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Updated: Jul 9, 2025

Fabrication and Characterization of Disordered Polymer Optical Fibers for Transverse Anderson Localization of Light

Fabrication and Characterization of Disordered Polymer Optical Fibers for Transverse Anderson Localization of Light

Published on: July 29, 2013

Universal Anderson localization in one-dimensional unitary maps.

Ihor Vakulchyk^1,2, Sergej Flach^1,2

¹Center for Theoretical Physics of Complex Systems, Institute for Basic Science (IBS), Daejeon 34126, Republic of Korea.

Chaos (Woodbury, N.Y.)

|December 7, 2023

Summary

This summary is machine-generated.

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We discovered universal Anderson localization in discrete-time quantum maps. Strong disorder leads to exponentially localized eigenstates with a single, tunable localization length, offering new insights into quantum chaos.

Area of Science:

Quantum physics
Condensed matter physics
Disordered systems

Background:

Anderson localization describes the suppression of wave function propagation in disordered systems.
Discrete-time quantum maps offer a simplified yet powerful model for studying quantum dynamics.

Purpose of the Study:

To investigate Anderson localization in one-dimensional discrete-time quantum maps.
To analyze the impact of disorder on quantum dynamics and eigenstate localization.
To develop an exact theory for the localization length.

Main Methods:

Studying Anderson localization in discrete-time quantum map dynamics.
Introducing nearest-neighbor hopping strength θ and quasienergies on the unit circle.
Analyzing the effect of strong disorder in a local phase field.

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Last Updated: Jul 9, 2025

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Main Results:

Demonstrated uniform spectrum gaplessly occupying the unit circle under strong disorder.
Observed that all resulting eigenstates are exponentially localized.
Found that Anderson localization is universal, with all eigenstates sharing the same localization length (Lloc).

Conclusions:

Developed an exact theory for calculating the localization length: 1/Lloc=|ln(|sin(θ)|)|.
Showcased that the localization length is tunable from zero to infinity by varying the hopping strength θ.
Confirmed universal Anderson localization in this quantum system.