Keith H Hughes | PubMed Health

PubMed2005

Dissipative quantum phase space dynamics on dynamically adapting grids.

A moving grid approach to a dynamical study of dissipative systems is described. The dynamics are studied in phase space for the Caldeira-Leggett master equation. The grid movement is based on the principle of equidistribution and, by using a grid smoothing technique, the grid points trace a path that continuously adapts to reflect the dynamics of a phase-space distribution function. The technique is robust and allows accurate computations to be obtained for long propagation times. The effects of dissipation on the dynamics are studied and results are presented for systems subject to both periodic and nonperiodic multiminimum potential functions.

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PubMed2004

Trajectory approach to dissipative quantum phase space dynamics: Application to barrier scattering.

The Caldeira-Leggett master equation, expressed in Lindblad form, has been used in the numerical study of the effect of a thermal environment on the dynamics of the scattering of a wave packet from a repulsive Eckart barrier. The dynamics are studied in terms of phase space trajectories associated with the distribution function, W(q,p,t). The equations of motion for the trajectories include quantum terms that introduce nonlocality into the motion, which imply that an ensemble of correlated trajectories needs to be propagated. However, use of the derivative propagation method (DPM) allows each trajectory to be propagated individually. This is achieved by deriving equations of motion for the partial derivatives of W(q,p,t) that appear in the master equation. The effects of dissipation on the trajectories are studied and results are shown for the transmission probability. On short time scales, decoherence is demonstrated by a swelling of trajectories into momentum space. For a nondissipative system, a comparison is made of the DPM with the "exact" transmission probability calculated from a fixed grid calculation.

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