A classical optical approach to the `non-local Pancharatnam-like phases' in Hanbury-Brown-Twiss correlations

We examine a recent proposal to show the presence of nonlocal Pancharatnam type geometric phases in a quantum mechanical treatment of intensity interferometry measurements upon inclusion of polarizing elements in the setup. It is shown that a completely classical statistical treatment of such effects is adequate for practical purposes. Further we show that the phase angles that appear in the correlations, while at first sight appearing to resemble Pancharatnam phases in their mathematical structure, cannot actually be interpreted in that manner. We also describe a simpler Mach-Zehnder type setup where similar effects can be observed without use of the paraxial approximation.Comment: Minor corrections, published versio

Entanglement and Complete Positivity: Relevance and Manifestations in Classical Scalar Wave Optics

Entanglement of states and Complete Positivity of maps are concepts that have achieved physical importance with the recent growth of quantum information science. They are however mathematically relevant whenever tensor products of complex linear (Hilbert) spaces are involved. We present such situations in classical scalar paraxial wave optics where these concepts play a role: propagation characteristics of coherent and partially coherent Gaussian beams; and the definition and separability of the family of Twisted Gaussian Schell Model (TGSM) beams. In the former, the evolution of the width of a projected one-dimensional beam is shown to be a signature of entanglement in a two-dimensional amplitude. In the latter, the partial transpose operation is seen to explain key properties of TGSM beams.Comment: 7 pages Revtex 4-

Arithmetic Circuits and the Hadamard Product of Polynomials

Motivated by the Hadamard product of matrices we define the Hadamard product of multivariate polynomials and study its arithmetic circuit and branching program complexity. We also give applications and connections to polynomial identity testing. Our main results are the following. 1. We show that noncommutative polynomial identity testing for algebraic branching programs over rationals is complete for the logspace counting class \ceql, and over fields of characteristic $p$ the problem is in \ModpL/\Poly. 2.We show an exponential lower bound for expressing the Raz-Yehudayoff polynomial as the Hadamard product of two monotone multilinear polynomials. In contrast the Permanent can be expressed as the Hadamard product of two monotone multilinear formulas of quadratic size.Comment: 20 page

Antioxidant and antihypertensive activities of rice bran peptides

Protein isolates and peptide fractions from food sources (cereal grains), have been shown to exert bioactive properties including antiobesity, anticancer, antiangiogenic, etc. One such food source is rice bran, which is an underutilized co-product of rough rice milling. It contains 90% of the nutrients and nutraceuticals of value to health, including high quality protein. The high quality protein is a potential source to generate peptides that can reduce hypertension and oxidative stress, both being important risk factors for cardiovascular diseases. The objective of this study was to extract peptide hydrolysates from heat stabilized defatted rice bran by enzymatic hydrolysis, evaluate the hydrolysates for gastrointestinal (GI) resistance, fractionate the GI-resistant hydrolysates by ultrafiltration to obtain \u3e50 and 10-50 kDa fractions, and determine antihypertensive and antioxidant activities in the fractions. For antihypertension activity, angiotension-1 converting enzyme (ACE) assay, and for antioxidant activity, the 2,2-Diphenyl-1-Picrylhydrazyl (DPPH) assay was conducted. We report that the ACE-I inhibition activity values for the unfractionated and unhydrolyzed (control), and fractions of \u3e50 kDa, and 10-50 kDa were 6% (control), 78%, and 55%, respectively, clearly denoting antihypertensive activity for the peptide fractions. When tested for antioxidant activity, the \u3e50 kDa fraction decreased from an initial DPPH of 95.48 to 78.99 mg/g, while the 10-50 kDa fraction decreased from an initial 110.35 to 76.53 mg/g, depicting reduction of radical-induced oxidant stress. The results demonstrated that the high molecular sized peptide hydrolysate fractions (\u3e50 and 10-50 kDa) from rice bran bear antihypertensive and antioxidant properties and could possibly find a place as a health beneficial nutraceutical ingredient in food applications

The Sampling Theorem and Coherent State Systems in Quantum Mechanics

The well known Poisson Summation Formula is analysed from the perspective of the coherent state systems associated with the Heisenberg--Weyl group. In particular, it is shown that the Poisson summation formula may be viewed abstractly as a relation between two sets of bases (Zak bases) arising as simultaneous eigenvectors of two commuting unitary operators in which geometric phase plays a key role. The Zak bases are shown to be interpretable as generalised coherent state systems of the Heisenberg--Weyl group and this, in turn, prompts analysis of the sampling theorem (an important and useful consequence of the Poisson Summation Formula) and its extension from a coherent state point of view leading to interesting results on properties of von Neumann and finer lattices based on standard and generalised coherent state systems.Comment: 20 pages, Late