Quantum hydrodynamics and a new approach to mixed quantum-classical theory.

Irène Burghardt, Klaus B. Møller, Keith H. Hughes

Keith H. Hughes, Steven M. Parry, Irène Burghardt +2 more

Irène Burghardt, Klaus B. Møller, Gérard Parlant +2 more

Abstract The formulation of quantum hydrodynamics for mixed states provides a complement, in a quantum‐statistical context, to its pure‐state “Bohmian mechanics” analogue. We summarize our recent work in this area, focusing on two key aspects. We first describe the formulation of a generalized hydrodynamic force, which includes the effects of thermal fluctuations and “quantum fluctuations” and thus determines the time evolution under the influence of dissipation. Second, we introduce a mixed hydrodynamic–Liouville space representation in terms of partial moments, as applied in the context of coupled electronic states and mixed quantum‐classical dynamics. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004

D. D. H. Yee

The current-current commutation relations, satisfied by the microscopic currents, are used to determine the algebraic properties of the basic hydrodynamic variables in quantum hydrodynamics. Using a Hamiltonian as suggested by the microscopic theory, a new system of hydrodynamic equations is obtained which contained the classical hydrodynamic equations including vortex motion in the classical limit. The concept of the fluid velocity in quantum mechanics of many particles is also discussed.

Darryl D. Holm, Jonathan Rawlinson, Cesare Tronci

Starting with the exact factorization of the molecular wavefunction, this paper presents the results from the numerical implementation in ab-initio nonadiabatic dynamics of the recently proposed bohmion method. Within the context of quantum hydrodynamics, the regularized nuclear Bohm potential in the bohmion method admits solutions comprising a train of $\delta$-functions which serve as a finite-dimensional sampling of the hydrodynamic flow paths. In addition, the nonlocal structure of the regularized Bohm potential admits nuclear quantum tunneling events. After reviewing the general theory, the bohmion method is applied to the well-known Tully models, which are used here as benchmark problems for the comparison of the new bohmion method with previous mixed quantum-classical methods.

Moise Bonilla–Licea, Dieter Schuch