arXiv subjects

Swapna Mahapatra

Publications and source records attributed to Swapna Mahapatra.

At least 19 recordsLinked to original sources

arXiv2025

On Critical Temperature and Finite Size Scaling of Continuous Spin $2d$ Ising Model

In this paper, we have studied the critical temperature $T_c$ of continuous spin $2d$ square-lattice Ising model using Monte-Carlo simulation. We have considered spins $s$ in a bounded interval, where $s \in [-1,+1]$ in square-lattice configuration with periodic boundary condition. We have observed that the critical temperature $T_c$ is approximately $0.925$, showing a clear second order phase transition. Considering finite size scaling, we have also obtained the critical exponents associated with susceptibility, specific heat, magnetization and we find that these values are in good agreement with the corresponding values obtained for the standard $2d$ Ising universality class.

cond-mat.stat-mech↗

arXiv2024

Weyl-Lewis-Papapetrou coordinates, self-dual Yang-Mills equations and the single copy

We consider the dimensional reduction to two dimensions of certain gravitational theories in $D \geq 4$ dimensions at the two-derivative level. It is known that the resulting field equations describe an integrable system in two dimensions which can also be obtained by a dimensional reduction of the self-dual Yang-Mills equations in four dimensions. We use this relation to construct a single copy prescription for classes of gravitational solutions in Weyl-Lewis-Papapetrou coordinates. In contrast with previous proposals, we find that the gauge group of the Yang-Mills single copy carries non-trivial information about the gravitational solution. We illustrate our single copy prescription with various examples that include the extremal Reissner-Nordstrom solution, the Kaluza-Klein rotating attractor solution, the Einstein-Rosen wave solution and the self-dual Kleinian Taub-NUT solution.

hep-th↗

arXiv2022

Anisotropic expansion, dissipative hydrodynamics from kinetic theory

We consider Kasner space-time describing anisotropic three dimensional expansion of the fluid and obtain the dissipative evolution equations for shear stress tensor and energy density from kinetic theory. For this, we use the iterative solution of relativistic Boltzmann equation with relaxation time approximation. We show that our results for second and third order evolution equations reduce to those of one dimensional expansion case under suitable conditions for the anisotropic parameters in Kasner space-time.

hep-th↗

arXiv2021

Anisotropic expansion, second order hydrodynamics and holographic dual

We consider Kasner space-time describing anisotropic three dimensional expansion of RHIC and LHC fireball and study the generalization of Bjorken's one dimensional expansion by taking into account second order relativistic viscous hydrodynamics. Using time dependent AdS/CFT correspondence, we study the late time behaviour of the Bjorken flow. From the conditions of conformal invariance and energy-momentum conservation, we obtain the explicit expression for the energy density as a function of proper time in terms of Kasner parameters. The proper time dependence of the temperature and entropy have also been obtained in terms of Kasner parameters. We consider Eddington-Finkelstein type coordinates and discuss the gravity dual of the anisotropically expanding fluid in the late time regime.

hep-th↗

arXiv2020

A comparative study of $2d$ Ising model at different boundary conditions using non-deterministic Hexagonal Cellular Automata

The spin system of the $2d$ Ising model having a hexagonal-lattice is simulated using non-deterministic Cellular Automata. The method to implement this program is outlined and our results show a good approximation to the exact analytic solution. The phase transition in $2d$ Ising model is studied with a $40\times40$ hexagonal-lattice with five different boundary conditions (bcs) i.e., adiabatic, periodic, reflexive, fixed $+1$ and fixed $-1$ with random orientation of spins as initial conditions in the absence of an external applied magnetic field. The critical temperature below which the spontaneous magnetization appears as well as other physical quantities such as the magnetization, energy, specific heat, susceptibility and entropy with each of the bcs are calculated. The phase transition occurs around $T^H_c$ = 1.5 which approximates well with the result obtained from exact analytic solution by Wannier and Houtappel. We compare the behavior of magnetisation per cell for five different types of bcs by calculating the number of points close to the line of zero magnetization for $T>T^H_c$. We find that the periodic, adiabatic and reflexive bcs give closer approximation to the value of $T^H_c$ than fixed $+1$ and fixed $-1$ bcs with all three initial conditions for lattice size less than $50\times50$. However, for lattice size between $50\times50$ and $200\times200$, fixed $+1$ bc and fixed $-1$ bc give closer approximation to the $T^H_c$ with initial conditions in which all spins are in down configuration and all spins are in up configuration respectively.

cond-mat.stat-mech↗

arXiv2018

A comparative study of $2d$ Ising model at different boundary conditions using Cellular Automata

