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Non-Hermitian localization and delocalization.

J Feinberg1, A Zee

  • 1Institute for Theoretical Physics, University of California at Santa Barbara, Santa Barbara, CA 93106, USA. joshua@physics.technion.ac.il

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|April 24, 2002
PubMed
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This study explores quantum systems with non-Hermitian Hamiltonians, revealing a unique "forked" structure in their density of states and analyzing localization-delocalization transitions.

Area of Science:

  • Condensed Matter Physics
  • Quantum Mechanics

Background:

  • Non-Hermitian Hamiltonians are crucial for modeling open quantum systems and phenomena like vortex pinning in superconductors.
  • Understanding localization and delocalization transitions is key to predicting material properties and system behavior.

Purpose of the Study:

  • To investigate localization and delocalization phenomena in non-Hermitian Hamiltonians.
  • To analytically describe the emergence of a forked structure in the density of states.
  • To calculate the divergence of localization length at phase transitions.

Main Methods:

  • Analytical descriptions of simplified non-Hermitian models.
  • Calculation of localization length divergence.
  • Mapping to a two-dimensional random walker problem.

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Main Results:

  • Analytic descriptions of nonperturbative forked structures (wings) in the density of states.
  • Quantification of localization length divergence at the transition point.
  • Identification of intricate density of states structures in specific models.

Conclusions:

  • Non-Hermitian Hamiltonians exhibit complex behaviors, including unique spectral structures.
  • The study provides a framework for understanding localization-delocalization transitions in these systems.
  • Connections to random walker models offer new perspectives on quantum phenomena.