Anderson localization as a parametric instability of the linear kicked oscillator

Area of Science:

• Condensed Matter Physics
• Quantum Chaos
• Statistical Mechanics

Background:

• The Anderson model describes electron localization in disordered systems.
• The kicked oscillator is a classical system exhibiting chaotic behavior.

Purpose of the Study:

• To establish a rigorous connection between the Anderson model and a classical noisy kicked oscillator.
• To understand Anderson localization through the lens of classical parametric instability.

Main Methods:

• Analysis of the one-dimensional standard Anderson model.
• Comparison with a classical kicked oscillator featuring a noisy frequency.

Main Results:

• Anderson localization corresponds to parametric instability in the oscillator.
• Localization length is directly related to the oscillator's energy growth rate.
• An analytical expression for weak disorder was derived, applicable across the energy band.

Conclusions:

• A clear correspondence exists between quantum Anderson localization and classical oscillator instability.
• This provides a new perspective for studying localization phenomena.