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Fluctuations and persistence in quantum diffusion on regular lattices.

Cheng Ma1, Omar Malik1, G Korniss1

  • 1Rensselaer Polytechnic Institute, Rensselaer Polytechnic Institute, Department of Physics, Applied Physics and Astronomy, Troy, New York 12180, USA and Network Science and Technology Center, Troy, New York 12180, USA.

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This summary is machine-generated.

We studied quantum persistence in diffusion, analyzing wave function fluctuations. Persistence probability shows exponential-like tails in 1, 2, and 3 dimensions, revealing insights into quantum system dynamics.

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Area of Science:

  • Quantum mechanics
  • Statistical physics
  • Wave phenomena

Background:

  • Quantum systems exhibit complex dynamics influenced by wave function fluctuations.
  • Understanding persistence probability is key to characterizing quantum diffusion and system stability.
  • Classical diffusion models provide a framework for analogy, but quantum specifics require dedicated investigation.

Purpose of the Study:

  • To analyze amplitude and phase fluctuations of the wave function in a free-particle Schrödinger equation.
  • To define and investigate quantum persistence probability analogous to classical diffusion.
  • To characterize the decay behavior of persistence probability in various spatial dimensions.

Main Methods:

  • Solving the time-dependent free-particle Schrödinger equation.
  • Initializing the quantum system with local random uncorrelated Gaussian amplitude and phase fluctuations.
  • Analyzing two-point spatial and temporal correlation functions in the small fluctuation limit.

Main Results:

  • Quantum persistence probability exhibits exponential-like tails across dimensions.
  • In d=1, decay is a stretched exponential; in d=2 and d=3, it is exponential.
  • Long-time asymptotic analysis shows time-homogeneous temporal correlation functions for fluctuations.

Conclusions:

  • Quantum diffusion persistence is governed by stationary Gaussian processes under specific conditions.
  • The findings offer insights into the long-time behavior and stability of quantum systems.
  • The study bridges classical diffusion concepts with quantum mechanical phenomena.