Moshinsky's work on diffraction in time is recognized as a particular case of monoenergetic, quantum dispersion process. Diffraction in time is extended to include new initial conditions, which under free evolution exhibit temporal quantum interference patterns in close analogy to spatial diffraction patterns found in optics. We show that free propagation of states, which initially are stationary states of infinite potential wells, diffract in time similarly as a plane wave by a double slit. We introduce the concepts of mass transport by transient Fraunhofer and Fresnel dispersion currents.
With the help of quantum-scattering-theory methods and the approximation of stationary phase, a one-dimensional coherent random-walk model which describes both tunneling and scattering above the potential diffusion of particles in a periodic one-dimensional lattice is proposed. The walk describes for each lattice cell, the time evolution of modulating amplitudes of two opposite-moving Gaussian wave packets as they are scattered by the potential barriers. Since we have a coherent process, interference contributions in the probabilities bring about strong departures from classical results. In the near-equilibrium limit, Fick’s law and its associated Landauer diffusion coefficient are obtained as the incoherent contribution to the quantum current density along with a novel coherent contribution which depends on the lattice properties as [(1−R)/R]1/2.
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