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Fabrication and Characterization of Disordered Polymer Optical Fibers for Transverse Anderson Localization of Light
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Published on: July 29, 2013

Quantum localization in open chaotic systems.

Jung-Wan Ryu1, G Hur, Sang Wook Kim

  • 1Department of Physics Education and Department of Physics, Pusan National University, Busan 609-735, Korea.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 15, 2008
PubMed
Summary
This summary is machine-generated.

We investigated dynamical localization in open quantum systems. Lossy quasibound states near absorbing boundaries show reduced localization lengths and enhanced decay rates, following a specific mathematical relationship.

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Area of Science:

  • Quantum mechanics
  • Open quantum systems
  • Dynamical localization

Background:

  • The delta-kicked rotor is a standard model for studying quantum chaos.
  • Open quantum systems introduce dissipation and loss, altering quantum behavior.
  • Dynamical localization is a phenomenon where quantum wave packets cease to spread.

Purpose of the Study:

  • To investigate the nature of dynamical localization in open quantum systems.
  • To analyze the behavior of quasibound states near absorbing boundaries.
  • To establish a relationship between localization length and decay rates.

Main Methods:

  • Studying a delta-kicked rotor model with absorbing boundaries.
  • Analyzing lossy quasibound states near the system's edge.
  • Deriving a relationship between localization length (xi) and decay rate (Gamma).

Main Results:

  • Localization lengths (xi) of lossy quasibound states decrease near absorbing boundaries.
  • Corresponding decay rates (Gamma) are dramatically enhanced as states approach boundaries.
  • A relationship xi approximately Gamma(-1/2) was found and explained via finite-time diffusion.

Conclusions:

  • The observed relationship between localization length and decay rate is explained by finite-time diffusion.
  • This concept is applicable to random unitary operator models.
  • The findings are conjectured to be valid for systems with classical diffusion and quantum localization.