Deterministic Weak Localization in Periodic Structures

TL;DR

This paper demonstrates the existence of deterministic weak localization in perfect periodic structures with classical diffusion, showing quantum effects like power law decay and robustness against weak randomness, and discusses state localization and tunneling effects.

Contribution

It introduces the concept of deterministic weak localization in periodic structures and analyzes its characteristics and robustness, which is a novel insight in quantum chaos and condensed matter physics.

Findings

Weak localization occurs in perfect periodic structures with classical diffusion.

Quantum power law decay appears at four times the Ehrenfest time.

Weak localization is robust against weak randomness such as impurities.

Abstract

The weak localization is found for perfect periodic structures exhibiting deterministic classical diffusion. In particular, the velocity autocorrelation function develops a universal quantum power law decay at 4 times Ehrenfest time, following the classical stretched-exponential type decay. Such deterministic weak localization is robust against weak enough randomness (e.g., quantum impurities). In the 1D and 2D cases, we argue that at the quantum limit states localized in the Bravis cell are turned into Bloch states by quantum tunnelling.