dynamics) 37 1. Single particle in a harmonic potential. 40 2. Collapse (and revival) of a coherent state 42 3. Spin dynamics in a linearly changing magnetic field: multi-level Landau-Zener problem. 44 4. Exercises 46 H. Path integral derivation. 46 1. Exercises 53 I. Ergodicity in the semiclassical limit. Berry’s conjecture 53
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