arXiv subjects

Tapobrata Sarkar

Publications and source records attributed to Tapobrata Sarkar.

At least 37 records · Page 2Linked to original sources

arXiv2023

FOTOC complexity in an extended Lipkin-Meshkov-Glick model

We study fidelity out-of-time-order correlators (FOTOCs) in an extended Lipkin-Meshkov-Glick model and demonstrate that these exhibit distinctive behaviour at quantum phase transitions in both the ground and the excited states. We show that the dynamics of the FOTOC have different behaviour in the symmetric and broken-symmetry phases, and as one approaches phase transition. If we rescale the FOTOC operator with time, then for small times, we establish that it is identical to the Loschmidt echo. We also compute the Nielsen complexity of the FOTOC operator in both phases, and apply this operator on the ground and excited states to obtain the quasi-scrambled state of the model. The FOTOC operator introduces a small perturbation on the original ground and excited states. For this perturbed state, we compute the quantum information metric to first order in perturbation, in the thermodynamic limit. We find that the associated Ricci scalar diverges at the phase transition on the broken-symmetry phase side, in contrast to the zeroth order result. Finally, we comment upon the Fubini-Study complexity in this model.

quant-ph↗

arXiv2022

Regularising the JNW and JMN naked singularities

We extend the method of Simpson and Visser (SV) of regularising a black hole spacetime, to cases where the initial metric represents a globally naked singularity. We choose two particular geometries, the Janis-Newman-Winicour (JNW) metric representing the solution of an Einstein-scalar field system, and the Joshi-Malafarina-Narayan (JMN) metric that represents the asymptotic equilibrium configuration of a collapsing star supported by tangential pressures as the starting configuration. We illustrate several novel features for the modified versions of the JNW and JMN spacetimes. In particular, we show that, depending on the values of the parameters involved the modified JNW metric may represents either a two way traversable wormhole or it may retain the original naked singularity. On the other hand, the SV modified JMN geometry is always a wormhole. Particle motion and observational aspects of these new geometries are investigated and are shown to posses interesting features. We also study the quasinormal modes of different branches of the regularised spacetime and explore their stability properties.

gr-qc↗

arXiv2022

Deviation in stellar trajectory induced by asymmetry in partial tidal disruption

We study partial tidal disruption and present a quantitative analysis of the orbital dynamics of the remnant self-bound core. We perform smoothed particle hydrodynamical simulations to show that partial disruption of a star due to the tidal field of a black hole leads to a jump in the specific orbital energy and angular momentum of the core. It directly leads to deviation in the core's trajectory apart from getting a boost in its velocity. Our analysis shows that the variations in the specific orbital energy and angular momentum are higher when the pericentre distance is lower. We conclude that higher mass asymmetry of the two tidal tails increases the magnitude of the trajectory deviations. Our study reveals that observable deviations are only possible when mass ratio $q \lesssim 10^3 $, which indicates the range of intermediate-mass black holes.

astro-ph.HE↗

arXiv2022

Conformal Fisher information metric with torsion

We consider torsion in parameter manifolds that arises via conformal transformations of the Fisher information metric, and define it for information geometry of a wide class of physical systems. The torsion can be used to differentiate between probability distribution functions that otherwise have the same scalar curvature and hence define similar geometries. In the context of thermodynamic geometry, our construction gives rise to a new scalar - the torsion scalar defined on the manifold, while retaining known physical features related to other scalar quantities. We analyse this in the context of the Van der Waals and the Curie-Weiss models. In both cases, the torsion scalar has non trivial behaviour on the spinodal curve.

physics.class-ph↗

arXiv2022

Complexity and quenches in models with three and four spin interactions

We study information theoretic quantities in models with three and four spin interactions. These models show distinctive characteristics compared to their nearest neighbour counterparts. Here, we quantify these in terms of the Nielsen complexity in static and quench scenarios, the Fubini-Study complexity, and the entanglement entropy. The models that we study have a rich phase structure, and we show how the difference in the nature of phase transitions in these, compared to ones with nearest neighbour interactions, result in different behaviour of information theoretic quantities, from ones known in the literature. For example, the derivative of the Nielsen complexity does not diverge but shows a discontinuity near continuous phase transitions, and the Fubini-Study complexity may be regular and continuous across such transitions. The entanglement entropy shows a novel discontinuity both at first and second order quantum phase transitions. We also study multiple quench scenarios in these models and contrast these with quenches in the transverse XY model.

quant-ph↗

arXiv2022

Evolution of circuit complexity in a harmonic chain under multiple quenches

We study Nielsen's circuit complexity in a periodic harmonic oscillator chain, under single and multiple quenches. In a multiple quench scenario, it is shown that the complexity shows remarkably different behaviour compared to the other information theoretic measures, such as the entanglement entropy. In particular, after two successive quenches, when the frequency returns to its initial value, there is a lower limit of complexity, which cannot be made to approach zero. Further, we show that by applying a large number of successive quenches, the complexity of the time evolved state can be increased to a high value, which is not possible by applying a single quench. This model also exhibits the interesting phenomenon of crossover of complexities between two successive quenches performed at different times.

