Study of the Survival Probability and the Phase Diagram of the Electronic Frenkel-Kontorova Model(1)Current topics of quantum chaos in nanosciences, Chaos and Nonlinear Dynamics in Quantum-Mechanical and Macroscopic Systems)

Abstract

Electron transport in the Frenkel-Kontorova(FK) model is studied. The survival probability and, in particular, the dependence of the survival probability on the system size, is investigated. Based on these results, we obtain an approximate phase diagram of the FK model. The FK model is either Harper-like or Fibonacci-like, and there is a critical point separating these two states. It seems that this point corresponds to the breaking of analyticity transition critical point in the classical FK model.