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

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

2008-05-29

arxiv.org/abs/0805.4590v2

Phys. Rev. B 78, 035337 (2008)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

5 pages, 4 figures. v2-minor changes

Scientific paper

10.1103/PhysRevB.78.035337

The statistical properties of quantum transport through a chaotic cavity are encoded in the traces $\T={\rm Tr}(tt^\dag)^n$, 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 $$ 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.

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