Classical limit of quantum chaos

✍ Scribed by Mario Feingold; Nimrod Moiseyev; Asher Peres

• Publisher: Elsevier Science
• Year: 1985
• Tongue: English
• Weight: 300 KB
• Volume: 117
• Category: Article
• ISSN: 0009-2614
• DOI: 10.1016/0009-2614(85)85241-6

✦ Synopsis

When a quantum system has a ciassieally chaotic analog, the expce~atlon value (E[AlE> of any dynamical variable A. for an energy eigenstare IE). lends to tie ciassiul microcanonical average of the analog variable A. 01 the Same energy E Some numerical examples are discti. Although there is no consensus on the definition ornature ofquantum chaos, nor even on its existence, there appears to be a growing body of theoretical [l-71 and numerical [S-12] evidence in support of the followmg property: If a quantum system has a classically chaotic analog, then, in the semiclassical limit fi --f 0, the energy eigenfunctions fill the entire accessible phase space and, moreover, their Wigner distributions [13] ffuctuate around the classical microcanonical phase space density. * This result was pre&ctcd by Berry 1261. An interesting problem, which we did not solve, is to estimate the deviahon of the. quantum results from the classical ones. It probably behawx as a power of 7l_ 346