arXiv subjects

Subir Ghosh

Publications and source records attributed to Subir Ghosh.

At least 55 records · Page 3Linked to original sources

arXiv2017

Galilei Group with multiple central extension, vorticity and entropy generation: "Exotic" fluid in 3+1-dimensions

A noncommutative extension of an ideal (Hamiltonian) fluid model in $3+1$-dimensions is proposed. The model enjoys several interesting features: it allows a multi-parameter central extension in Galilean boost algebra (which is significant being contrary to existing belief that similar feature can appear only in $2+1$-dim.); noncommutativity generates vorticity in a canonically irrotational fluid; it induces a non-barotropic pressure leading to a non-isentropic system. (Barotropic fluids are entropy preserving as pressure depends only on matter density.) Our fluid model is termed "Exotic" since it has close resemblance with the extensively studied planar (2+1-dim.) Exotic models and Exotic (noncommutative) field theories.

hep-th↗

arXiv2017

Motion of charged particle in Reissner-Nordstrom spacetime: A Jacobi metric approach

The present work discusses motion of neutral and charged particles in Reissner - Nordstrom spacetime. The constant energy paths are derived in a variational principle framework using the Jacobi metric which is parameterized by conserved particle energy. Of particular interest is the case of particle charge and Reissner-Nordstrom black hole charge being of same sign since this leads to a clash of opposing forces - gravitational (attractive) and Coulomb (repulsive). Our paper aims to compliment the recent works of Pugliese, Quevedo and Ruffini [1,2]. The energy dependent Gaussian curvature (induced by Jacobi metric), plays an important role in classifying the trajectories.

gr-qc↗

arXiv2017

Weyl and transverse diffeomorphism invariant spin-2 models in D=2+1

There are two covariant descriptions of massless spin-2 particles in $D=3+1$ via a symmetric rank-2 tensor: the linearized Einstein-Hilbert (LEH) theory and the Weyl plus transverse diffeomorphism (WTDIFF) invariant model. From the LEH theory one can obtain the linearized New Massive Gravity (NMG) in $D=2+1$ via Kaluza-Klein dimensional reduction followed by a dual master action. Here we show that a similar route takes us from the WTDIFF model to a linearized scalar tensor NMG which belongs to a larger class of consistent spin-0 modifications of NMG. We also show that a traceless master action applied to a parity singlet furnishes two new spin-2 selfdual models. Moreover, we examine the singular replacement $h_{μν} \to h_{μν} - η_{μν}h/D$ and prove that it leads to consistent massive spin-2 models in $D=2+1$. They include linearized versions of unimodular topologically massive gravity (TMG) and unimodular NMG. Although the free part of those unimodular theories are Weyl invariant, we do not expect any improvement in the renormalizability. Both the linearized K-term (in NMG) and the linearized gravitational Chern-Simons term (in TMG) are invariant under longitudinal reparametrizations $δh_{μν} = \p_μ\p_νζ$ which is not a symmetry of the WTDIFF Einstein-Hilbert term. Therefore, we still have one degree of freedom whose propagator behaves like $1/p^2$ for large momentum.

hep-th↗

arXiv2017

Noncommutative Geometry and Fluid Dynamics

In the present paper we have developed a Non-Commutative (NC) generalization of perfect fluid model from first principles, in a Hamiltonian framework. The noncommutativity is introduced at the Lagrangian (particle) coordinate space brackets and the induced NC fluid bracket algebra for the Eulerian (fluid) field variables is derived. Together with a Hamiltonian this NC algebra generates the generalized fluid dynamics that satisfies exact local conservation laws for mass and energy thereby maintaining mass and energy conservation. However, nontrivial NC correction terms appear in charge and energy fluxes. Other non-relativistic spacetime symmetries of the NC fluid are also discussed in detail. This constitutes the study of kinematics and dynamics of NC fluid. In the second part we construct an extension of Friedmann-Robertson-Walker (FRW) cosmological model based on the NC fluid dynamics presented here. We outline the way in which NC effects generate cosmological perturbations bringing in anisotropy and inhomogeneity in the model. We also derive a NC extended Friedmann equation.

hep-th↗

arXiv2016

Particle on a torus knot: a Hamiltonian analysis

We have studied the dynamics and symmetries of a particle constrained to move in a torus knot. The Hamiltonian system turns out to be Second Class in Dirac's formulation and the Dirac brackets yield novel noncommutative structures. The equations of motion are obtained for a path in general where the knot is present in the particle orbit but it is not restricted to a particular torus. We also study the motion when it is restricted to a specific torus. The rotational symmetries are studied as well. We have also considered the behavior of small fluctuations of the particle motion about a fixed torus knot.

hep-th↗

arXiv2016

Particle on a Torus Knot: Constrained Dynamics and Semi-Classical Quantization in a Magnetic Field

