Wave function structure, ergodicity, and localization in quantum chaotic systems

Lev Kaplan, University of Washington

We discuss recent progress in the study of quantum wave functions and transport in classically ergodic
systems. Surprisingly, short-time classical dynamics leaves permanent imprints on long-time and stationary
quantum behavior, imprints that are absent from the long-time classical motion. These imprints can lead to
fine-scale quantum behavior that differs greatly from random matrix theory expectations. Robust and
quantitative predictions are obtained using semiclassical methods. Applications include wave structure on a
disordered lattice, distribution of tunneling rates in an open system, structure of many-body fermion
systems with random 2-body interactions, and the Coulomb blockade conductance peak distribution in quantum