Largest Schmidt eigenvalue of random pure states and conductance distribution in chaotic cavities

Purity distribution for bipartite random pure states

Transmission Eigenvalue Densities and Moments in Chaotic Cavities from Random Matrix Theory

We point out that the transmission eigenvalue density and higher order correlation functions in chaotic cavities for an arbitrary number of incoming and outgoing leads (N1, N2) are analytically known from the Jacobi ensemble of Random Matrix Theory. Using this result and a simple linear statistic, we give an exact and non-perturbative expression for moments of the form 〈λ1 〉 for m > −|N1−N2|−1 ...

The Largest Eigenvalue Of Sparse Random Graphs

We prove that for all values of the edge probability p(n) the largest eigenvalue of a random graph G(n, p) satisfies almost surely: λ1(G) = (1 + o(1))max{ √ ∆, np}, where ∆ is a maximal degree of G, and the o(1) term tends to zero as max{ √ ∆, np} tends to infinity.

Statistics of Conductance and Shot-Noise Power for Chaotic Cavities

We report on an analytical study of the statistics of conductance, g, and shot-noise power, p, for a chaotic cavity with arbitrary numbers N1,2 of channels in two leads and symmetry parameter β = 1, 2, 4. With the theory of Selberg’s integral the first four cumulants of g and first two cumulants of p are calculated explicitly. We give analytical expressions for the conductance and shot-noise di...

Semiclassical approach to the ac conductance of chaotic cavities

We address frequency-dependent quantum transport through mesoscopic conductors in the semiclassical limit. By generalizing the trajectory-based semiclassical theory of dc quantum transport to the ac case, we derive the average screened conductance as well as ac weak-localization corrections for chaotic conductors. Thereby we confirm respective random matrix results and generalize them by accoun...