Evolution of semiclassical quantum states in phase space

作者: M V Berry

DOI: 10.1088/0305-4470/12/5/012

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摘要: We derive a semiclassical formula for the Wigner function W(q, p, f) describing evolution in two-dimensional phase space qp of nonstationary quantum state $(q, i) system with one degree freedom. The initial 0) corresponds to family classical orbits represented by curve V0 qp. Under motion Vo evolves into V,; we show that region where W is large hugs V, an adiabatic fashion, and has oscillations depending only on geometry (e, neighbouring curves. As t + CO, can get very complicated, classify its convolutions as 'whorls' 'tendrils', associated respectively stable unstable motion. In these circumstances cannot resolve details V,, at time f, there transition new regimes, which make predictions about morphology $ from way fills regions t-r CO. regimes whorls tendrils are different. expect = O(h-2'3) I, O(ln h-') tendrils.

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