[Paper Review] On the physical nature of Anderson localization effect

V. A. Kuz’menko|arXiv (Cornell University)|Dec 18, 2007

Cold Atom Physics and Bose-Einstein Condensates7 references3 citations

TL;DR

This paper challenges the conventional interference-based explanation of Anderson localization by proposing that its physical origin lies in the time-reversal noninvariance of quantum processes, particularly the dramatically higher differential cross-section of fully reversed transitions. It argues that the return of waves to their initial position is due to the dominance of time-reversed processes—especially in systems like cold atoms in optical lattices—where coherent feedback via mirrors enables near-perfect state reconstruction, offering a more fundamental and experimentally testable mechanism than wave interference.

ABSTRACT

An alternative explanation of the physical nature of Anderson localization phenomenon and one of the most direct ways of its experimental study are discussed.

Motivation & Objective

• To challenge the widely accepted interference-based explanation of Anderson localization.
• To propose that time-reversal noninvariance—specifically the hierarchy of differential cross-sections in forward, partially reversed, and fully reversed transitions—is the true physical origin of Anderson localization.
• To advocate for experimental measurement of differential cross-sections in quantum transitions as a direct way to study localization.
• To highlight cold atom systems in vertical optical lattices as ideal platforms for testing the proposed mechanism.

Proposed method

• Proposes a hierarchy of differential cross-sections: σ_FR ≫ σ_PR ≫ σ_F > σ_B, based on time-reversal symmetry breaking in quantum transitions.
• Analyzes scattering processes in two-level systems, distinguishing forward (σ_F), backward (σ_B), partially reversed (σ_PR), and fully reversed (σ_FR) transitions.
• Uses thought experiments with mirrors to enable fully reversed transitions (σ_FR), where photons and atoms return to initial states.
• Applies Bohmian mechanics and non-local quantum potential to explain nonlocal awareness of mirrors in reversed processes.
• Identifies cold atoms in vertical optical lattices as a realizable system for observing σ_FR dominance via Bloch oscillations.
• Argues that measuring differential cross-sections as functions of laser frequency, phase, direction, and atomic position is essential for testing the model.

Experimental results

Research questions

• RQ1 Why do scattered waves in Anderson localization return to their initial position, contrary to the diffusion model?
• RQ2 What physical mechanism underlies the suppression of wave diffusion in disordered media, beyond wave interference?
• RQ3 How does time-reversal noninvariance manifest in quantum scattering processes and affect differential cross-sections?
• RQ4 Can fully reversed quantum transitions explain the localization of light or matter waves more fundamentally than interference?
• RQ5 Why has the paradigm of time-reversal invariance in physics hindered the recognition of this mechanism?

Key findings

• The differential cross-section of fully reversed transitions (σ_FR) is predicted to exceed those of forward and partially reversed processes by more than four orders of magnitude in cold atom systems.
• Bloch oscillations of cold atoms in vertical optical lattices—observed to last ~10^4 cycles—provide strong indirect evidence for σ_FR dominance.
• The hierarchy σ_FR ≫ σ_PR ≫ σ_F > σ_B is proposed as the fundamental reason for wave localization, replacing interference as the primary mechanism.
• The return of photons to their initial state in mirror-assisted systems is explained not by interference but by the high probability of time-reversed processes.
• The nonlocality in mirror-assisted reversed transitions is resolved via non-local quantum potential, suggesting quantum systems retain memory of initial states.
• The authors conclude that the widespread belief in time-reversal invariance of physical laws is a paradigmatic obstacle to recognizing this mechanism.