Attila Askar

Koc University, 80860 Istinye, Istanbul, TURKEY

The quantum fluid dynamics (QFD) formalism, the associated numerical formulation and the application of the formulation to multidimensional wavepacket dynamics are presented. The applications include wave packets in four dimensional  quadratic potentials and two coordinate photo-dissociation problems for NOCl and NO2. The QFD formulation is based on the separation of the amplitude and phase of the complex wave function in Schrodinger’s equation. The approach leads to two conservation laws, one for “mass” and one for “momentum”, similar to those in hydrodynamics. In the QFD analogy, the solution of the time dependent Schrodinger's equation is transformed to observing the dynamics of an equivalent gas continuum”. The classical fluid dynamics equations are treated numerically in two equivalent but conceptually different formats called as the Lagrangian [1]and Eulerian [2] approaches. These correspond repectively to following the particles of the fluid continuum and observing the dynamics at the points of a fixed coordinate frame. The numerical implementation of the QFD equations leads to a dramatically short times as compared with other integration methods of the time dependent Schrodinger equation. This special computational efficiency comes from the combination of QFD representation in dealing with the near monotonic amplitude and phase of the complex wave function and the use of an explicit time integrator where the computational effort grows only linearly with the number of discrete points. Moreover, the Lagrangian description concentrates the computation effort to regions of highest probability as an optimal adaptive grid and the Eulerian scheme allows the formulation of multidimensional problems as a set of one-dimensional problems within an alternating direction methodology.

[1] Quantum fluid dynamics (QFD) in the Lagrangian representation with applications to photo-dissociation problems”,
    F. Sales, A. Askar and H. A. Rabitz, J. Chem Phys. 110, 2423 (1999)
[2] Multidimensional wave-packet dynamics within the fluid dynamical formulation of the Schrodinger equation”,
    B. Dey, A. Askar and H. A. Rabitz, J. Chem. Phys. 109, 8770 (1998)