Search

We use Boltzmann’s transport equation to calculate the 3D incoherent Landauer equation for neutrons and photons diffusing in a slab of amorphous material. We use the P[sub 1] approximation to calculate the multiple-scattering transmission coefficient as a function of the diffusion coefficient. The 3D transmission coefficient obtained is smaller than the 1D case. The P[sub 1] result, valid only for thick slabs, is proved to be an excellent approximation to the exact solution. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Introduces multiple scattering transmission an reflection coefficients in addition to the diffusion coefficient D for the description of ballistic diffusion in the presence of absorption. Measurement of only one between T and D factors imposing restrictions on possible values.

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. [ABSTRACT FROM AUTHOR]

With the help of the quantum theory of scattering, a set of simultaneous difference equations is proposed, defining a diffusive stochastic process (correlated walk), which describes a semiclassical, one-dimensional, tunneling diffusion process in a periodic lattice. The jump probabilities are just the quantum transmission coefficients of the unit cell. With this process, we prove that by quantum tunneling or scattering above the potential, the particles diffuse in a one-dimensional lattice with a diffusion coefficient given by the Landauer formula. Next, the theory is generalized to include higher dimensions, and a square lattice case is shown as an example. There we show that the Landauer formula will not be obtained for 2D or 3D cases. Finally, examples are given, in which the Landauer formula is also valid for other cases of one-dimensional Markovian correlated walks. [ABSTRACT FROM AUTHOR]

Abstract: We prove for one-dimensional time-dependent quantum absorbing (and reflecting) slits that for right-moving incident waves, the Laplace transform of the boundary function must have singular points at the complex roots of . We test our result against the exact case of the Moshinsky absorbing (and reflecting) shutter, and the agreement is perfect. In the same Moshinsky problem, when the approximated Kirchhoff boundary condition is used, the transmitted wave is a superposition of right- and left-moving Moshinsky packets. Neglecting the wrong directed wave components we get the exact solution. [Copyright &y& Elsevier]

Abstract: We report new transient stationary spherical waves generated by the time evolution of wave functions with angular momentum. In the study the 3D problem of the sudden release of a particle which initially was inside a spherical trap, the exact solution for the particle''s time evolution is described by expected traveling incoming and outgoing spherical waves. However, unexpected transient stationary spherical waves are also present. The traveling waves have amplitudes describing diffraction in time, in a way similar to the optical diffraction by a single slit. In striking contrast with the similar 1D problem, the angular momentum generates unexpected transient stationary spherical waves which have their main contribution at points inside the sphere but only for very short times. [Copyright &y& Elsevier]

Abstract: We get the exact result for the problem of the statistical mixtures of Moshinsky states for electrons emitted from a metal by quantum thermionic emission. We find that diffraction oscillations are completed suppressed for all temperatures and times. The temperature only affects the size of the scales to measure length and time. Our results are also valid for classical effusion, electric-field assisted thermionic emission, and photoelectric effect. [Copyright &y& Elsevier]

Abstract: The conductivity σ of vanadium dioxide (VO2) drops at a metal–insulator transition by four orders of magnitude due to the structural change between tetragonal and monoclinic crystals. In order to elucidate this conductivity drop, we introduce the semiclassical equation of motion to describe the dynamics of the conduction electron (wave packet), where the existence of a k-vector k is prerequisite for the conduction. We showed that the periodicity using the non-orthogonal bases does not legitimize the electron dynamics in solids. The theory suggests that the decrease in the dimensionality of the k-vectors due to the structural change is the cause of the conductivity drop. [Copyright &y& Elsevier]

A new formula for the Seebeck coefficient S is obtained: S = (21n2/3)(qn)[sup -1]&epsilon[sub F]k[sub B] × (N/V), where q, n, ε[sub F], Af and V are, respectively, charge, carrier density, Fermi energy, density of states at εF and volume. Seebeck (S) and Hall (R[sub H]) coefficients in alkali metals are both negative while these coefficients in noble metals have opposite signs. This difference is shown to arise from the different shapes of the Fermi surface. [ABSTRACT FROM AUTHOR]