arXiv subjects

Subir Ghosh

Publications and source records attributed to Subir Ghosh.

At least 37 records · Page 2Linked to original sources

arXiv2020

Quantum Mechanics of Particle on a torus knot: Curvature and Torsion Effects

Constraints play an important role in dynamical systems. However, the subtle effect of constraints in quantum mechanics is not very well studied. In the present work we concentrate on the quantum dynamics of a point particle moving on a non-trivial torus knot. We explicitly take into account the role of curvature and torsion, generated by the constraints that keep the particle on the knot. We exploit the "Geometry Induced Potential (GIP) approach" to construct the Schrodinger equation for the dynamical system, obtaining thereby new results in terms of particle energy eigenvalues and eigenfunctions. We compare our results with existing literature that completely ignored the contributions of curvature and torsion. In particular, we explicitly show how the "knottedness" of the path influences the results. In the process we have revealed a (possibly un-noticed) "topological invariant".

hep-th↗

arXiv2020

Hawking radiation in a non-covariant frame: the Jacobi metric approach

The present paper deals with a reformulation of the derivation of Hawking temperature for static and stationary black holes. In contrast to the conventional approach, where the covariant form of the metrics are used, we use the manifestly non-covariant Jacobi metric for the black holes in question. In the latter, a restricted form of Hamilton-Jacobi variational principle is exploited where the energy of the particle (pertaining to Hawking radiation) appears explicitly in the metric as a constant parameter. Our analysis shows that, as far as computation of Hawking temperature (for stationary black holes) is concerned, the Jacobi metric framework is more streamlined and yields the result with less amount of complications, (as for example, considerations of positive and negative energy modes and signature change of the metric across horizon do not play any direct role in the present analysis).

gr-qc↗

arXiv2020

Stimulated Hawking Emission From Electromagnetic Analogue Black Hole: Theory and Observation

In this paper we consider possible analogue Hawking radiation from a normal dielectric and metamaterial composite, having an analogue horizon where the dielectric parameters vanish and change sign upon crossing this transition zone. We follow a complex path analysis to show the presence of an analogue Hawking temperature at the horizon and subsequent photon production from the ambient electromagnetic field. Possibility of experimental observation is also commented upon.

hep-th↗

arXiv2019

Duality Between Dirac Fermions in Curved Spacetime and Optical solitons in Non-Linear Schrodinger Model: Magic of $1+1$-Dimensional Bosonization

Bosonization in curved spacetime maps massive Thirring model (self-interacting Dirac fermions) to a generalized sine-Gordon model, both living in $1+1$-dimensional curved spacetime. Applying this duality we have shown that the Thirring model fermion, in non-relativistic limit, gets identified with the soliton of non-linear Scrodinger model with Kerr form of non-linearity. We discuss one particular optical soliton in the latter model and relate it with the Thirring model fermion.

hep-th↗

arXiv2019

Observational constraints of a new unified dark fluid and the $H_0$ tension

Unified cosmological models have received a lot of attention in astrophysics community for explaining both the dark matter and dark energy evolution. The Chaplygin cosmologies, a well known name in this group have been investigated matched with observations from different sources. Obviously, Chaplygin cosmologies have to obey restrictions in order to be consistent with the observational data. As a consequence, alternative unified models, differing from Chaplygin model, are of special interest. In the present work we consider a specific example of such a unified cosmological model, that is quantified by only a single parameter $μ$, that can be considered as a minimal extension of the $Λ$-cold dark matter cosmology. We investigate its observational boundaries together with an analysis of the universe at large scale. Our study shows that at early time the model behaves like a dust, and as time evolves, it mimics a dark energy fluid depicting a clear transition from the early decelerating phase to the late cosmic accelerating phase. Finally, the model approaches the cosmological constant boundary in an asymptotic manner. We remark that for the present unified model, the estimations of $H_0$ are slightly higher than its local estimation and thus alleviating the $H_0$ tension.

