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The phase-space approach to time evolution of quantum states in confined systems: The spectral split-operator method

Kołaczek Damian, Spisak Bartłomiej J., Wołoszyn Maciej

International Journal of Applied Mathematics and Computer Science

2019

Vol. 29, no. 3

439--451

Using the phase space approach, we consider the quantum dynamics of a wave packet in an isolated confined system with three different potential energy profiles. We solve the Moyal equation of motion for the Wigner function with the highly efficient spectral split-operator method. The main aim of this study is to compare the accuracy of the employed algorithm through analysis of the total energy expectation value, in terms of deviation from its exact value. This comparison is performed for the second and fourth order factorizations of the time evolution operator.

Wigner distribution function for propagation in a nonlinear Kerr medium

Nasalski W.

Journal of Technical Physics

1998

Vol. 39, no 1

105-114

Beam propagation in a nonlinear Kerr medium is considered within a frame of first-order nonlinear optics. An optical signal of cylindrical symmetry is described by its variance matrix of second-order moments. The beam propagation through the nonlinear sample is traced by a nonlinearly modified ray transfer matrix. The Wigner distribution function in a novel semi-linear analytic form is defined by use of booth these matrices in a scaled phase space. Numerical data pertaining to beam tracing at a self-trapping power level are given for initially chirped signals and for propagation distances that include self-collapse points.