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A quantum random walk model on a fluctuating lattice shows directed motion is possible. Nonzero transition rates are essential for particle velocity, which can reverse direction multiple times.

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Area of Science:

  • Quantum mechanics
  • Condensed matter physics
  • Statistical mechanics

Background:

  • Quantum random walks (QRWs) are fundamental in quantum information and computation.
  • Modeling dynamical systems with fluctuating properties is crucial for understanding complex behaviors.

Purpose of the Study:

  • To establish a quantum random-walk model on a fluctuating one-dimensional periodic lattice.
  • To analyze the conditions and characteristics of directed motion in such a system.

Main Methods:

  • Development of a model using Lindblad rate equations to describe lattice state transitions.
  • Leveraging system symmetries to derive a finite set of equations for particle velocity.
  • Analytical derivation of long-time limit velocity for directed motion analysis.

Main Results:

  • Particle velocity can be described by a finite set of equations despite an infinite-dimensional state space.
  • An analytical expression for long-time limit velocity was obtained.
  • Multiple velocity inversions were observed, indicating complex dynamics.
  • Directed motion requires distinct, nonzero transition rates between lattice states.

Conclusions:

  • The study provides a theoretical framework for understanding quantum walks on fluctuating lattices.
  • Nonzero transition rates are a critical requirement for achieving directed motion.
  • The model offers insights into the control and characteristics of quantum transport in dynamic environments.