量子图:在量子混沌和通用谱统计中的应用

IF 13.8 1区物理与天体物理 Q1 PHYSICS, CONDENSED MATTER

Advances in Physics Pub Date : 2006-05-12 DOI:10.1080/00018730600908042

Sven Gnutzmann∥, U. Smilansky

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引用次数: 290

摘要

在过去的几年里，量子图已经成为量子混沌的一个范例，从光谱统计到混沌散射和波函数统计都有应用。本文第一部分详细介绍了量子图的谱理论，讨论了谱的精确迹公式和量子-经典对应关系。本文第二部分讨论量子图的谱统计在量子混沌中的应用。特别地，我们总结了基于周期轨道方法和超对称方法两种方法的一般大量子图谱统计的最新进展。后者为随机矩阵理论所预测的谱统计量的普适性提供了一个条件和证明。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Quantum graphs: Applications to quantum chaos and universal spectral statistics

During the last few years quantum graphs have become a paradigm of quantum chaos with applications from spectral statistics to chaotic scattering and wavefunction statistics. In the first part of this review we give a detailed introduction to the spectral theory of quantum graphs and discuss exact trace formulae for the spectrum and the quantum-to-classical correspondence. The second part of this review is devoted to the spectral statistics of quantum graphs as an application to quantum chaos. In particular, we summarize recent developments on the spectral statistics of generic large quantum graphs based on two approaches: the periodic-orbit approach and the supersymmetry approach. The latter provides a condition and a proof for universal spectral statistics as predicted by random-matrix theory.

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来源期刊

Advances in Physics 物理-物理：凝聚态物理

CiteScore

67.60

自引率

0.00%

发文量

期刊介绍： Advances in Physics publishes authoritative critical reviews by experts on topics of interest and importance to condensed matter physicists. It is intended for motivated readers with a basic knowledge of the journal’s field and aims to draw out the salient points of a reviewed subject from the perspective of the author. The journal''s scope includes condensed matter physics and statistical mechanics: broadly defined to include the overlap with quantum information, cold atoms, soft matter physics and biophysics. Readership: Physicists, materials scientists and physical chemists in universities, industry and research institutes.