Statistics of quantum transport in chaotic cavities with broken time-reversal symmetry

Abstract

The statistical properties of quantum transport through a chaotic cavity are encoded in the traces $\T={\rm Tr}(tt^†)^n$, where $t$ is the transmission matrix. Within the Random Matrix Theory approach, these traces are random variables whose probability distribution depends on the symmetries of the system. For the case of broken time-reversal symmetry, we present explicit closed expressions for the average value and for the variance of $\T$ for all $n$. In particular, this provides the charge cumulants $\Q$ of all orders. We also compute the moments $<g^n>$ of the conductance $g={\mathcal{T}}_1$. All the results obtained are exact, {\it i.e.} they are valid for arbitrary numbers of open channels.

arXiv comment5 pages, 4 figures. v2-minor changes

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