Kinematics and dynamics of a particle moving on a torus knot poses an interesting problem as a constrained system. In the first part of the paper we have derived the modified symplectic structure or Dirac brackets of the above model in Dirac's Hamiltonian framework, both in toroidal and Cartesian coordinate systems. This algebra has been used to study the dynamics, in particular small fluctuations in motion around a specific torus. The spatial symmetries of the system have also been studied. In the second part of the paper we have considered the quantum theory of a charge moving in a torus knot in the presence of a uniform magnetic field along the axis of the torus in a semiclassical quantization framework. We exploit the Einstein - Brillouin - Keller (EBK) scheme of quantization that is appropriate for multidimensional systems. Embedding of the knot on a specific torus is inherently two dimensional that gives rise to two quantization conditions. This shows that although the system, after imposing the knot condition reduces to a one dimensional system, even then it has manifest non-planar features which shows up again in the study of fractional angular momentum. Finally we compare the results obtained from EBK (multi-dimensional) and Bohr-Sommerfeld (single dimensional) schemes. The energy levels and fractional spin depend on the torus knot parameters that specifies its non-planar features. Interestingly, we show that there can be non-planar corrections to the planar anyon-like fractional spin.

hep-th↗

arXiv2015

Analogue White Hole Horizon and its Impact on Sediment Transport

Motivated by the ideas of analogue gravity, we have performed experiments in a flume where an analogue White Hole horizon is generated, in the form of a wave blocking region, by suitably tuned uniform fluid (water) flow and counter-propagating shallow water waves. We corroborate earlier experimental observations by finding a critical wave frequency for a particular discharge above which the waves are effectively blocked beyond the horizon. An obstacle, in the form of a bottom wave, is introduced to generate a sharp blocking zone. All previous researchers used this obstacle. A novel part of our experiment is where we do not introduce the obstacle and find that wave blocking still takes place, albeit in a more diffused zone. Lastly we replace the fixed bottom wave obstacle by a movable sand bed to study the sediment transport and the impact of the horizon or wave blocking phenomenon on the sediment profile. We find signatures of the wave blocking zone in the ripple pattern.

physics.flu-dyn↗

arXiv2015

Hamiltonian analysis of interacting fluids

Ideal fluid dynamics is studied as a relativistic field theory with particular importance on its hamiltonian structure. The Schwinger condition, whose integrated version yields the stress tensor conservation, is explicitly verified both in equal-time and light-cone coordinate systems. We also consider the hamiltonian formulation of fluids interacting with an external gauge field. The complementary roles of the canonical(Noether) stress tensor and the symmetric one obtained by metric variation are discussed. Finally, a non-relativistic reduction of the system in light-cone coordinates has been carried out which reproduces results found earlier in the literature.

hep-th↗

arXiv2015

Noncommutative Extension of AdS-CFT and Holographic Superconductors

In this Letter, we consider a Non-Commutative (NC) extension of AdS-CFT correspondence and its effects on holographic superconductors. NC corrections are incorporated via the NC generalization of Schwarzschild black hole metric in AdS with the probe limit. We study NC effects on the relations connecting the charge density and the critical temperature of the Holographic Superconductors. Furthermore, condensation operator of the superconductor has been analyzed. Our results suggest that generically, NC effects increase the critical temperature of the holographic superconductor.

hep-th↗

arXiv2014

Conformal Invariance in noncommutative geometry and mutually interacting Snyder Particles

A system of relativistic Snyder particles with mutual two-body interaction that lives in a Non-Commutative Snyder geometry is studied. The underlying novel symplectic structure is a coupled and extended version of (single particle) Snyder algebra. In a recent work by Casalbuoni and Gomis, Phys.Rev. D90, 026001 (2014), a system of interacting conventional particles (in commutative spacetime) was studied with special emphasis on it's Conformal Invariance. Proceeding along the same lines we have shown that our interacting Snyder particle model is also conformally invariant. Moreover, the conformal Killing vectors have been constructed. Our main emphasis is on the Hamiltonian analysis of the conformal symmetry generators. We demonstrate that the Lorentz algebra remains undeformed but validity of the full conformal algebra requires further restrictions.

hep-th↗

arXiv2014

Effects of a Maximal Energy Scale in Thermodynamics for Photon Gas and Construction of Path Integral

In this article, we discuss some well-known theoretical models where an observer-independent energy scale or a length scale is present. The presence of this invariant scale necessarily deforms the Lorentz symmetry. We study different aspects and features of such theories about how modifications arise due to this cutoff scale. First we study the formulation of energy-momentum tensor for a perfect fluid in doubly special relativity (DSR), where an energy scale is present. Then we go on to study modifications in thermodynamic properties of photon gas in DSR. Finally we discuss some models with generalized uncertainty principle (GUP).

gr-qc↗

arXiv2014

Electrodynamics of a Generalized Charged Particle in Doubly Special Relativity Framework

In the present paper, dynamics of generalized charged particles are studied in the presence of external electromagnetic interactions. This particular extension of the free relativistic particle model lives in Non-Commutative $κ$-Minkowski space-time, compatible with Doubly Special Relativity, that is motivated to describe Quantum Gravity effects. Furthermore we have also considered the electromagnetic field to be dynamical and have derived the modified forms of Lienard-Wiechert like potentials for these extended charged particle models. In all the above cases we exploit the new and extended form of $κ$-Minkowski algebra where electromagnetic effects are incorporated in the lowest order, in the Dirac framework of Hamiltonian constraint analysis.

