Statistics of fluctuations for two types of crossover: from ballistic to diffusive regime and from orthogonal to unitary ensemble

TL;DR

This paper investigates the statistical properties of wave intensity fluctuations during the crossover from ballistic to diffusive transport and from orthogonal to unitary ensemble, revealing effects of coherence and magnetic field on distribution functions.

Contribution

It introduces a diagrammatic approach to analyze fluctuations during these crossovers, highlighting the impact of coherent components on intensity distributions.

Findings

Coherent contributions halve the intensity distribution at low intensities.

Oscillations appear in the distribution function due to coherence effects.

Wave function fluctuations are characterized during the orthogonal to unitary crossover.

Abstract

In our previous publication [Kogan et al, Phys. Rev. {\bf 48}, 9404 (1993)] we considered the issue of statistics of radiation diffusively propagating in a disordered medium. The consideration was in the framework of diagrammatic techniques and a new representation for the intensity distribution function in terms of connected diagrams only was proposed. Here we use similar approach to treat the issue of statistics in the regime of the crossover between ballistic and diffusive transport. We find that even small contribution from coherent component decreases by one half the intensity distribution function for small values of intensity and also produces oscillations of the distribution function. We also apply this method to study statistics of fluctuations of wave functions of chaotic electrons in a quantum dot in an arbitrary magnetic field, by calculating the single state local density in the regime of the crossover between the orthogonal and unitary ensemble.