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R. Parthasarathy

Publications and source records attributed to R. Parthasarathy.

At least 19 recordsLinked to original sources
arXiv2018

Classical Defocussing of world lines from Higher Dimensions

A five-dimensional gravity theory, motivated by the brane-world picture, with Kaluza scalar in the 5 - dimensional metric as $g_{55}(r); r=\sqrt{x^2+y^2+z^2}$, is considered near the possible singularity (small distance scales where gravity is strong) and is shown to give rise to a positive contribution to the Raychaudhuri equation. This inhibits the focusing of world lines and contributes to non - focusing of the worldlines in the 5-dimensional space. It is also shown that the results extend to time dependent cases such as those relevant for black hole interiors and cosmology.

gr-qc↗
arXiv2018

Five dimensional Gravity and Big Bang Singularity

A 5-dimensional gravity theory, motivated by the brane world picture, with factorisable metric and with Kaluza scalar $G_{55}(r)$, is shown to give rise to a positive contribution to the Raychaudhuri equation. This inhibits the focusing of geodesics and possibly cause non-focusing of the geodesics. This feature is translated into the situation in which the universe has an infinite age and hence no beginning avoiding the big bang singularity.

gr-qc↗
arXiv2016

Photons with half-integral spin as q-Fermions

The recently discovered 'light (photons) with half-integral spin' is interpreted as q-Fermions proposed by us in 1991, as these q-Fermions satisfy q-deformed anti-commutation relations (pertaining to spin half) and have the property that more than one q-Fermion can occupy a given quantum state. In this article, in view of the recent discovery, we recall the construction of q-Fermions and give the statistical properties of q-Fermion gas, based on our preprint in 1992.

hep-th↗
arXiv2012

Causality of the Brane Universe - OPERA and ICARUS

The apparent violation of causality in the brane Universe can be avoided by taking the bulk spacetime modelled by a 5-dimensional Kaluza theory with factorizable ansatz for the 5-dimensional metric whose components do not depend on the fifth coordinate and with $G_{55}$ not a constant. The geodesic in the bulk does not correspond to a free particle. The Kaluza scalar makes it non-inertial. The implication on the neutrino experiment is that there is no superluminal propagation even after invoking sterile neutrinos.

hep-ph↗
arXiv2010

A q-deformed logistic map and its implications

A new q-deformed logistic map is proposed and it is found to have concavity in parts of the x-space. Its one-cycle and two-cycle non-trivial fixed points are obtained which are found to be qualitatively and quantitatively different from those of the usual logistic map. The stability of the proposed q-logistic map is studied using Lyapunov exponent and with a change in the value of the deformation parameter q, one is able to go from the chaotic to regular dynamical regime. The implications of this q-logistic map on Parrondo's paradox are examined.

nlin.CD↗
arXiv2010

Stable Chromomagnetic QCD Vacuum and Confinement

The stable chromomagnetic vacuum for SU(2) Yang-Mills theory found earlier is shown to give a model for confinement in QCD, using Wilson loop, and a linear potential (in the leading order) for quark-antiquark interaction. The coefficient $k$ in this potential is found to be $\sim 0.25 GeV^2$, in satisfactory agreement with non-relativistic potential model calculations for charmonium. At finite temperature, the real effective energy density found earlier is used to obtain estimates of the deconfining temperature agreeing reasonably with lattice study for SU(2).

hep-th↗
arXiv2009

The Ehrenfest Theorem in Quantum Field Theory

The validity of the Ehrenfest's theorem in Abelian and non-Abelian quantum field theories is examined. The gauge symmetries are taken to be unbroken. By suitably choosing the physical subspace, the above validity is proven in both the cases.

math-ph↗
arXiv2008

Low Energy Pion-Pion Elastic Scattering in Sakai-Sugimoto Model

We have considered the holographic large $N_c$ QCD model proposed by Sakai and Sugimoto and evaluated the non-Abelian DBI-action on the D8-brane upto $(α')^4$ terms. Restricting to the pion sector, these corrections give rise to four derivative contact terms for the pion field. We derive the Weinberg's phenemenological lagrangian. The coefficients of the four derivative terms are determined in terms of $g_{YM}^2$. The low energy pion-pion scattering amplitudes are evaluated. Numerical results are presented with the choice of $M_{KK}=0.94 GeV$ and $N_c=11$. The results are compared with the amplitudes calculated using the experimental phase shifts. The agreement with the experimental data is found to be satisfactory.

hep-th↗
arXiv2007

$(α')^4$ Corrections in Holographic Large N_c QCD and $π- π$ Scattering

We calculate the ${α'}^4$ corrections to the non-Abelian DBI action on the D8-brane in the holographic dual of large N_c QCD proposed by Sakai and Sugimoto. These give rise to higher derivative terms, in particular, four derivative contact terms for the pion field with the coupling uniquely determined. We calculate the pion-pion scattering amplitude near threshold. The results respecting unitarity are in qualitative agreement with the experimental curves.

