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Kinjal Banerjee

Publications and source records attributed to Kinjal Banerjee.

At least 19 recordsLinked to original sources

Asymptotic Symmetries at Spatial Infinity

We describe asymptotic symmetries at spatial infinity of asymptotically flat spacetimes within the context of a generalization of the Beig-Schmidt-Ashtekar-Romano-framework. We demonstrate that it is possible to relax certain smoothness requirements of the asymptotic transformations considered previously, without violating asymptotic flatness. This leads to an enhancement of the asymptotic symmetry group that includes logarithmic supertranslations at spatial infinity. Our results complement several recent results which confirm the existence of logarithmic supertranslations at spatial infinity in the Hamiltonian formalism.

gr-qc

Constructing Viable Interacting Dark Matter and Dark Energy Models: A Dynamical Systems Approach

We study the evolution of $k=-1$ FLRW cosmological models for two interacting Dark Matter-Dark Energy Models using dynamical system analysis. Since we are interested in late time evolution, the sign of the interaction term is chosen such that it facilitates the transfer of energy from dark matter to dark energy. We also explore the $k=0$ invariant subspace of these models. We find that both these models have sectors which have a stable fixed point where we can recover an accelerating universe with a negative equation of state. This indicates these can be viable models for our universe. We also rule out certain sectors of these models because they do not give the correct late time observational features. We observe that although we start with a dust-like Dark Matter, its effective equation of state evolves due to its interaction with Dark Energy. As a result, the Dark Matter can display features of stiff matter and exotic matter in the course of evolution.

gr-qc

One-Loop Quantum Effects in Carroll Scalars

Carrollian field theories at the classical level possess an infinite number of space-time symmetries, namely the supertranslations. In this article, we inquire whether these symmetries for interacting Carrollian scalar field theory survive in the presence of quantum effects. For interactions polynomial in the field, the answer is in the affirmative. We also study a renormalization group flow particularly tailored to respect the manifest Carroll invariance and analyze the consequences of introducing Carroll-breaking deformations. The renormalization group flow, with perturbative loop-level effects taken into account, indicates a new fixed point apart from the Gaussian ones.

hep-th

de Sitterization via Kerr-Schild

Spatially homogeneous cosmological spacetimes, evolving in the presence of a positive cosmological constant and matter satisfying some reasonable energy conditions, typically approach the de Sitter geometry asymptotically (at least locally). In this work, we propose an alternate way to characterize this phenomena. We focus on a subset of such models admitting a generalized Kerr-Schild representation. We argue that the functions which define such a representation can be chosen, such that, their asymptotic behavior make the evolution towards the de Sitter spacetime manifest through the representation. We verify our claim for the Kantowski-Sachs family of cosmological spacetimes.

gr-qc

Realizing the potential of deep neural network for analyzing neutron star observables and dense matter equation of state

The difficulty in describing the equation of state (EoS) for nuclear matter at densities above the saturation density ($\rho_0$) has led to the emergence of a multitude of models based on different assumptions and techniques. These EoSs, when used to describe a neutron star (NS), lead to differing values of observables. An outstanding goal in astrophysics is to constrain the dense matter EoS by exploiting astrophysical and gravitational wave measurements. Nuclear matter parameters appear as Taylor coefficients in the expansion of the EoS around the saturation density of symmetric and asymmetric nuclear matter and provide a physically-motivated representation of the EoS. In this paper, we introduce a deep learning-based methodology to predict key neutron stars observables such as the NS mass, NS radius, and tidal deformability from a set of nuclear matter parameters. Using generated mock data, we confirm that the neural network model is able to accurately capture the underlying physics of finite nuclei and replicate inter-correlations between the symmetry energy slope, its curvature, and the tidal deformability arising from a set of physical constraints. We also test our network with mock data generated by a different class of physics model, which was not part of the training, to explore the limitations of model dependency in the results. We also study the validity of our trained model using Bayesian inference and show that the performance of our model is on par with physics-based models with the added benefit of much lower computational cost.

nucl-th

Quantization of Interacting Galilean Field theories

We present the quantum field description of Galilean electrodynamics minimally coupled to massless Galilean fermion in (3 + 1) dimensions. At the classical level, the Lagrangian is obtained as a null reduction of a relativistic theory in one higher dimension. We use functional techniques to develop the quantum field description of the theory. Quantum corrections to the propagators and vertex are obtained upto first order and the theory is found to be renormalizable to this order. The beta function of the theory is found to grow linearly; the theory is not asymptotically free.