Using Cellular Automata, we simulate spin systems corresponding to $2d$ Ising model with various kinds of boundary conditions (bcs). The appearance of spontaneous magnetization in the absence of magnetic field is studied with a $64\times64$ square lattice with five different bcs, i.e., periodic, adiabatic, reflexive, fixed ($+1$ or $-1$) bcs with three initial conditions (all spins up, all spins down and random orientation of spins). In the context of $2d$ Ising model, we have calculated the magnetisation, energy, specific heat, susceptibility and entropy with each of the bcs and observed that the phase transition occurs around $T_c$ = 2.269 as obtained by Onsager. We compare the behaviour of magnetisation vs temperature for different types of bcs by calculating the number of points close to the line of zero magnetisation after $T>T_c$ at various lattice sizes. We observe that the periodic, adiabatic and reflexive bcs give closer approximation to the value of $T_c$ than fixed +1 and fixed -1 bcs with all three initial conditions for lattice size less than $70\times70$. However, for lattice size between $70\times70$ and $100\times100$, fixed +1 bc and fixed -1 bc give closer approximation to the $T_c$ with initial conditions all spin down configuration and all spin up configuration respectively.

cond-mat.stat-mech↗

arXiv2017

Physics Potential of the ICAL detector at the India-based Neutrino Observatory (INO)

The upcoming 50 kt magnetized iron calorimeter (ICAL) detector at the India-based Neutrino Observatory (INO) is designed to study the atmospheric neutrinos and antineutrinos separately over a wide range of energies and path lengths. The primary focus of this experiment is to explore the Earth matter effects by observing the energy and zenith angle dependence of the atmospheric neutrinos in the multi-GeV range. This study will be crucial to address some of the outstanding issues in neutrino oscillation physics, including the fundamental issue of neutrino mass hierarchy. In this document, we present the physics potential of the detector as obtained from realistic detector simulations. We describe the simulation framework, the neutrino interactions in the detector, and the expected response of the detector to particles traversing it. The ICAL detector can determine the energy and direction of the muons to a high precision, and in addition, its sensitivity to multi-GeV hadrons increases its physics reach substantially. Its charge identification capability, and hence its ability to distinguish neutrinos from antineutrinos, makes it an efficient detector for determining the neutrino mass hierarchy. In this report, we outline the analyses carried out for the determination of neutrino mass hierarchy and precision measurements of atmospheric neutrino mixing parameters at ICAL, and give the expected physics reach of the detector with 10 years of runtime. We also explore the potential of ICAL for probing new physics scenarios like CPT violation and the presence of magnetic monopoles.

physics.ins-det↗

arXiv2015

Accretion of radiation and rotating Primordial black holes

We consider rotating Primordial black holes (PBHs) and study the effect of accretion of radiation in the radiation dominated era. The central part of our analysis deals with the role of the angular momentum parameter on the evolution of PBHs. We find that both the accretion rate and evaporation rate decrease with increase in angular momentum parameter, but the rate of evaporation decreases more rapidly than the rate of accretion. This shows that the evaporation time of PBHs get prolonged with increase in angular momentum parameter. We also note that the lifetime of rotating PBHs increase with increase in accretion efficiency of the radiation as in the case of nonrotating PBHs.

gr-qc↗

arXiv2012

Non-holomorphic deformations of special geometry and their applications

The aim of these lecture notes is to give a pedagogical introduction to the subject of non-holomorphic deformations of special geometry. This subject was first introduced in the context of N=2 BPS black holes, but has a wider range of applicability. A theorem is presented according to which an arbitrary point-particle Lagrangian can be formulated in terms of a complex function F, whose features are analogous to those of the holomorphic function of special geometry. A crucial role is played by a symplectic vector that represents a complexification of the canonical variables, i.e. the coordinates and canonical momenta. We illustrate the characteristic features of the theorem in the context of field theory models with duality invariances. The function F may depend on a number of external parameters that are not subject to duality transformations. We introduce duality covariant complex variables whose transformation rules under duality are independent of these parameters. We express the real Hesse potential of N=2 supergravity in terms of the new variables and expand it in powers of the external parameters. Then we relate this expansion to the one encountered in topological string theory. These lecture notes include exercises which are meant as a guidance to the reader.

hep-th↗

arXiv2008

Moduli and (un)attractor black hole thermodynamics

We investigate four-dimensional spherically symmetric black hole solutions in gravity theories with massless, neutral scalars non-minimally coupled to gauge fields. In the non-extremal case, we explicitly show that, under the variation of the moduli, the scalar charges appear in the first law of black hole thermodynamics. In the extremal limit, the near horizon geometry is $AdS_2\times S^2$ and the entropy does not depend on the values of moduli at infinity. We discuss the attractor behaviour by using Sen's entropy function formalism as well as the effective potential approach and their relation with the results previously obtained through special geometry method. We also argue that the attractor mechanism is at the basis of the matching between the microscopic and macroscopic entropies for the extremal non-BPS Kaluza-Klein black hole.

hep-th↗

arXiv2005

Exploring the relation between 4D and 5D BPS solutions

Based on recent proposals linking four and five-dimensional BPS solutions, we discuss the explicit dictionary between general stationary 4D and 5D supersymmetric solutions in N=2 supergravity theories with cubic prepotentials. All these solutions are completely determined in terms of the same set of harmonic functions and the same set of attractor equations. As an example, we discuss black holes and black rings in Gödel-Taub-NUT spacetime. Then we consider corrections to the 4D solutions associated with more general prepotentials and comment on analogous corrections on the 5D side.