gr-qc↗

arXiv2019

Relativistic Anyon Beam: Construction and Properties

Motivated by recent interest in photon and electron vortex beams, we propose the construction of a relativistic anyon beam. Following Jackiw and Nair [Phys. Rev. D 43, 1933 (1991)] we derive explicit form of relativistic plane wave solution of a single anyon. Subsequently we construct the planar anyon beam by superposing these solutions. Explicit expressions for the conserved anyon current are derived. Finally, we provide expressions for the anyon beam current using the superposed waves and discuss its properties. We also comment on the possibility of laboratory construction of anyon beam.

hep-th↗

arXiv2019

Geometric Phases for Classical and Quantum Dynamics: Hannay angle and Berry Phase for Loops on a Torus

In this paper we have considered closed trajectories of a particle on a two-torus where the loops are noncontractible (poloidal and toroidal loops and knots embedded on a regular torus). We have calculated Hannay angle and Berry phase for particle traversing such loops and knots when the torus itself is adiabatically revolving. Since noncontractible loops do not enclose any area Stokes theorem has to be applied with caution. In our computational scheme we have worked with line integrals directly thus avoiding Stokes theorem.

quant-ph↗

arXiv2019

Note on Morita Inequality for Planar Noncommutative Inverted Oscillator

A recent conjecture of Morita predicts a lower bound in temperature $T$ of a chaotic system, $T\geq (\hbar/2π)Λ$, $Λ$ being the Lyapunov exponent, which was demonstrated for a one dimensional inverse harmonic oscillator. In the present work we discuss the robustness of this demonstration in an extended version of the above model, where the inverse harmonic oscillator lives a in two dimensional noncommutative space. We show that, without noncommutativity, Morita's conjecture survives in an essentially unchanged way in two dimensions. However, if noncommutativity is switched on, the noncommutativity induced correction terms conspire to produce, in classical framework, a purely oscillating non-chaotic system without any exponential growth so that Lyapunov exponent is not defined. On the other hand, following Morita's analysis, we show that quantum mechanically an effective temperature with noncommutative corrections is generated. Thus Morita's conjecture is not applicable in the noncommutative plane. A dimensionless parameter $σ=mαθ^2$, (where $m, α, θ$ are the particle mass, coupling strength with inverse oscillator and the noncommutative parameter respectively) plays a crucial role in our analysis.

hep-th↗

arXiv2019

Thermodynamics and Phase Transition in Shapere-Wilczek {\it fgh} model: Cosmological Time Crystal in Quadratic Gravity

The Shapere-Wilczek model \cite{wil}, or so called $ fgh$ model, enjoys the remarkable features of a Time Crystal (TC) that has a non-trivial time dependence in its lowest energy state (or the classical ground state). We construct a particular form of $ fgh$ model (with specified $f,g,h$ functions) that is derived from a Mini-superspace version of a quadratic $f(R,R_{μν})$ gravity theory. Main part of the investigation deals with thermodynamic properties of such systems from classical statistical mechanics perspective. Our analysis reveals the possibility of a {\it phase transition}. Because of the higher (time) derivative nature of the model computation of the partial function is non-trivial and requires newly discovered techniques. We speculate about possible connection between our model and the Multiverse scenario.

hep-th↗

arXiv2018

Quasinormal mode spectra for odd parity perturbations in spacetimes with smeared matter sources

We have found the Quasi Normal Mode (QNM) frequencies of a class of static spherically symmetric spacetimes having a {\it {smeared}} matter distribution, parameterized by $Θ$ - an inherent length scale. Here our main focus is on the QNMs for the odd parity perturbation in this background geometry. The results presented here for diffused mass distribution reveal significant changes in the QNM spectrum. This could be relevant for future generation (cosmological) observations, specifically to distinguish the signals of GW from a non-singular source in contrast to a singular geometry. We also provide numerical estimates for the $Θ$-corrected QNM spectrum applicable to typical globular cluster like spherical galaxies having a Gaussian spread in their mass distribution. We find that the $Θ$-correction to the GW signal due to smeared distribution is accessible to present day observational precision.

