Phase Space Trajectory Description of Quantum Dynamics

Hai-Woong Lee, Marlan O. Scully

Quantum and classical dynamics of a Morse oscillator are investigated in a phase space using the Wigner distribution function. The phase-space description offers a pictorial representation of quantum dynamics in terms of trajectories. Based on the comparison of these trajectories with classical trajectories, a systematic scheme accurately describing quantum dynamics is presented.

Anatoli Polkovnikov

Vladimir S. Filinov

Irène Burghardt, Gérard Parlant

A new approach to the coupling of quantum and classical dynamics is developed, by combining a hydrodynamic, Bohmian description for the quantum subsystem with a Liouville-space description for the classical subsystem. To this end, partial hydrodynamic moments are introduced, the dynamics of which is determined by a hierarchy of equations derived from the quantum Liouville equation. We focus on pure states (wave functions) and introduce a trajectory representation in a hybrid hydrodynamic-Liouvillian phase space. The interleaved trajectory dynamics is guided by a new type of quantum force. For illustration, we consider a pair of bilinearly coupled harmonic oscillators, for which the method is exact.

Kazuma Nagao

Urszula Kaczor, Bogusław Klimas, Dominik Szydłowski +2 more

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.