Journal of Probability and Statistics
Volume 2010 (2010), Article ID 751395, 12 pages
Research Article

Universal and Nonuniversal Dynamical Conductivity in Small Metallic Grains: An Ambivalent Role of T-Invariance at Finite Frequency

Institute of Physics, University of Tsukuba, Tennodai Tsukuba 305-8571, Japan

Received 1 September 2009; Revised 12 May 2010; Accepted 15 May 2010

Academic Editor: Zhidong Bai

Copyright © 2010 Nobuhiko Taniguchi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The idea of random matrix theory is applicable not only to the level statistics but also to various physical observables. Taking the dynamical conductivity in isolated quantum dots with diffusive dynamics, we investigate analytically intertwining effects of the time-reversal invariance, level repulsion and quantum interference. We clarify an ambivalent role of the time-reversal invariance at finite frequency by a new invariant analysis respecting the symmetry of the effective field theory. A subtlety of the operator insertion, and the fast-slow mode separation within the effective field description is pointed out.