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-

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

The Schwinger SU(3) Construction - II: Relations between Heisenberg-Weyl and SU(3) Coherent States

The Schwinger oscillator operator representation of SU(3), studied in a previous paper from the representation theory point of view, is analysed to discuss the intimate relationships between standard oscillator coherent state systems and systems of SU(3) coherent states. Both SU(3) standard coherent states, based on choice of highest weight vector as fiducial vector, and certain other specific systems of generalised coherent states, are found to be relevant. A complete analysis is presented, covering all the oscillator coherent states without exception, and amounting to SU(3) harmonic analysis of these states.Comment: Latex, 51 page

On `orbital' and `spin' angular momentum of light in classical and quantum theories -- a general framework

We develop a general framework to analyze the two important and much discussed questions concerning (a) `orbital' and `spin' angular momentum carried by light and (b) the paraxial approximation of the free Maxwell system both in the classical as well as quantum domains. After formulating the classical free Maxwell system in the transverse gauge in terms of complex analytical signals we derive expressions for the constants of motion associated with its Poincar\'{e} symmetry. In particular, we show that the constant of motion corresponding to the total angular momentum ${\bf J}$ naturally splits into an `orbital' part ${\bf L}$ and a `spin' part ${\bf S}$ each of which is a constant of motion in its own right. We then proceed to discuss quantization of the free Maxwell system and construct the operators generating the Poincar\'{e} group in the quantum context and analyze their algebraic properties and find that while the quantum counterparts $\hat{{\bf L}}$ and $\hat{{\bf S}}$ of ${\bf L}$ and ${\bf S}$ go over into bona fide observables, they fail to satisfy the angular momentum algebra precluding the possibility of their interpretation as `orbital' and `spin' operators at the classical level. On the other hand $\hat{{\bf J}}=\hat{{\bf L}}+ \hat{{\bf S}}$ does satisfy the angular momentum algebra and together with $\hat{{\bf S}}$ generates the group $E(3)$. We then present an analysis of single photon states, paraxial quantization both in the scalar as well as vector cases, single photon states in the paraxial regime. All along a close connection is maintained with the Hilbert space $\mathcal{M}$ that arises in the classical context thereby providing a bridge between classical and quantum descriptions of radiation fields.Comment: Revtex 4-1 16 page

Indigenous traditional knowledge (ITK) from forest dwellers of Gondia district, Maharashtra

Indians have great knowledge of phytomedicines. This valuable knowledge has been conserved in the living folk traditions in ethnic communities.  An attempt has been made to explore traditional medicinal knowledge of plant materials, available in forest villages of Goregaon and Deori forest range of Gondia district, Maharashtra state. Gondia is one of the prominently categorized districts with maximum tribal population in Maharashtra which includes mostly Gond, Gowari, Halbi, Manah tribes with great numbers. In this study we documented about 49 plant species of various families which are commonly used by the tribal people to cure some common diseases viz. Dysentery, acute headache, toothache and carries, urinary troubles, skin diseases, antidote against snake bite, vomiting and many more. Ethnobotanical information were gathered through several visits, group discussions and cross checked with traditional medical practitioner of the study area

The development of quantum, mechanics: a story of people, places and philosophies

A historical account of the development of quantum mechanics,and the roles played by many outstanding physicists, theirviews and philosophical attitudes is presented. Ingenious andpath-breaking experiments that helped this development alongare highlighted. Ideas and notions that initially arose in thecourse of discussions on foundations of quantum mechanicsand later paved the way for the emergence of the fieldof Quantum Information Science and Technology are brieflytouched upon