Regensburg 2007 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 20: Quantum chaos I

DY 20.2: Vortrag

Mittwoch, 28. März 2007, 14:30–14:45, H2

Statistical theory of irregular eigenfunctions: a semiclassical approach — •Juan Diego Urbina and Klaus Richter — Institute for Theoretical Physics, Regensburg University, 93040 Regensburg, Germany

The spatial fluctuations of quantum wavefunctions in systems with chaotic classical dynamics or in the presence of disorder, show a remarkable universality.

In clean chaotic systems, such universality is encoded in Berry’s Random Wave Model (RWM)[1] while the exact theory of wavefunction statistics in disordered systems has been conjectured to describe not only the diffusive, but also the clean, ballistic case [2] by the so-called Ballistic Sigma Model (BSM). In particular, the BSM seems not to be compatible with the Gaussian distribution for the wavefunction’s amplitude typical of the RWM.

However, the results of the BSM can indeed be derived by means of a natural generalization of Berry’s conjecture, keeping the wavefunction’s distribution strictly Gaussian [3]. The key point is the consistent use of the diagonal approximation in order to eliminate oscillatory contributions neglected by the BSM.

In this contribution, we present the three basic ingredients of this generalization, namely, how to incorporate arbitrary boundaries into the Random Wave Model, the semiclassical approximation for the averages, and the diagonal approximation providing the link with the results for disordered systems.

[1] M. V. Berry J. Phys. A: Math. Gen. 10, 2083 (1977).

[2] A. D. Mirlin Phys. Rep. 326, 259 (2000).

[3] J. D. Urbina and K. Richter Phys. Rev. Lett. 97, 214101 (2006).