Exact solution for the distribution of transmission eigenvalues in a disordered wire and comparison with randommatrix theory
Abstract
We consider the complete probability distribution P(\{T_{n}\}) of the transmission eigenvalues T_{1},T_{2},...,T_{N} of a disordered quasionedimensional conductor (length L much greater than width W and mean free path l). The FokkerPlanck equation which describes the evolution of P with increasing L is mapped onto a Schrödinger equation by a Sutherlandtype transformation. In the absence of timereversal symmetry (e.g., because of a magnetic field), the mapping is onto a freefermion problem, which we solve exactly. The resulting distribution is compared with the predictions of randommatrix theory (RMT) in the metallic regime (L<<Nl) and in the insulating regime (L>>Nl). We find that the logarithmic eigenvalue repulsion of RMT is exact for T_{n}'s close to unity, but overestimates the repulsion for weakly transmitting channels. The nonlogarithmic repulsion resolves several longstanding discrepancies between RMT and microscopic theory, notably in the magnitude of the universal conductance fluctuations in the metallic regime, and in the width of the lognormal conductance distribution in the insulating regime.
 Publication:

Physical Review B
 Pub Date:
 March 1994
 DOI:
 10.1103/PhysRevB.49.7499
 arXiv:
 arXiv:condmat/9310066
 Bibcode:
 1994PhRvB..49.7499B
 Keywords:

 72.10.Bg;
 05.60.+w;
 72.15.Rn;
 73.50.Bk;
 General formulation of transport theory;
 Localization effects;
 General theory scattering mechanisms;
 Condensed Matter
 EPrint:
 20 pages, REVTeX3.0, INLOPUB931028a