Out for a spin? The vibronic coupling in quantum cellular automata based on the square planar mixed valence molecular cells comprising four paramagnetic centers and two mobile electrons is analyzed. model involves double exchange, Heisenberg-Dirac-Van Vleck exchange of with breathing local modes. latter interaction shown to amplify polarization working cell by driver cell. This leads revision c...

Abstract In this paper we consider a spatial discretization scheme with an adaptive grid for the Nagumo PDE and establish existence of travelling waves. particular, time dependent mesh adaptation method that aims to equidistribute arclength solution under consideration. We assume equidistribution is strictly enforced, which leads non-local problem infinite range interactions derived in Hupkes V...

Although there is good experimental evidence for the Aharonov Bohm phase shift occurring when a solenoid is placed between the beams forming a double-slit electron interference pattern, there has been very little analysis of the relevant classical electromagnetic forces. These forces between a point charge and a solenoid involve subtle relativistic effects of order v c analogous to those discus...

Propagation of the Wigner function is studied on two levels of semiclassical propagation, one based on the van-Vleck propagator, the other on phase-space path integration. Leading quantum corrections to the classical Liouville propagator take the form of a time-dependent quantum spot. Its oscillatory structure depends on whether the underlying classical flow is elliptic or hyperbolic. It can be...

This is the second installment of a two-part paper on developments in quantum dispersion theory leading up to Heisenberg’s Umdeutung paper. In telling this story, we have taken a paper by John H. Van Vleck (1924b,c) as our main guide. In this second part we present the detailed derivations on which our narrative in the first part rests. The central result that we shall derive is the Kramers dis...

Heisenberg’s breakthrough to matrix mechanics was directly stimulated by studies of interaction of quantized material systems with electromagnetic radiation which came to a head in the Kramers-Heisenberg paper on dispersion theory in January 1925. In this talk, we will review the important contributions of Kramers, van Vleck, and Born to this subject. Important results from classical physics wi...

[1] Professor of Mathematics; University of Vermont, 1999-present. [1] Visiting Associate Professor of Mathematics; Rutgers University (New Brunswick, New Jersey) [on sabbatical from UVM], 1992-1993. [2] Associate Professor of Mathematics; University of Vermont, 1991-1999. [3] Assistant Professor of Mathematics; University of Vermont, 1986-1991. [4] Van Vleck Assistant Professor; University of ...