A Feynman-Kac Formula for Anticommuting Brownian Motion

Motivated by application to quantum physics, anticommuting analogues of Wiener measure and Brownian motion are constructed. The corresponding Ito integrals are defined and the existence and uniqueness of solutions to a class of stochastic differential equations is established. This machinery is used to provide a Feynman-Kac formula for a class of Hamiltonians. Several specific examples are considered.Comment: 21 page

From dispersionless to soliton systems via Weyl-Moyal like deformations

The formalism of quantization deformation is reviewed and the Weyl-Moyal like deformation is applied to systematic construction of the field and lattice integrable soliton systems from Poisson algebras of dispersionless systems.Comment: 26 page

Quantum Convolutional Coding with Shared Entanglement: General Structure

We present a general theory of entanglement-assisted quantum convolutional coding. The codes have a convolutional or memory structure, they assume that the sender and receiver share noiseless entanglement prior to quantum communication, and they are not restricted to possess the Calderbank-Shor-Steane structure as in previous work. We provide two significant advances for quantum convolutional coding theory. We first show how to "expand" a given set of quantum convolutional generators. This expansion step acts as a preprocessor for a polynomial symplectic Gram-Schmidt orthogonalization procedure that simplifies the commutation relations of the expanded generators to be the same as those of entangled Bell states (ebits) and ancilla qubits. The above two steps produce a set of generators with equivalent error-correcting properties to those of the original generators. We then demonstrate how to perform online encoding and decoding for a stream of information qubits, halves of ebits, and ancilla qubits. The upshot of our theory is that the quantum code designer can engineer quantum convolutional codes with desirable error-correcting properties without having to worry about the commutation relations of these generators.Comment: 23 pages, replaced with final published versio

Recognizing faces prone to occlusions and common variations using optimal face subgraphs

An intuitive graph optimization face recognition approach called Harmony Search Oriented-EBGM (HSO-EBGM) inspired by the classical Elastic Bunch Graph Matching (EBGM) graphical model is proposed in this contribution. In the proposed HSO-EBGM, a recent evolutionary approach called harmony search optimization is tailored to automatically determine optimal facial landmarks. A novel notion of face subgraphs have been formulated with the aid of these automated landmarks that maximizes the similarity entailed by the subgraphs. For experimental evaluation, two sets of de facto databases (i.e., AR and Face Recognition Grand Challenge (FRGC) ver2.0) are used to validate and analyze the behavior of the proposed HSO-EBGM in terms of number of subgraphs, varying occlusion sizes, face images under controlled/ideal conditions, realistic partial occlusions, expression variations and varying illumination conditions. For a number of experiments, results justify that the HSO-EBGM shows improved recognition performance when compared to recent state-of-the-art face recognition approaches

The quantum dynamic capacity formula of a quantum channel

The dynamic capacity theorem characterizes the reliable communication rates of a quantum channel when combined with the noiseless resources of classical communication, quantum communication, and entanglement. In prior work, we proved the converse part of this theorem by making contact with many previous results in the quantum Shannon theory literature. In this work, we prove the theorem with an "ab initio" approach, using only the most basic tools in the quantum information theorist's toolkit: the Alicki-Fannes' inequality, the chain rule for quantum mutual information, elementary properties of quantum entropy, and the quantum data processing inequality. The result is a simplified proof of the theorem that should be more accessible to those unfamiliar with the quantum Shannon theory literature. We also demonstrate that the "quantum dynamic capacity formula" characterizes the Pareto optimal trade-off surface for the full dynamic capacity region. Additivity of this formula simplifies the computation of the trade-off surface, and we prove that its additivity holds for the quantum Hadamard channels and the quantum erasure channel. We then determine exact expressions for and plot the dynamic capacity region of the quantum dephasing channel, an example from the Hadamard class, and the quantum erasure channel.Comment: 24 pages, 3 figures; v2 has improved structure and minor corrections; v3 has correction regarding the optimizatio

Nature of 45 degree vortex lattice reorientation in tetragonal superconductors

The transformation of the vortex lattice in a tetragonal superconductor which consists of its 45 degree reorientation relative to the crystal axes is studied using the nonlocal London model. It is shown that the reorientation occurs as two successive second order (continuous) phase transitions. The transition magnetic fields are calculated for a range of parameters relevant for borocarbide superconductors in which the reorientation has been observed

Vortex lattice structure in a d_{x^2-y^2}-wave superconductor

The vortex lattice structure in a d_{x^2-y^2}-wave superconductor is investigated near the upper critical magnetic field in the framework of the Ginzburg Landau theory extended by including the correction terms such as the higher order derivatives derived from the Gor'kov equation. On lowering temperature, the unit cell shape of the vortex lattice gradually varies from a regular triangular lattice to a square lattice through the shape of an isosceles triangle. As for the orientation of the vortex lattice, the base of an isosceles triangle is along the a axis or the b axis of the crystal. The fourfold symmetric structure around a vortex core is also studied in the vortex lattice case. It is noted that these characteristic features appear even in the case the induced s-wave order parameter is absent around the vortex of the d_{x^2-y^2}-wave superconductivity. We also investigate the effect of the induced s-wave order parameter. It enhances (suppresses) these characteristic features of the d_{x^2-y^2}-wave superconductor when the s-wave component of the interaction is attractive (repulsive).Comment: 20 pages, RevTex, 9 figures in 3 PS-files and 5 GIF-file

The ethical challenge of Touraine's 'living together'

In Can We Live Together? Alain Touraine combines a consummate analysis of crucial social tensions in contemporary societies with a strong normative appeal for a new emancipatory 'Subject' capable of overcoming the twin threats of atomisation or authoritarianism. He calls for a move from 'politics to ethics' and then from ethics back to politics to enable the new Subject to make a reality out of the goals of democracy and solidarity. However, he has little to say about the nature of such an ethics. This article argues that this lacuna could usefully be filled by adopting a form of radical humanism found in the work of Erich Fromm. It defies convention in the social sciences by operating from an explicit view of the 'is' and the 'ought' of common human nature, specifying reason, love and productive work as the qualities to be realised if we are to move closer to human solidarity. Although there remain significant philosophical and political differences between the two positions, particularly on the role to be played by 'the nation', their juxtaposition opens new lines of inquiry in the field of cosmopolitan ethics

Effect of transport-induced charge inhomogeneity on point-contact Andreev reflection spectra at ferromagnet-superconductor interfaces

We investigate the transport properties of a ferromagnet-superconductor interface within the framework of a modified three-dimensional Blonder-Tinkham-Klapwijk formalism. In particular, we propose that charge inhomogeneity forms via two unique transport mechanisms, namely, evanescent Andreev reflection and evanescent quasiparticle transmission. Furthermore, we take into account the influence of charge inhomogeneity on the interfacial barrier potential and calculate the conductance as a function of bias voltage. Point-contact Andreev reflection (PCAR) spectra often show dip structures, large zero-bias conductance enhancement, and additional zero-bias conductance peak. Our results indicate that transport-induced charge inhomogeneity could be a source of all these anomalous characteristics of the PCAR spectra.Comment: 9 pages, 6 figure