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

作者：Guerrero Pilar^*; Luis Lopez Jose; Montejo Gamez Jesus

来源：Journal of Physics A-Mathematical and Theoretical, 2014, 47(3): 035303.

DOI：10.1088/1751-8113/47/3/035303

• nonlinear Schrodinger equation
• logarithmic nonlinearity
• quantum Fokker-Planck dynamics

A nonlinear Schrodinger 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 Schrodinger 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.

• 出版日期2014-1-24