The expansion dynamics of bosonic gases in optical lattices has recently been the focus of an incresing attention, both experimental and theoretical. We consider, by means of numerical Bethe ansatz, the expansion dynamics of initially confined wave packets of two interacting bosons on a lattice. We show that a correspondence between the asymptotic expansion velocities and the projection of the evolved wave function over the bound states of the system exists, clarifying the existing picture for such situations. Moreover, we investigate the role of the lattice in this kind of evolution.
The huge spin precession frequency observed in recent experiments with spin-polarized beams of hot electrons shot through magnetized films is interpreted as being caused by Zeeman coupling of the electron spins to the so-called Weiss exchange field in the film. A "Stern-Gerlach experiment" for electrons moving through an inhomogeneous exchange field is proposed. The microscopic origin of exchange interactions and of large mean exchange fields, leading to different types of magnetic order, is elucidated. A microscopic derivation of the equations of motion of the Weiss exchange field is presented. Novel proofs of the existence of phase transitions in quantum XY -models and antiferromagnets, based on an analysis of the statistical distribution of the exchange field, are outlined.
The effects of the nonrelativistic Zitterbemegung (trembling motion), originated by interband transitions, on the electron-phonon interaction is considered. It is shown that the one-phonon matrix elements of intraband transitions are damped with respect to the single-band case. In two-band systems, the lowest-order damping is equivalent to a Debye-Wailer factor, with the decay length given by the spatial amplitude of the Zitterbewegung. Two-band systems whose Hamiltonian becomes Dirac-like along a certain direction (defined as pseudorelativistic) are discussed. They show an extreme effect in the zerogap limit, i.e. , the total suppression of one-phonon processes, closely related to the divergence of the Zitterbeuregung amplitude near the I point.
The notion of the dimension of a relativistic quantum mechanical path is illustrated. An elementary introduction to the concept of a fractal curve allows the discussion of the evolution of the quantum mechanical wave packet for free particles in terms of Hausdorff dimensions of quantum ‘‘trajectories.’’ The results of a previous work by Abbott and Wise can be generalized to relativistic quantum mechanics of spin-1/2 particles in the Foldy–Wouthuysen representation. A further extension to spin-zero particles is briefly outlined. By simple considerations, an understanding of the notion of a Hausdorff dimension and its values can be introduced.
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