Dresden 2009 – scientific programme
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DY: Fachverband Dynamik und Statistische Physik
DY 15: Quantum chaos I
DY 15.2: Talk
Wednesday, March 25, 2009, 14:30–14:45, HÜL 386
Quantum corrections to the fidelity — •Daniel Waltner1, Boris Gutkin2, Martha Gutiérrez1, Jack Kuipers1, and Klaus Richter1 — 1Institut für Theoretische Physik, Universität Regensburg, 93040 Regensburg, Germany — 2Fachbereich Physik, Universität Duisburg-Essen, 47048 Duisburg, Germany
We study semiclassically quantum corrections to the fidelity for a classically chaotic system. We consider in addition to the diagonal approximation [1], also the effect of very similar trajectory pairs differing in encounters [2] in different regimes of the fidelity decay. We find agreement of our results for the Fermi Golden Rule regime with predictions from Random Matrix Theory (RMT) [3]. Going beyond RMT, we also study the effect of a finite Ehrenfest time on our results for the Fermi Golden Rule regime and make predictions for nondiagonal corrections to the fidelity in the Lyapunov regime inaccessible to RMT.
Using recursion relations to count the considered diagrams, we further show the unitarity of our theory and a relation between the fidelity amplitude and the spectral form factor [4].
[1] F. M. Cucchietti, H. M. Pastawski, R. A. Jalabert, Phys. Rev.
B 70, 035311 (2004),
[2] D. Waltner, M. Gutiérrez, A. Goussev, K. Richter, Phys. Rev.
Lett. 101, 174101 (2008),
[3] H.-J. Stöckmann, R. Schäfer, New J. Phys. 6, 199 (2004),
[4] H. Kohler, I.E. Smolyarenko, C. Pineda, T. Guhr, F. Leyvraz,
T.H. Seligman, Phys. Rev. Lett. 100, 190404 (2008).