Multidimensional wave packet dynamics within the fluid dynamical formulation of the Schrödinger equation

Abstract

This paper explores the quantum fluid dynamical ͑QFD͒ representation of the time-dependent Schrödinger equation for the motion of a wave packet in a high dimensional space. A novel alternating direction technique is utilized to single out each of the many dimensions in the QFD equations. This technique is used to solve the continuity equation for the density and the equation for the convection of the flux for the quantum particle. The ability of the present scheme to efficiently and accurately describe the dynamics of a quantum particle is demonstrated in four dimensions where analytical results are known. We also apply the technique to the photodissociation of NOCl and NO 2 where the systems are reduced to two coordinates by freezing the angular variable at its equilibrium value.

Quantum-fluid-dynamics approach for strong-field processes: Application to the study of multiphoton ionization and high-order harmonic generation of He and Ne atoms in intense laser fields

“…Figures 7͑a͒ and 7͑b͒ present the profile of the timedependent norm N(t) ͑normalized to unity͒ for the two laser intensities, 5ϫ10 13 2 p) norm obtained from the more accurate all-electron TD KLI-SIC calculations ͓4͔. The overall agreement is satisfactory, well within 0.1%.…”

Coherent optimal control of multiphoton molecular excitation

“…The equations (13), (16), (18) and (19) are non-linear thereby calling for iteration to solve(see ref. [24] and [25] for details). Finally the desired control electric field is given from Eq.…”

Quantum initial value representations using approximate Bohmian trajectories

“…These equations, along with dx j /dt = S (1) j /m are an infinite hierarchy of equations for both C and S and their derivatives evaluated along the path x j (t). In this hierarchy, the equation for the n th order derivative of C involves up to the n + 2 and order derivative of S and up to the n + 1 order derivative of C. Likewise, the equation of motion for the n th order derivative of S involves up to 2 higher order terms of C and one higher order term of S. The C (n) k and S (n) k terms are in essence n th -order cumulants of the wavefunction evaluated at x k (t).…”

“…In spite of 3-4 years of intense effort by a number of groups [1,2,3,4,5,6,7,13,14,15,16] , including our own, there has yet to emerge a satisfactory and robust way to compute Q and the quantum force − ∇Q directly from the quantum trajectories in multidimensional systems. This severely limits the applicability of a quantum trajectory based approach for computing exact quantum dynamics for all but the most trivial systems.…”

“…[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17] This formulation is based upon Bohm's "hidden variable" representation [18,19,20] is initiated by substituting the amplitude-phase decomposition of the time-dependent quantum wavefunction, ψ(y, t) = R(y, t) exp(iS(y, t)/h), into the time-dependent Schrödinger equation,…”