Quantum Hydrodynamic Analysis of Decoherence

The hydrodynamic formulation of quantum mechanics is used to analyze the mechanism of decoherence for a system interacting with a bath in which the initial system wavefunction is a superposition of spatially separated components. In order to study the decoherence, the various time-evolving hydrodynamic fields are monitored for the two composite systems, each having a single bath mode. In one of these, the system and bath are uncoupled, but in the other they are coupled through an interaction term. For the uncoupled system, a large interference feature develops between the two separated components of the initial superposition. The reduced density matrix for the system initially displays two large off-diagonal peaks and as time proceeds, these peaks broaden but do not disappear. For the coupled system, the interference feature that attempts to form between the two initially separated wavepackets is largely suppressed. Although the quantum force again tends to push fluid elements toward the interference region, this is counteracted by the classical force, which attempts to separate the centers of the two wavepackets into two descending valleys. An essential feature of flux maps for this case is that in the mid-region between the two initial density peaks, an intersecting set of attractors and repellors for flux vectors form and these funnel density away from the central region. As time proceeds, the reduced density matrix for the system shows increasing concentration along the diagonal. The Wigner function for the system shows gradually decaying ripples lying between the two density maxima which themselves are separating with opposite momenta. Finally, at later times, the reduced density matrix for the system is very similar to that obtained from a mixture of independently evolving components.