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Localization-delocalization transition in discrete-time quantum walks with long-range correlated disorder.

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Area of Science:

  • Quantum mechanics
  • Condensed matter physics
  • Complex systems

Background:

  • Quantum walks are fundamental tools for quantum computation and simulation.
  • Disorder is crucial for understanding localization phenomena in quantum systems.
  • Long-range correlated disorder presents unique challenges compared to short-range disorder.

Purpose of the Study:

  • To investigate the impact of spatially long-range correlated phase disorder on a quantum walk on a line.
  • To analyze the scaling behavior of the walker's wave packet under such disorder.
  • To identify and characterize the localization-delocalization transition and intermediate dynamical regimes.

Main Methods:

  • Implementation of a Hadamard quantum walk on a line.
  • Introduction of long-range correlated phase disorder using fractional Brownian motion with a power-law spectrum (1/k^{2α}).
  • Analysis of the wave packet's scaling behavior and localization properties.

Main Results:

  • A localization-delocalization transition was observed, controlled by the correlation exponent α.
  • Two distinct intermediate dynamical regimes were identified between full localization and complete delocalization.
  • The exponent α dictates the degree of correlation and influences the walker's transport properties.

Conclusions:

  • Spatially long-range correlated disorder significantly alters quantum walk dynamics.
  • The correlation exponent α provides a tunable parameter to control the transition between localization and delocalization.
  • The study reveals novel intermediate dynamical regimes, expanding the understanding of quantum transport in disordered systems.