Bäcker A, Fürstberger S, Schubert R
Institut für Theoretische Physik, TU Dresden, D-01062 Dresden, Germany.
Phys Rev E Stat Nonlin Soft Matter Phys. 2004 Sep;70(3 Pt 2):036204. doi: 10.1103/PhysRevE.70.036204. Epub 2004 Sep 14.
For the representation of eigenstates on a Poincare section at the boundary of a billiard different variants have been proposed. We compare these Poincare Husimi functions, discuss their properties, and based on this select one particularly suited definition. For the mean behavior of these Poincare Husimi functions an asymptotic expression is derived, including a uniform approximation. We establish the relation between the Poincare Husimi functions and the Husimi function in phase space from which a direct physical interpretation follows. Using this, a quantum ergodicity theorem for the Poincare Husimi functions in the case of ergodic systems is shown.
对于在台球边界的庞加莱截面上本征态的表示，已经提出了不同的变体。我们比较这些庞加莱胡西米函数，讨论它们的性质，并在此基础上选择一个特别合适的定义。对于这些庞加莱胡西米函数的平均行为，推导了一个渐近表达式，包括一个一致逼近。我们建立了庞加莱胡西米函数与相空间中的胡西米函数之间的关系，由此可得出直接的物理解释。利用这一点，证明了遍历系统情况下庞加莱胡西米函数的量子遍历性定理。
