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DY: Dynamik und Statistische Physik

DY 27: Quantenchaos II

DY 27.3: Vortrag

Dienstag, 12. März 2002, 17:00–17:15, H3

Gaussian hypothesis for wave functions in clean chaotic systems: A semiclassical approach to interaction matrix element statistics — •Juan Diego Urbina and Klaus Richter — Institut for Theoretical Physics, University of Regensburg, D-93040 Regensburg

The Gaussian hypothesis for chaotic clean systems states [1] that the amplitude fluctuations of chaotic wave functions in the semiclassical regime are Gaussian distributed. Further generalizations of the conjecture by Srednicki and Hortikar [2,3] have been shown to agree with the corresponding disordered-systems approach in the universal limit of very large wave number.

On the other hand, explicit calculations show deviations form the Gaussian behaviour in disorderd systems [4] beyond a certain scale.

We present a formal derivation of the Gaussian hypothesis using semiclassical methods and succesfully show that its range of validity in ballistic systems is much larger than in the disordered case. Explicit numerical calculations for interaction matrix element’s distributions are in accordance with our results.
[1]. M. V. Berry, J. Phys A 10, 2083 (1977).
[2]. S. Hortikar and M Srednicki, Phys. Rev. Lett. 80, 1646 (1998).
[3]. S. Hortikar and M Srednicki, Phys. Rev. E 57, 7313 (1998).
[4]. I.V. Gonyi and A.D Mirlin, cond-math/0105103