Fractional Schrödinger dynamics and decoherence

Kay Kirkpatrick, Yanzhi Zhang

Research output: Contribution to journalArticlepeer-review


We study the dynamics of the Schrödinger equation with a fractional Laplacian (−Δ)α, and the decoherence of the solution is observed. Analytically, we obtain equations of motion for the expected position and momentum in the fractional Schödinger equation, equations that are the fractional counterpart of the well-known Newtonian equations of motion for the standard (α=1) Schrödinger equation. Numerically, we propose an explicit, effective numerical method for solving the time-dependent fractional nonlinear Schrödinger equation—a method that has high order spatial accuracy, requires little memory, and has low computational cost. We apply our method to study the dynamics of fractional Schrödinger equation and find that the nonlocal interactions from the fractional Laplacian introduce decoherence into the solution. The local nonlinear interactions can however reduce or delay the emergence of decoherence. Moreover, we find that the solution of the standard NLS behaves more like a particle, but the solution of the fractional NLS behaves more like a wave with interference effects.

Original languageEnglish (US)
Pages (from-to)41-54
Number of pages14
JournalPhysica D: Nonlinear Phenomena
StatePublished - Oct 1 2016


  • Center of mass
  • Decoherence
  • Fourier pseudo-spectral method
  • Fractional Schrödinger equation
  • Fractional momentum

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics


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