Interacting Quantum Trajectories and Dwell Times for Particles with Spin 1/2

Time propagation of non-relativistic quantum systems of spin 1/2, traditionally modeled by spinor wavefunctions obeying Pauli equation, will be examined within the context of quantum trajectory methods (QTMs). First, a new variation of QTMs, known as the interacting quantum trajectory (IQT) method, which has been developed for non-relativistic spin-free particles, will be presented for both a free-particle system called the ‘quantum spin flipper’ and the Stern-Gerlach experiment. This method replaces the wavefunction or ‘pilot wave’ in the de Broglie-Bohm (dBB) theory with an ensemble of trajectories where the quantum effects manifest as interactions between the trajectories. The 1D cases will be presented where three real-valued field quantities, one particle position and two angles designating orientation of spin, each depending on time and a trajectory labeling coordinate, are guided by three non-linear coupled PDEs. Novel numerical techniques will be introduced in the propagation in order demonstrate stable dynamics. Second, quantum dwell times and dwell time distributions in the context of dBB QTMs, will be presented for a benchmark 3D spin-1/2 particle system which was analyzed in an earlier study using QTM-based arrival time distributions. Recent work has established a connection between QTMs and dwell times, but only in the context of time-independent stationary scattering applications. This present analysis extends these concepts to more general multi-dimensional and time-dependent cases. In addition, dwell time formulation in terms of bipolar quantum trajectories will be presented which offers another possible theoretical candidate for comparison to experimental quantum time measurements.