Generalized circular ensemble of scattering matrices for a chaotic cavity with nonideal leads
Abstract
We consider the problem of the statistics of the scattering matrix S of a chaotic cavity (quantum dot), which is coupled to the outside world by nonideal leads containing N scattering channels. The Hamiltonian H of the quantum dot is assumed to be an M×M Hermitian matrix with probability distribution P(H)~det[λ2+(H-ɛ)2]-(βM+2-β)/2, where λ and ɛ are arbitrary coefficients and β=1,2,4 depending on the presence or absence of time-reversal and spin-rotation symmetry. We show that this ``Lorentzian ensemble'' agrees with microscopic theory for an ensemble of disordered metal particles in the limit M-->∞, and that for any M>=N it implies P(S)~||det(1-S¯ °S)||-(βM+2-β), where S¯ is the ensemble average of S. This ``Poisson kernel'' generalizes Dyson's circular ensemble to the case S¯≠0 and was previously obtained from a maximum entropy approach. The present work gives a microscopic justification for the case that chaotic motion in the quantum dot is due to impurity scattering.
- Publication:
-
Physical Review B
- Pub Date:
- June 1995
- DOI:
- 10.1103/PhysRevB.51.16878
- arXiv:
- arXiv:cond-mat/9501025
- Bibcode:
- 1995PhRvB..5116878B
- Keywords:
-
- 05.45.+b;
- 72.10.Bg;
- General formulation of transport theory;
- Condensed Matter
- E-Print:
- 15 pages, REVTeX-3.0, 2 figures, submitted to Physical Review B.