Jeremy B. Maddox

Quantum relaxation dynamics using Bohmian trajectories

We present a new Bohmian trajectory based treatment of quantum dynamics suitable for dissipative systems. Writing the density matrix in complex-polar form, we derive and define quantum equations of motion for Liouville-space trajectories for a generalized system coupled to a dissipative environment. Our theory includes a vector potential which mixes forward and backwards propagating components and pulls coherence amplitude away from the diagonal region of the density matrix. Quantum effects enter via a double quantum potential, Q(x,y), which is a measure of the local curvature of the density amplitude. We discuss how decoherence can be thought of as a balancing between localization brought on by contact with a thermal environment which increases the local curvature of the density matrix and delocalization due to the internal pressure of the quantum force which seeks to minimize the local curvature. The quantum trajectories are then used to propagate an adaptive Lagrangian grid which carries the density ma...

Estimating Bohm’s quantum force using Bayesian statistics

In this paper we develop an approximate methodology for estimating the multidimensional quantum density associated with a statistical bundle of de Broglie–Bohm trajectories. The quantum density is constructed as a discrete sum of nonequivalent Gaussian components. We incorporate the ideas of Bayesian statistical analysis and an expectation-maximization procedure to compute an approximate quantum force that drives the statistical ensemble quantum trajectories.In this paper we develop an approximate methodology for estimating the multidimensional quantum density associated with a statistical bundle of de Broglie–Bohm trajectories. The quantum density is constructed as a discrete sum of nonequivalent Gaussian components. We incorporate the ideas of Bayesian statistical analysis and an expectation-maximization procedure to compute an approximate quantum force that drives the statistical ensemble quantum trajectories.