Abstract
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.
Highlights
Since the dawn of mesoscopic physics, dynamical properties of small metallic grains have been attracting much attention both in experiments and in theories; they have been recognized as very useful physical realizations of the random matrix theory, because energy levels of such systems are known to exhibit strong repulsion as in random matrices
From a theoretical point of view, dynamical responses are much more complicated to investigate than energy level statistics
In a pioneering paper by Gor’kov and Eliashberg GE 1, a phenomenological theory of dynamical responses was built based on the two statistical hypothesis: i independent fluctuations between matrix elements and energy levels to single out the effect of the level repulsion, and ii the DOS correlator approximated by the Wigner-Dyson level correlator Journal of Probability and Statistics
Summary
Since the dawn of mesoscopic physics, dynamical properties of small metallic grains have been attracting much attention both in experiments and in theories; they have been recognized as very useful physical realizations of the random matrix theory, because energy levels of such systems are known to exhibit strong repulsion as in random matrices. From a theoretical point of view, dynamical responses are much more complicated to investigate than energy level statistics. It is because the former requires an additional knowledge of electron wavefunctions or matrix elements in addition to energy spectra. In a pioneering paper by Gor’kov and Eliashberg GE 1 , a phenomenological theory of dynamical responses was built based on the two statistical hypothesis: i independent fluctuations between matrix elements and energy levels to single out the effect of the level repulsion , and ii the DOS correlator approximated by the Wigner-Dyson level correlator. The effect has been unnoticed in the treatments based on the statistical hypothesis This new effect should affect the dynamical magnetto-conductivity, whose magnetic dependence can be either positive or negative by the frequency observed 12, 13. We will stress the importance of the global and gauge invariance in evaluating σ ω
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