Regensburg 2004 – scientific programme

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DY: Dynamik und Statistische Physik

DY 46: Poster

DY 46.43: Poster

Thursday, March 11, 2004, 16:00–18:00, Poster D

Stochastic Webs and Localization in a Quantum Mechanical Kick System — •Ulf Martin Engel and Peter Eckelt — Institut für Theoretische Physik, Universität Münster, Wilhelm-Klemm-Straße 9, D-48149 Münster

The classical kicked harmonic oscillator is characterized by a very special scenario of weak chaos: in the case of resonance between the eigenfrequency of the harmonic oscillator and the frequency of the periodic forcing, periodic stochastic webs in phase space are generated [1]. We investigate the quantum dynamics [2] of this model system and show that the resulting Husimi distributions in quantum phase space exhibit the same web-like structures as in the classical case. The quantum dynamics is characterized by diffusive energy growth — just as the classical dynamics in the channels of the webs. In the case of nonresonance, the classically diffusive dynamics is quantum mechanically suppressed. We explain this bounded energy growth (which corresponds to localization in quantum phase space) by mapping the system onto the Anderson model, in a way that is motivated by the standard treatment of the quantum kicked rotor [3].

[1] G. M. Zaslavsky et al., Weak Chaos and Quasi-Regular Patterns, Cambridge University Press, Cambridge 1991. [2] G. P. Berman, V. Y. Rubaev and G. M. Zaslavsky, Nonlinearity, 4 543 (1991). [3] S. Fishman, D. R. Grempel and R. E. Prange, Phys. Rev. Lett. 49, 509 (1982). [4] U. M. Engel, Dissertation Universität Münster (2003).