hep-th

The Neutron Star Outer Crust Equation of State: A Machine Learning approach

Constructing the outer crust of the neutron stars requires the knowledge of the Binding Energy (BE) of the atomic nuclei. Although the BE of a lot of the nuclei is experimentally determined and can be obtained from the AME data table, for the others we need to depend on theoretical models. There exist a lot of physical theories to predict the BE, each with its own strengths and weaknesses. In this paper, we apply Machine Learning (ML) algorithms on AME2016 data set to predict the Binding Energy {of atomic nuclei}. The novel feature of our work is that it is model independent. We do not assume or use any nuclear physics model but use only ML algorithms directly on the AME2016 data set. Our results are further refined by using another ML algorithm to train the errors of the first algorithm, and repeating this process iteratively. Our best algorithm gives $σ_{\rm rms} \approx 0.58$ MeV for Binding Energy on randomized testing sets. This is comparable to all physics models or ML improved physics models studied in literature till date. Using the predictions of our Machine Learning algorithm, we construct the outer crust equation of state (EoS) of a neutron star and show that our model is comparable to existing models. This work also demonstrates the use of various ML algorithms and a detailed analysis on how we arrived at our best algorithm. It will help the physics community in understanding how to choose an ML algorithm which would be suited for their data set. Our algorithms and best fit model is also made publicly available for the use of the community.

physics.comp-ph

Interacting Conformal Carrollian Theories: Cues from Electrodynamics

We construct the free Lagrangian of the magnetic sector of Carrollian electrodynamics. The construction relies on Helmholtz integrability condition for differential equations in a self consistent algorithm, working hand in hand with imposing invariance under infinite dimensional Conformal Carroll algebra. It requires inclusion of new fields in the dynamics and the system is free of gauge redundancies. We next add interaction (quartic) terms to the free Lagrangian, strictly constrained by conformal invariance and Carrollian symmetry. The dynamical realization of the non-semi simple infinite dimensional symmetry algebra at the level of charge algebra is exact and free from central terms.

hep-th

Uniqueness of Galilean Conformal Electrodynamics and its Dynamical Structure

We investigate the existence of action for both the electric and magnetic sectors of Galilean Electrodynamics using Helmholtz conditions. We prove the existence of unique action in magnetic limit with the addition of a scalar field in the system. The check also implies the non existence of action in the electric sector of Galilean electrodynamics. Dirac constraint analysis of the theory reveals that there are no local degrees of freedom in the system. Further, the theory enjoys a reduced but an infinite dimensional subalgebra of Galilean conformal symmetry algebra as global symmetries. The full Galilean conformal algebra however is realized as canonical symmetries on the phase space. The corresponding algebra of Hamilton functions acquire a state dependent central charge.

hep-th

Properties of Neutron Stars with hyperon cores in parameterized hydrostatic conditions

Models of neutron stars (NSs) with hyperon cores are constructed with an effective chiral model in mean-field approximation. The hyperon couplings are fixed by reproducing their experimentally determined binding energies. The impact of these couplings on population of different particles and the equation of state (EoS) are studied in this work. The global properties of NSs like gravitational mass, radius, baryonic mass and central density are calculated using parameterized Tolman-Oppenheimer-Volkoff equations (PTOV) with special emphasis on two effects of pressure - one contributing to total mass density and the other to self gravity of the star. We find that with PTOV solutions in static conditions, a softer EoS (including hyperons) can also lead to massive stellar configurations of NSs, which are in well agreement with the observed maximum mass bound of $\approx 2 M_{\odot}$ (PSR J0348-0432). Estimates of $R_{1.4}$ and $R_{1.6}$, obtained with the PTOV equations are consistent with the recent findings of the same from the data analysis of gravitational waves (GW170817) observation. Keywords: Neutron Star; Hyperons; Equation of State; parameterized Tolman-Oppenheimer-Volkoff equations

nucl-th

Nuclear symmetry energy with mesonic cross-couplings in the effective chiral model

The effective chiral model is extended by introducing the contributions from the cross-couplings between isovector and isoscalar mesons. These cross-couplings are found to be instrumental in improving the density content of the nuclear symmetry energy. The nuclear symmetry energy as well as its slope and curvature parameters at the saturation density are in harmony with those deduced from a diverse set of experimental data. The equation of state for pure neutron matter at sub-saturation densities is also in accordance with the ones obtained from different microscopic models. The maximum mass of neutron star is consistent with the measurement and the radius at the canonical mass of the neutron star is within the empirical bounds.

