Geometric phases in a scattering process

The study of geometric phase in quantum mechanics has so far be confined to discrete (or continuous) spectra and trace preserving evolutions. Consider only the transmission channel, a scattering process with internal degrees of freedom is neither a discrete spectrum problem nor a trace preserving process. We explore the geometric phase in a scattering process taking only the transmission process into account. We find that the geometric phase can be calculated by the some method as in an unitary evolution. The interference visibility depends on the transmission amplitude. The dependence of the geometric phase on the barrier strength and the spin-spin coupling constant is also presented and discussed.Comment: 4 pages, 5 figure

Geometrical statistics and vortex structures in helical and nonhelical turbulences

In this paper we conduct an analysis of the geometrical and vortical statistics in the small scales of helical and nonhelical turbulences generated with direct numerical simulations. Using a filtering approach, the helicity flux from large scales to small scales is represented by the subgrid-scale (SGS) helicity dissipation. The SGS helicity dissipation is proportional to the product between the SGS stress tensor and the symmetric part of the filtered vorticity gradient, a tensor we refer to as the vorticity strain rate. We document the statistics of the vorticity strain rate, the vorticity gradient, and the dual vector corresponding to the antisymmetric part of the vorticity gradient. These results provide new insights into the local structures of the vorticity field. We also study the relations between these quantities and vorticity, SGS helicity dissipation, SGS stress tensor, and other quantities. We observe the following in both helical and nonhelical turbulences: (1) there is a high probability to find the dual vector aligned with the intermediate eigenvector of the vorticity strain rate tensor; (2) vorticity tends to make an angle of 45 with both the most contractive and the most extensive eigendirections of the vorticity strain rate tensor; (3) the vorticity strain rate shows a preferred alignment configuration with the SGS stress tensor; (4) in regions with strong straining of the vortex lines, there is a negative correlation between the third order invariant of the vorticity gradient tensor and SGS helicity dissipation fluctuations. The correlation is qualitatively explained in terms of the self-induced motions of local vortex structures, which tend to wind up the vortex lines and generate SGS helicity dissipation. In helical turbulence, we observe that the joint probability density function of the second and third tensor invariants of the vorticity gradient displays skewed distributions, with the direction of skewness depending on the sign of helicity input. We also observe that the intermediate eigenvalue of the vorticity strain rate tensor is more probable to take negative values. These interesting observations, reported for the first time, call for further studies into their dynamical origins and implications. (C) 2010 American Institute of Physics. [doi: 10.1063/1.3336012

Suppression of ferromagnetic ordering in doped manganites: Effects of the superexchange interaction

From a Monte Carlo study of the ferromagnetic Kondo lattice model for doped manganites, including the antiferromagnetic superexchange interaction ($J_{AF}$), we found that the ferromagnetic ordering was suppressed as $J_{AF}$ increased. The ferromagnetic transition temperature $T_c$, as obtained from a mean field fit to the calculated susceptibilities, was found to decrease monotonically with increasing $J_{AF}$. Further, the suppression in $T_c$ scales with the bandwidth narrowing induced by the antiferromagnetic frustration originating from $J_{AF}$. From these results, we propose that the change in the superexchange interaction strength between the $t_{2g}$ electrons of the Mn ions is one of the mechanisms responsible for the suppression in $T_c$ observed in manganites of the type (La$_{0.7-y}$Pr$_{y}$)Ca$_{0.3}$MnO$_3$.Comment: 5 pages, 6 figures. To appear in PR

Density oscillations in trapped dipolar condensates

We investigated the ground state wave function and free expansion of a trapped dipolar condensate. We find that dipolar interaction may induce both biconcave and dumbbell density profiles in, respectively, the pancake- and cigar-shaped traps. On the parameter plane of the interaction strengths, the density oscillation occurs only when the interaction parameters fall into certain isolated areas. The relation between the positions of these areas and the trap geometry is explored. By studying the free expansion of the condensate with density oscillation, we show that the density oscillation is detectable from the time-of-flight image.Comment: 7 pages, 9 figure