hep-th↗

arXiv2014

Spontaneous Generation of a Crystalline Ground State in a Higher Derivative Theory

The possibility of Spontaneous Symmetry Breaking in momentum space in a generic Lifshitz scalar model - a non-relativistic scalar field theory with higher spatial derivative terms - has been studied. We show that the minimum energy state, the ground state, has a lattice structure, where the translation invariance of the continuum theory is reduced to a discrete translation symmetry. The scale of translation symmetry breaking (or induced lattice spacing) is proportional to the inverse of the momentum of the condensate particle. The crystalline ground state is stable under excitations below a certain critical velocity. The small fluctuations above the ground state can have a phonon like dispersion under suitable choice of parameters. At the beginning we have discussed the effects of next to nearest neighbour interaction terms in a model of linear triatomic molecule depicted by a linear system of three particles of same mass connected by identical springs. This model is relevant since in the continuum limit the next to nearest neighbour interaction terms generate higher (spatial) derivative wave equation, the main topic of this paper.

hep-th↗

arXiv2013

Quantum Gravity Effects in Geodesic Motion and Predictions of Equivalence Principle Violation

We show that the Equivalence Principle (EP) is violated by Quantum Gravity (QG) effects. The predicted violations are compared to experimental observations for Gravitational Redshift, Law of Reciprocal Action and Universality of Free Fall. This allows us to derive explicit bounds for $β$ - the QG scale. In our approach, there appears a deviation in the geodesic motion of a particle. This deviation is induced by a non-commutative spacetime, consistent with a Generalized Uncertainty Principle (GUP). GUP admits the presence of a minimum length scale, that is advocated by QG theories. Remarkably, the GUP induced corrections are quite robust since the bound on $β$ obtained by us, {\it{in General Relativity scenario in an essentially classical setting}} of modified geodesic motion, is closely comparable to similar bounds in recent literature \cite{vag}. The latter are computed in purely {\it{quantum}} physics domain in {\it{flat}} spacetime.

gr-qc↗

arXiv2013

Spontaneous Photoemission From Metamaterial Junction: A Conjecture

The possibility of spontaneous photon pair emission from a normal material - metamaterial junction is investigated in a quantum field theory setting. We consider a pair of photons arising from vacuum fluctuations of the electromagnetic field close to the junction where one photon each comes from the normal and metamaterial sectors. Mixing between the positive and negative norm photon modes can give rise to spontaneous photoemission, the rate of which is calculated.

physics.optics↗

arXiv2013

Inertial spin Hall effect in noncommutative space

In the present paper the study of inertial spin current(that appears in an accelerated frame of reference) is extended to Non-Commutative (NC) space. The $θ$-dependence, ($θ$ being the NC parameter), of the inertial spin current is derived explicitly. We have provided yet another way of experimentally measuring $θ$. Our bound on $θ$ matches with previous results. In Hamiltonian framework, the Dirac Hamiltonian in an accelerating frame is computed in the low energy regime by exploiting the Foldy-Wouthuysen scheme. The NC $θ$-effect appears from the replacement of normal products and commutators by Moyal *-products and *-commutators. In particular, the commutator between the external magnetic vector potential and the potential induced by acceleration becomes non-trivial. Expressions for $θ$-corrected inertial spin current and conductivity are derived. The $θ$ bound is obtained from the out of plane spin polarization, which is experimentally observable.

cond-mat.mes-hall↗

arXiv2013

GUP-based and Snyder Non-Commutative Algebras, Relativistic Particle models and Deformed Symmetries: A Unified Approach

We have developed a unified scheme for studying Non-Commutative algebras based on Generalized Uncertainty Principle (GUP) and Snyder form in a relativistically covariant point particle Lagrangian (or symplectic) framework. Even though the GUP based algebra and Snyder algebra are very distinct, the more involved latter algebra emerges from an approximation of the Lagrangian model of the former algebra. Deformed Poincare generators for the systems that keep space-time symmetries of the relativistic particle models have been studied thoroughly. From a purely constrained dynamical analysis perspective the models studied here are very rich and provide insights on how to consistently construct approximate models from the exact ones when non-linear constraints are present in the system. We also study dynamics of the GUP particle in presence of external electromagnetic field.

hep-th↗

arXiv2013

On the Stability of Coherent States for Pais-Uhlenbeck Oscillator

We have constructed coherent states for the higher derivative Pais-Uhlenbeck Oscillator. In the process we have suggested a novel way to construct coherent states for the oscillator having only negative energy levels. These coherent states have negative energies in general but their coordinate and momentum expectation values and dispersions behave in an identical manner as that of normal (positive energy) oscillator. The coherent states for the Pais-Uhlenbeck Oscillator have constant dispersions and a modified Heisenberg Uncertainty Relation. Moreover, under reasonable assumptions on parameters these coherent states can have positive energies.

math-ph↗