Directed Quantum Chaos
Abstract
Quantum disordered problems with a direction (imaginary vector potential) are discussed and mapped onto a supermatrix σ model. It is argued that the 0D version of the σ model may describe a broad class of phenomena that can be called directed quantum chaos. It is demonstrated by explicit calculations that these problems are equivalent to those of random asymmetric or nonHermitian matrices. A joint probability of complex eigenvalues is obtained. The fraction of states with real eigenvalues proves to be always finite for time reversal invariant systems.
 Publication:

Physical Review Letters
 Pub Date:
 July 1997
 DOI:
 10.1103/PhysRevLett.79.491
 arXiv:
 arXiv:condmat/9702091
 Bibcode:
 1997PhRvL..79..491E
 Keywords:

 Condensed Matter  Disordered Systems and Neural Networks;
 Condensed Matter  Mesoscale and Nanoscale Physics;
 Nonlinear Sciences  Chaotic Dynamics
 EPrint:
 4 pages, revtex, no figures