Quantum fluid dynamics in the Lagrangian representation and applications to photodissociation problems

Abstract

This paper considers the practical utility of quantum fluid dynamics (QFD) whereby the time-dependent Schrodinger's equation is transformed to observing the dynamics of an equivalent "gas continuum." The density and velocity of this equivalent gas continuum are respectively the probability density and the gradient of the phase of the wave function. The numerical implementation of the QFD equations is carried out within the Lagrangian approach, which transforms the solution of Schrodinger's equation into following the trajectories of a set of mass points, i.e., subparticles, obtained by discretization of the continuum equations. The quantum dynamics of the subparticles which arise in the present formalism through numerical discretization are coupled by the density and the quantum potential. Numerical illustrations are performed for photodissociation of nocl and NO2 treated as two-dimensional models. The dissociation cross sections sigma(omega) are evaluated in the dramatically short CPU times of 33 s for nocl and 40 s for NO2 on a Pentium-200 mhz PC machine. The computational efficiency comes from a combination of (a) the QFD representation dealing with the near monotonic amplitude and phase as dependent variables, (b) the Lagrangian description concentrating the computation effort at all times into regions of highest probability as an optimal adaptive grid, and (c) the use of an explicit time integrator whereby the computational effort grows only linearly with the number of discrete points.