Nonlinear Sciences – Chaotic Dynamics
Scientific paper
2001-12-25
J. Phys. A: Math. Gen. 36 (2003) 9081-9103
Nonlinear Sciences
Chaotic Dynamics
published version, 33 pages, 7 figres
Scientific paper
10.1088/0305-4470/36/34/310
We consider generalized Husimi distributions for many-body systems, and show that their moments are good measures of complexity of many-body quantum states. Our construction of the Husimi distribution is based on the coherent state of the single-particle transformation group. Then the coherent states are independent-particle states, and, at the same time, the most localized states in the Husimi representation. Therefore delocalization of the Husimi distribution, which can be measured by the moments, is a sign of many-body correlation (entanglement). Since the delocalization of the Husimi distribution is also related to chaoticity of the dynamics, it suggests a relation between entanglement and chaos. Our definition of the Husimi distribution can be applied not only to the systems of distinguishable particles, but also to those of identical particles, i.e., fermions and bosons. We derive an algebraic formula to evaluate the moments of the Husimi distribution.
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