Quantum Trajectory Method for Particles with Spin 1/2

Time propagation of non-relativistic spin-free quantum systems can be modeled with ensembles of real-valued interacting trajectories obeying a Newton-like equation, instead of the traditional formalism involving wavefunctions obeying the time-dependent Schrödinger equation. The new approach has been fully developed by Poirier [Chemical Physics, 370, 4-14 (2010)] and successfully applied to molecular dynamics simulations accurately capturing nuclear quantum effects. We present an extension of this work to address non-relativistic spin 1/2 systems traditionally modeled by spinor wavefunctions obeying the Pauli equation. Under this new formalism, we will show that the dynamical model for a free-particle system with translational motion restricted to one-dimension and spin in three-dimensions turns into a set of three coupled PDEs. Quantum force and quantum spin force terms appear in these equations, which both also arise in the Bohmian hydrodynamic formulation of quantum mechanics. Novel numerical techniques [L. Dupuy, F. Talotta, F. Agostini, D. Lauvergnat, B. Poirier, and Y. Scribano, Journal of Chemical Theory and Computation (accepted)] are introduced in the propagation showing stable dynamics.