hep-th↗

arXiv2018

AdS-CFT Correspondence in Noncommutative background, related thermodynamics and Holographic Superconductor in Magnetic Field

In this work, we formulate a Non-Commutative (NC) extension of AdS-CFT correspondence that is manifested in the modification of behavior of a holographic superconductor. The noncommutativity is introduced in the model through the NC corrected AdS charged black hole metric developed by Nicolini, Smailagic and Spallucci. First of all we discuss thermodynamic properties of this black hole in Euclidean formalism. In particular, we compute trace of the boundary energy-momentum tensor which, as expected, is non-zero due to the NC scale introduced in the model. Our findings indicate that the non-commutative effects tend to work against the black hole hair formation. This, in turn, has an adverse effect on the holographic superconductor by making the superconducting phase more fragile. This is reflected in the reduced value of the critical magnetic field and critical temperature. Finally, we comment on a qualitative agreement between our (holographic superconductor) result and that obtained for a conventional superconductor in NC space in a purely condensed matter scenario. In both cases noncommutativity tends to oppose the superconducting phase.

hep-th↗

arXiv2018

Development of bed forms due to waves blocked by a counter current

Experiments are conducted in a laboratory flume on the propagation of a surface wave against unidirectional flow with a sediment bed. This paper presents the spatial variation of bed forms induced by the wave-blocking phenomenon by a suitably tuned uniform fluid flow and a counter-propagating wave. The occurrence of wave-blocking is confirmed by finding a critical wave frequency in a particular flow discharge in which the waves are effectively blocked and is established using the linear dispersion relation. The novelty of this work is to identify the wave-blocking and its influence on the development of bed forms over the sediment bed. Interesting bed form signatures are observed at a transition of bed forms in three zones, with asymmetric ripples having a steeper slope downstream face induced by the incoming current, followed by flat sand bars beneath the wave-blocking zone and more symmetric ripples below the wave-dominated region at the downstream. This phenomenon suggests that the sediment bed is segmented into three different regions of bed geometry along the flow. The deviations of mean flows, Reynolds stresses, turbulent kinetic energy, and power spectral density due to the wave-blocking phenomenon are presented along the non-uniform flow over sediment bed. The bottom shear stress, bed roughness and stochastic nature of the bed form features are also discussed. The results are of relevance to engineers and geoscientists concerned with contemporary process as well as those interested in the interpretation of palaeoenvironmental conditions from fossil bed forms.

physics.flu-dyn↗

arXiv2018

Noncommutative fluid and Growing Modes of Inhomogeneity in (Newtonian) Cosmology

Time evolution of modes of density contrast, in particular the growing modes, dictate the structure formation in Universe. In this paper we explicitly show how (spatial) Non-Commutativity (NC) can affect the behavior of the modes, that is we compute NC corrected power law profiles of the density contrast modes. We develop a generalized fluid model that lives in NC space. The dynamical equations of fluid, namely the continuity and Euler equations receive NC contributions. When mapped to comoving coordinates these generate the NC extended versions of continuity and Friedmann equations for cosmology. Introducing cosmological perturbations finally yield the NC corrected evolution of density contrast modes. The construction of the NC fluid model from first principles and development of the formal aspects of its Hamiltonian formulation have been presented in the first part.

hep-th↗

arXiv2018

Back Reaction Inhomogeneities in Cosmological Parameter Evolution via Noncommutative Fluid

The paper discusses back reaction effects in cosmology, (á la Buchert et. al.), induced by noncommutative geometry effects in fluid. We have used generalizations of an action formulation of noncommutative fluid model, proposed earlier by us. We show that the noncommutative effects, depending on its nature, can play either roles of (kinematical) dark matter or Cosmological Constant.

hep-th↗

arXiv2018

Cosmological Time Crystal: Cyclic Universe with a small $Λ$ in a toy model approach