hep-th↗

arXiv2003

De Sitter vacua from N=2 gauged supergravity

Typical de Sitter (dS) vacua of gauged supergravity correspond to saddle points of the potential and often the unstable mode runs into a singularity. We explore the possibility to obtain dS points where the unstable mode goes on both sides into a supersymmetric smooth vacuum. Within N=2 gauged supergravity coupled to the universal hypermultiplet, we have found a potential which has two supersymmetric minima (one of them can be flat) and these are connected by a de Sitter saddle point. In order to obtain this potential by an Abelian gauging, it was important to include the recently proposed quantum corrections to the universal hypermultiplet sector. Our results apply to four as well as five dimensional gauged supergravity theories.

hep-th↗

arXiv2001

Noncommutativity in linear dilaton background

We consider quantization of open string theories in linear dilaton and constant antisymmetric tensor backgrounds and discuss the noncommutativity of space-time coordinates arising in such theories, including their relationship with light-like noncommutativity as well as backgrounds with null isometries. It is argued that the results can also be understood using space-time equations of motion of the string modes. We then present N= 2 supersymmetric generalization of these theories and the associated noncommutativity structure.

hep-th↗

arXiv2000

Supersymmetric configurations in Euclidean Freedman-Schwarz model

We study Euclidean D=4, N=4 gauged $SU(2) \times SU(1,1)$ supergravity theory which has been obtained from dimensional reduction of N=1, D=10 supergravity on $S^3 \times AdS_3$. We obtain supersymmetric configurations like domain wall, electro-vac type of solutions with geometries $E^2 \times S^2$, $E^2 \times AdS_2$ and axio-vac type $E^1 \times S^3$ solution in this Euclidean Freedman-Schwarz (EFS) model. We also show that the Euclidean gravitational instantons with nontrivial (anti)self-dual U(1) gauge fields are stable vacua preserving one fourth of the original supersymmetry.

hep-th↗

arXiv1999

Eguchi-Hanson metric from various limits

In this note, we review various seemingly different ways of obtaining Eguchi-Hanson metric with or without a cosmological constant term. Interestingly, the conformal class of metric corresponding to hyperbolic $n$-monopole solution obtained from the generalized Gibbons-Hawking ansatz, reduces to the Eguchi-Hanson metric in a particular limit. These results, though known from an algebraic geometry point of view, are useful while dealing with rotational killing symmetry of self-dual metrics in general theory of relativity as well as in the context of duality symmetry in string theory.

hep-th↗

arXiv1998

Black Holes and Flop Transitions in M-Theory on Calabi-Yau Threefolds

We present fivedimensional extreme black hole solutions of M-theory compactified on Calabi-Yau threefolds and study these solutions in the context of flop transitions in the extended Kahler cone. In particular we consider a specific model and present black hole solutions, breaking half of N=2 supersymmetry, in two regions of the extended Kahler cone, which are connected by a flop transition. The conditions necessary to match both solutions at the flop transition are analysed. Finally we also discuss the conditions to obtain massless black holes at the flop transition.

hep-th↗

arXiv1997

From Type IIA Black Holes to T-dual Type IIB D-Instantons in N=2, D=4 Supergravity

We discuss the T-duality between the solutions of type IIA versus IIB superstrings compactified on Calabi-Yau threefolds. Within the context of the N=2, D=4 supergravity effective Lagrangian, the T-duality transformation is equivalently described by the c-map, which relates the special Kahler moduli space of the IIA N=2 vector multiplets to the quaternionic moduli space of the N=2 hyper multiplets on the type IIB side (and vice versa). Hence the T-duality, or c-map respectively, transforms the IIA black hole solutions, originating from even dimensional IIA branes, of the special Kahler effective action, into IIB D-instanton solutions of the IIB quaternionic sigma-model action, where the D-instantons can be obtained by compactifying odd IIB D-branes on the internal Calabi-Yau space. We construct via this mapping a broad class of D-instanton solutions in four dimensions which are determinded by a set of harmonic functions plus the underlying topological Calabi-Yau data.

hep-th↗

arXiv1997

Planetoid strings : solutions and perturbations

A novel ansatz for solving the string equations of motion and constraints in generic curved backgrounds, namely the planetoid ansatz, was proposed recently by some authors. We construct several specific examples of planetoid strings in curved backgrounds which include Lorentzian wormholes, spherical Rindler spacetime and the 2+1 dimensional black hole. A semiclassical quantisation is performed and the Regge relations for the planetoids are obtained. The general equations for the study of small perturbations about these solutions are written down using the standard, manifestly covariant formalism. Applications to special cases such as those of planetoid strings in Minkowski and spherical Rindler spacetimes are also presented.

hep-th↗