## Semiclassical Approach to Mesoscopic Systems: Classical Trajectory Correlations and Wave InterferenceThis volume describes mesoscopic systems with classically chaotic dynamics using semiclassical methods which combine elements of classical dynamics and quantum interference effects. Experiments and numerical studies show that Random Matrix Theory (RMT) explains physical properties of these systems well. This was conjectured more than 25 years ago by Bohigas, Giannoni and Schmit for the spectral properties. Since then, it has been a challenge to understand this connection analytically. The author offers his readers a clearly-written and up-to-date treatment of the topics covered. He extends previous semiclassical approaches that treated spectral and conductance properties. He shows that RMT results can in general only be obtained semiclassically when taking into account classical configurations not considered previously, for example those containing multiply traversed periodic orbits. Furthermore, semiclassics is capable of describing effects beyond RMT. In this context he studies the effect of a non-zero Ehrenfest time, which is the minimal time needed for an initially spatially localized wave packet to show interference. He derives its signature on several quantities characterizing mesoscopic systems, e. g. dc and ac conductance, dc conductance variance, n-pair correlation functions of scattering matrices and the gap in the density of states of Andreev billiards. |

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### Contents

1 Introduction | 1 |

2 Semiclassical Techniques | 12 |

3 Survival Probability and Fidelity Decay | 41 |

4 EhrenfestTime Effects in Mesoscopic Systems | 88 |

5 Semiclassical Analogues to FieldTheoretical Effects | 149 |

6 Conclusions and Outlook | 167 |

Appendix A Recursion Relations for Transport | 172 |

Appendix A Recursion Relations for Transport | 175 |

Appendix B Encounter Integrals for Nonzero EhrenfestTime | 176 |

Appendix C Conductance Variance with Tunnel Barriers | 177 |

References | 181 |

### Other editions - View all

Semiclassical Approach to Mesoscopic Systems: Classical Trajectory ... Daniel Waltner Limited preview - 2012 |

Semiclassical Approach to Mesoscopic Systems: Classical Trajectory ... Daniel Waltner No preview available - 2014 |

### Common terms and phrases

2-encounters action difference additionally Andreev billiard average cancel central periodic orbit chaotic systems configuration considered containing continuity equation correlation function decay deﬁned denoted density derived diagonal approximation duration dynamics effects Ehrenfest-time dependence encounter stretches energy exponential fidelity amplitude field-theoretical ﬁrst fringes generalised given Green function Heusler inside the system integrals Jacquod Kuipers last section leading order Lett loop Lyapunov exponent Mesoscopic Systems non-diagonal contributions non-zero Ehrenfest-time obtain orbit pairs orthogonal overlap partner perform perturbation phase phase-space Phys predicted prefactor pseudo orbits quantum chaos quantum correction quantum mechanical regime Richter RMT results Semiclassical Approach semiclassical calculation semiclassical contribution semiclassical expression semiclassical limit shown spectral determinant spectral form factor spin-orbit interaction subsection sum over orbits sum rule supersymmetry survival probability t-integral taking into account tenc time-reversal symmetry trajectories trajectory pairs transmission traversed unitary vector Waltner yields zero