Phase-space description of the coherent state dynamics in a small one-dimensional system

Abstract

Abstract:The Wigner-Moyal approach is applied to investigate the dynamics of the Gaussian wave packet moving in a double-well potential in the 'Mexican hat' form. Quantum trajectories in the phase space are computed for different kinetic energies of the initial wave packet in the Wigner form. The results are compared with the classical trajectories. Some additional information on the dynamics of the wave packet in the phase space is extracted from the analysis of the cross-correlation of the Wigner distribution function with itself at different points in time.

The Phase–Space Approach to time Evolution of Quantum States in Confined Systems: the Spectral Split–Operator Method

“…The presented algorithm based on the spectral split-operator method for a given initial WDF at time instant t = 0 allows one to find the time evolution of the WDF via successive application of the time evolution operator. We take the initial condition in the Wigner form of the Gaussian wave packet centered around some point (0, p 0 ) in the phase space (Kaczor et al, 2016),…”

Numerical Methods for the Wigner Equation with Unbounded Potential

“…Apart from the partial mass P r (t) defined in Eq. (4.10), we also calculate the autocorrelation of the Wigner function [20,31]:…”

“…The proposed scheme allows us to study the dynamics of many interesting quantum systems, like the Pöschl-Teller potential [18,19] and the double-well systems [17,20]. Several macroscopically measurable quantities, such as the differences in energy levels, the quantum tunneling rate, and the autocorrelation function can also be obtained with a satisfactory accuracy.…”