On the Production of Flux Vortices and Magnetic Monopoles in Phase Transitions

We examine the basic assumptions underlying a scenario due to Kibble that is widely used to estimate the production of topological defects. We argue that one of the crucial assumptions, namely the geodesic rule, although completely valid for global defects, becomes ill defined for the case of gauged defects. We address the issues involved in formulating a suitable geodesic rule for this case and argue that the dynamics plays an important role in the production of gauge defects.Comment: 9 pages, in LATEX, UMN-TH-1028/92, TPI-MINN-92/20-

Neuropsychological evidence for three distinct motion mechanisms

Published in final edited form as: Neurosci Lett. 2011 May 16; 495(2): 102–106. doi:10.1016/j.neulet.2011.03.048.We describe psychophysical performance of two stroke patients with lesions in distinct cortical regions in the left hemisphere. Both patients were selectively impaired on direction discrimination in several local and global second-order but not first-order motion tasks. However, only patient FD was impaired on a specific bi-stable motion task where the direction of motion is biased by object similarity. We suggest that this bi-stable motion task may be mediated by a high-level attention or position based mechanism indicating a separate neurological substrate for a high-level attention or position-based mechanism. Therefore, these results provide evidence for the existence of at least three motion mechanisms in the human visual system: a low-level first- and second-order motion mechanism and a high-level attention or position-based mechanism.Accepted manuscrip

Polarization enhancement in two- and three-component ferroelectric superlattices

Composition-dependent structural and polar properties of epitaxial short-period CaTiO_3/SrTiO_3/BaTiO_3 superlattices grown on a SrTiO_3 substrate are investigated with first-principles density-functional theory computational techniques. Polarization enhancement with respect to bulk tetragonal BaTiO_3 is found for two- and three-component superlattices with a BaTiO_3 concentration of more than 30%. Individual BaTiO_3 layer thickness is identified as an important factor governing the polarization improvement. In addition, the degree of inversion-symmetry breaking in three-component superlattices can be controlled by varying the thicknesses of the component layers. The flexibility allowed within this large family of structures makes them highly suitable for various applications in modern nano-electro-mechanical devices.Comment: The following article has been submitted to Applied Physics Letters. After it is published, it will be found at http://apl.aip.org

From GM Law to A Powerful Mean Field Scheme

A new and powerful mean field scheme is presented. It maps to a one-dimensional finite closed chain in an external field. The chain size accounts for lattice topologies. Moreover lattice connectivity is rescaled according to the GM law recently obtained in percolation theory. The associated self-consistent mean-field equation of state yields critical temperatures which are within a few percent of exact estimates. Results are obtained for a large variety of lattices and dimensions. The Ising lower critical dimension for the onset of phase transitions is $d_l=1+\frac{2}{q}$. For the Ising hypercube it becomes the Golden number $d_l=\frac{1+\sqrt 5}{2}$. The scheme recovers the exact result of no long range order for non-zero temperature Ising triangular antiferromagnets.Comment: 3M Conference Proceedings, San Jose, California (November, 1999

Lower bound on the number of Toffoli gates in a classical reversible circuit through quantum information concepts

The question of finding a lower bound on the number of Toffoli gates in a classical reversible circuit is addressed. A method based on quantum information concepts is proposed. The method involves solely concepts from quantum information - there is no need for an actual physical quantum computer. The method is illustrated on the example of classical Shannon data compression.Comment: 4 pages, 2 figures; revised versio