A wavefunction description of quantum Fokker&-Planck dissipation: derivation and numerical approximation of transient dynamics Articles uri icon

publication date

  • January 2014

start page

  • 1

end page

  • 21


  • 3, 035303


  • 47

International Standard Serial Number (ISSN)

  • 1751-8113

Electronic International Standard Serial Number (EISSN)

  • 1751-8121


  • A nonlinear Schrödinger equation describing how a quantum particle interacts with its surrounding reservoir is derived from the Wigner-Fokker-Planck equation (WFPE) via stochastic (Nelsonian) mechanical techniques. This model can be reduced just to a logarithmic Schr ̈odinger equation through a suitable gauge transformation that allows one to explore its steady state dynamics and makes its mathematical and numerical analysis more tractable. The transient behavior of the standard deviation from the mean position associated with its solutions is also studied numerically and compared with that stemming from the WFPE.


  • nonlinear schrödinger equation; logarithmic nonlinearity; quantum fokker-planck dynamics