hep-th↗
arXiv2006

SU(2) Yang-Mills Theory in Savvidy Background at Finite Temperature and Chemical Potential

The one-loop effective energy density of a pure SU(2) Yang-Mills theory in the Savvidy background, at finite temperature and chemical potential is examined with emphasis on the unstable modes. After identifying the stable and unstable modes, the stable modes are treated in the quadratic approximation. For the unstable modes, the full expansion including the cubic and the quartic terms in the fluctuations is used. The functional integrals for the unstable modes are evaluated and added to the results for the stable modes. The resulting energy density is found to be {\it{real}}, coinciding with the real part of the energy density in the quadratic approximation of earlier study. There is now {\it{no imaginary part.}} Numerical results are presented for the variation of the energy density with temperature for various choices of the chemical potential.

hep-th↗
arXiv2006

Skew-product for group-valued edge labellings of Bratteli diagrams

Group valued edge labellings $λ$ of a Bratteli diagram $B$ give rise to a skew-product Bratteli diagram $B(λ)$ on which the group acts. The quotient by the group action of the associated dynamics can be a nontrivial extension of the dynamics of $B$. We exhibit a Bratteli diagram for this quotient and construct a morphism to $B$ with unique path lifting property. This is shown to be an isomorphism for the dynamics if a property `loops lifting to loops' is satisfied by $B(λ)\to B$.

math.DS↗
arXiv2006

The K-group of substitutional systems

In another article we associated a dynamical system to a non-properly ordered Bratteli diagram. In this article we describe how to compute the $K-$group $K_0$ of the dynamical system in terms of the Bratteli diagram. In the case of properly ordered Bratteli diagrams this description coincides with what is already known, namely the so-called dimension group of the Bratteli diagram. The new ordered group defined here is more relevant for non-properly ordered Bratteli diagrams. We use our main result to describe $K_0$ of a substitutional system.

math.DS↗
arXiv2005

Explicitly connecting T and Buscher dualities in String Theory

Buscher duality is a sigma-model duality, implemented by transformation of the target space. Not only in the case of a flat target space, but in a general background, should the Buscher duality reduce to the T-duality familiar in the flat-space string context. We exhibit this reduction explicitly using a pp-wave background as a tractable example. String theory is solved in a compactified Nappi-Witten background and the Buscher-dual theory is likewise solved. The Hamiltonian is computed in both cases, and the results are verified to be T-dual.

hep-th↗
arXiv2005

Quantum Phase Transition of a Magnet in a Spin Bath

The excitation spectrum of a model magnetic system, LiHoF$_4$, has been studied using neutron spectroscopy as the system is tuned to its quantum critical point by an applied magnetic field. The electronic mode softening expected for a quantum phase transition is forestalled by hyperfine coupling to the nuclear spins. We show that interactions with the nuclear spin bath control the length scale over which the excitations can be entangled. This generic result limits how far it is possible to approach intrinsic electronic quantum criticality.

cond-mat.other↗
arXiv2004

Chiral Symmetry Breaking and Dual Gluon Mass in the Confining Region of QCD

The Dual Meissner Effect description of QCD in the confining region provides $\frac{1}{q^4}$ behaviour for the gluon propagator and involves the dual gluon mass $m$ as a parameter. This is used in the Schwinger-Dyson equation for the quarks in the infrared region to exhibit chiral symmetry breaking for light quarks. Using the light quark condensate as input, the dual gluon mass is determined and its importance in showing the asymptotic free behaviour of the extrinsic curvature coupling in the rigid QCD string is discussed.

hep-th↗
arXiv2004

A q-Generalization of Product Densities and Janossy Functions in Stochastic Point Processes

A q-generalization of the product densities in stochastic point processes is developed. The properties of these functions are studied and a q-generalization of the usual $C^r_s$ coefficients is obtained. This for fixed q-number of particles coincides with the q-Stirling numbers of the second kind. The q-product densities are investigated using q-Poisson distribution and this shows that the stochastic point processes involving consistent q-generalization are inherently correlated. A closely related function to q-product densities is a q-generalized Janossy function and a relation between the two is established.

math-ph↗
arXiv2004

q-Fermionic Numbers and Their Roles in Some Physical Problems

The q-fermion numbers emerging from the q-fermion oscillator algebra are used to reproduce the q-fermionic Stirling and Bell numbers. New recurrence relations for the expansion coefficients in the 'anti-normal ordering' of the q-fermion operators are derived. The roles of the q-fermion numbers in q-stochastic point processes and the Bargmann space representation for q-fermion operators are explored.

quant-ph↗