nucl-th

Plunges in the Bombay stock exchange: Characteristics and indicators

We study the various sectors of the Bombay Stock Exchange (BSE) for a period of eight years from January 2006 to March 2014. Using the data of the daily returns of a period of eight years we investigate the financial cross correlation co-efficients among the sectors of BSE and Price by Earning (PE) ratio of BSE Sensex. We show that the behavior of these quantities during normal periods and during crisis is very different. We show that the PE ratio shows a particular distinctive trend in the approach to a crash of the financial market and can therefore be used as an indicator of an impending catastrophe. We propose that a model of analysis of crashes in a financial market can be built using two parameters: (i) the PE ratio and (ii) the largest eigenvalue of the cross correlation matrix.

q-fin.ST

Towards a dS/MERA correspondence

Recent advances have suggested that spacetime itself emerges from the entanglement of the quantum degrees of freedom living on the boundary. In the case of the AdS spacetimes, a particular class of tensor networks has been shown to realize the same via Multi-Scale Entanglement Renormalization Ansatz (MERA). In this paper we suggest a prescription for the dS/MERA correspondence and recover a discrete version of de Sitter Penrose diagram by using the MERA on conformal theories identified with the future/past conformal boundaries of the de Sitter spacetime. As anticipated, time appears as the emergent direction. We comment on the possible interpretation that the de Sitter cosmological horizon entropy involves entanglement with degrees of freedom across the cosmological horizon as well as the implications of our construction for cosmology.

hep-th

Quantum Dynamics of Complex Hamiltonians

Non hermitian Hamiltonians play an important role in the study of dissipative quantum systems. We show that using states with time dependent normalization can simplify the description of such systems especially in the context of the classical limit. We apply this prescription to study the damped harmonic oscillator system. This is then used to study the problem of radiation in leaky cavity.

quant-ph

A Brief Review of Helmholtz Conditions

It is well known that the equations of motion obtained from Newtons second law of motion can be obtained from a Lagrangian via the Euler-Lagrangian formulation if and only if the equations of motion satisfy the Helmholtz conditions. In this pedagogical article we give a simple proof of the above statement and show its application to simple mechanical and dissipative systems.

math-ph

A Study of Correlations in the Stock Market

We study the various sectors of the Bombay Stock Exchange(BSE) for a period of 8 years from April 2006 - March 2014. Using the data of daily returns of a period of eight years we make a direct model free analysis of the pattern of the sectorial indices movement and the correlations among them. Our analysis shows significant auto correlation among the individual sectors and also strong cross-correlation among sectors. We also find that auto correlations in some of the sectors persist in time. This is a very significant result and has not been reported so far in Indian context These findings will be very useful in model building for prediction of price movement of equities, derivatives and portfolio management. We show that the Random Walk Hypothesis is not applicable in modeling the Indian market and Mean-Variance-Skewness-Kurtosis based portfolio optimization might be required. We also find that almost all sectors are highly correlated during large fluctuation periods and have only moderate correlation during normal periods.

q-fin.ST

Connection dynamics of a gauge theory of gravity coupled with matter

We study the coupling of the gravitational action, which is a linear combination of the Hilbert-Palatini term and the quadratic torsion term, to the action of Dirac fermions. The system possesses local Poincare invariance and hence belongs to Poincare gauge theory with matter. The complete Hamiltonian analysis of the theory is carried out without gauge fixing but under certain ansatz on the coupling parameters, which leads to a consistent connection dynamics with second-class constraints and torsion. After performing a partial gauge fixing, all second-class constraints can be solved, and a SU(2)-connection dynamical formalism of the theory can be obtained. Hence, the techniques of loop quantum gravity can be employed to quantize this Poincare gauge theory with non-zero torsion. Moreover, the Barbero-Immirzi parameter in loop quantum gravity acquires its physical meaning as the coupling parameter between the Hilbert-Palatini term and the quadratic torsion term in this gauge theory of gravity.

gr-qc

Hamiltonian Analysis of $R + T^2$ Action

We study a gravitational action which is a linear combination of the Hilbert-Palatini term and a term quadratic in torsion and possessing local Poincare invariance. Although this action yields the same equations of motion as General Relativity, the detailed Hamiltonian analysis without gauge fixing reveals some new points never shown in the Hilbert-Palatini formalism. These include that an additional term containing torsion appears in the spatial diffeomorphism constraint and that the primary second-class constraints have to be imposed in a manner different from that in the Hilbert-Palatini case. These results may provide valuable lessons for further study of Hamiltonian systems with torsion.

gr-qc