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Single-point position and transition defects in continuous time quantum walks.

Z J Li1, J B Wang2

  • 1Institute of Theoretical Physics, Shanxi University, Taiyuan, 030006, China.

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Summary
This summary is machine-generated.

We analyzed continuous time quantum walks (CTQW) with defects, finding bound states that control probability localization. Defect parameters allow precise quantum control over CTQW dynamics.

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Area of Science:

  • Quantum mechanics
  • Quantum information science
  • Condensed matter physics

Background:

  • Continuous time quantum walks (CTQW) are a quantum analogue of classical random walks.
  • Defects in quantum systems can significantly alter their behavior and properties.

Purpose of the Study:

  • To analyze CTQW with single-point position and transition defects.
  • To understand the influence of these defects on quantum walk dynamics and probability distributions.

Main Methods:

  • Analytical solutions for traveling waves and bound states were derived.
  • The state vector of CTQW was projected onto bound states.
  • The number of bound states was analyzed in relation to defect parameters.

Main Results:

  • Analytical solutions for traveling waves and bound states were obtained.
  • The number of bound states depends critically on defect parameters.
  • Localized probability peaks were achieved by projecting onto bound states.
  • Interference between bound states was observed with transition defects.

Conclusions:

  • Defects provide a mechanism for controlling CTQW dynamics.
  • Precise quantum control is achievable by tuning defect parameters.
  • The study offers insights into the localization and spreading of quantum probability.