A new form Time Crystal has been proposed and some of its consequences have been studied. The model is a generalization of the Friedmann-Robertson-Walker (FRW) cosmology endowed with noncommutative geometry corrections. In the mini-superspace approach the scale factor undergoes the time periodic behavior, or Sisyphus dynamics, which allows us to interpret this Cosmological Time Crystal as a physically motivated toy model to simulate cyclic universe. Analyzing our model purely from Time Crystal perspective reveals many novelties such as a complex singularity structure (more complicated than the previously encountered swallowtail catastrophe) and a richer form of Sisyphus dynamics. In the context of cosmology, the system can serve as a toy model in which, apart from inducing a form of cyclic universe feature, it is possible to generate an arbitrarily small positive effective Cosmological Constant. We stress that the model is purely geometrical without introduction of matter degrees of freedom.

hep-th↗

arXiv2018

Turbulence characteristics of wave-blocking phenomena

This study explores experimentally the turbulent flow in a laboratory flume, interacting with waves propagated against the flow. It focuses a region of wave-blocking for which there is a streamwise location on the water surface, where the wave propagation velocity vanishes. The observations are corroborated by finding a critical wave frequency for a particular discharge above which the waves are effectively blocked; and verified by the dispersion relation of monochromatic wave. The counter-current propagating waves show an evolutionary change in the flow with three segmented regions, viz, flow at the upstream, blocking at the mid-stream and waves in the downstream. The instantaneous velocity data were collected using 3D Micro-acoustic Doppler velocimeter (ADV) along the flume centerline. This study addresses the changes in the mean flows, Reynolds stresses, eddy viscosity, turbulence kinetic energy fluxes and associated contributions of burst-sweep cycles to the total Reynolds shear stress due to addition of surface waves against a current. The velocity power spectral analysis shows the energy distribution over the whole profile from upstream to downstream. The quadrant analysis is also used to highlight the turbulent event evolutions along the flow; and shows that at the waveblocking and wave dominated regions, the contributions from ejection and sweep to the total shear stress are dominant. The changes in turbulence key parameters due to waveblocking may affect the sediment transport in coastal region

physics.flu-dyn↗

arXiv2018

Particle on a Torus Knot: Anholonomy and Hannay Angle

The phenomenon of rotation of a vector under parallel transport along a closed path is known as anholonomy. In this paper we have studied the anholonomy for noncontractible loops - closed paths in a curved surface that do not enclose any area and hence Stokes theorem is not directly applicable. Examples of such closed paths are poloidal and toroidal loops and knots on a torus. The present study is distinct from conventional results on anholonomy for closed paths on $S_2$ since in the latter case all closed paths are contractible or trivial cycles. We find that for some nontrivial cycles the anholonomy cancels out over the complete cycle. Next we calculate Hannay angle for a particle traversing such noncontractible loops when the torus itself is revolving. Some new and interesting results are obtained especially for poloidal paths that is for paths that encircle the torus ring.

quant-ph↗

arXiv2018

On the equivalence among stress tensors in a gauge-fluid system

In this paper we bring out the subtleties involved in the study of a first order relativistic field theory with auxiliary field variables playing an essential role. In particular we discuss the nonisentropic Eulerian (or Hamiltonian) fluid model. Interactions are introduced by coupling the fluid to a {\it dynamical} Maxwell ($U(1)$) gauge field. This dynamical nature of the gauge field is crucial in showing the equivalence, on the physical subspace, of the stress tensor derived from two definitions, {\it{ie.}} the canonical (Noether) one and the symmetric one. In the conventional equal-time formalism, we have shown that the generators of the spacetime transformations obtained from these two definitions agree, modulo the Gauss constraint. This equivalence in the physical sector has been achieved only because of the dynamical nature of the gauge fields. Subsequently we have explicitly demonstrated the validity of the Schwinger condition. A detailed analysis of the model in lightcone formalism has also been done where several interesting features are revealed.

hep-th↗