quant-ph↗

arXiv2022

Stable Hydrogen burning limits in rapidly rotating very low mass objects

We present novel effects of uniform rapid stellar rotation on the minimum mass of stable hydrogen burning in very low mass stars, using an analytic model, and relaxing the assumption of spherical symmetry. We obtain an analytic formula for the minimum mass of hydrogen burning as a function of the angular speed of stellar rotation. Further, we show the existence of a maximum mass of stable hydrogen burning in such stars, which is purely an artefact of rapid rotation. The existence of this extremum in mass results in a minimum admissible value of the stellar rotation period $\sim 22$ min, below which a very low mass object does not reach the main sequence, within the ambits of our model. For a given angular speed, we predict a mass range beyond which such an object will not evolve into a main sequence star.

astro-ph.SR↗

arXiv2022

Complexity in the Lipkin-Meshkov-Glick Model

We study complexity in a spin system with infinite range interaction, via the paradigmatic Lipkin-Meshkov-Glick model, in the thermodynamic limit. Exact expressions for the Nielsen complexity (NC) and the Fubini-Study complexity (FSC) are derived, that helps us to establish several distinguishing features compared to complexity in other known spin models. In a time-independent LMG model, close to phase transition, the NC diverges logarithmically, much like the entanglement entropy. Remarkably however, in a time dependent scenario, this divergence is replaced by a finite discontinuity, as we show by using the Lewis-Riesenfeld theory of time-dependent invariant operators. The FSC of a variant of the LMG model shows novel behaviour compared to quasi free spin models. Namely, it diverges logarithmically when the target (or reference) state is near the separatrix. Numerical analysis indicates that this is due to the fact that geodesics starting with arbitrary boundary conditions are "attracted" towards the separatrix and that near this line, a finite change in the affine parameter of the geodesic produces an infinitesimal change of the geodesic length. The same divergence is shared by the NC of this model as well.

quant-ph↗

arXiv2022

Analogue metric in a black bounce background

The conventional approach of embedding an effective acoustic metric for sound motion in a background flat Minkowski space-time, has recently been extended to incorporate more general curved background metrics, which might contain a black hole. Though the observational aspects of these kinds of acoustics horizons, including the sonic shadow structure and quasi normal modes have received significant attention in the literature, it leaves room for discussions about embedding in more general classes of curved background space-times without optical horizons. Here we propose and study a new class of acoustic metrics that is embedded in a black-bounce space-time, thereby giving a suitable tuneable system to understand possible observational effects of the presence or absence of acoustic horizons. After showing that the metric can represent five types of different effective backgrounds for sound motion, including a novel "acoustic wormhole - optical wormhole" branch, we discuss how the distinctive features of sonic shadows can appear even in the absence of any acoustic horizon due to the wormhole throat present in the acoustic metric.

gr-qc↗

arXiv2021

Shadows in conformally related gravity theories

Null geodesics are invariant under a conformal transformation, and thus it might seem natural to assume that the observables corresponding to the shadow of a space-time are also conformally invariant. Here, we argue instead, that since the Arnowitt-Deser-Misner mass and the active gravitational mass of an asymptotically flat space-time are not, in general, invariant under such conformal transformations, the shadow radius for photon motion in a space-time would be quantitatively different, when viewed from two different conformally related frames, although the expression for the shadow radius is similar. We then use this fact to propose a novel method to constrain the relevant parameters in a gravity theory conformally related to general relativity. As examples of our method, we constrain the parameter space in Brans-Dicke theory, and a class of brane-world gravity models, by using the recent observational data of M$87^{*}$ by the Event Horizon Telescope.

gr-qc↗

arXiv2021

Complexity, Information Geometry, and Loschmidt Echo near Quantum Criticality

We consider the Nielsen complexity ${\mathcal C}_N$, the Loschmidt echo ${\mathcal L}$, and the Fubini-Study complexity $τ$ in the transverse XY model, following a sudden quantum quench, in the thermodynamic limit. At small times, the first two are related by ${\mathcal L} \sim e^{-{\mathcal C}_N}$. By computing a novel time-dependent quantum information metric, we show that in this regime, ${\mathcal C}_N \sim dτ^2$, up to lowest order in perturbation. The former relation continues to hold in the same limit at large times, whereas the latter does not. Our results indicate that in the thermodynamic limit, the Nielsen complexity and the Loschmidt echo show enhanced temporal oscillations when one quenches from a close neighbourhood of the critical line, while such oscillations are notably absent when the quench is on such a line. We explain this behaviour by studying the nature of quasi-particle excitations in the vicinity of criticality. Finally, we argue that the triangle inequality for the Nielsen complexity might be violated in certain regions of the parameter space, and point out why one should be careful about the nature of the interaction Hamiltonian, while using this measure.

quant-ph↗

arXiv2021

Nielsen complexity of coherent spin state operators

We calculate Nielsen's circuit complexity of coherent spin state operators. An expression for the complexity is obtained by using the small angle approximation of the Euler angle parametrisation of a general $SO(3)$ rotation. This is then extended to arbitrary times for systems whose time evolutions are generated by couplings to an external field, as well as non-linearly interacting Hamiltonians. In particular, we show how the Nielsen complexity relates to squeezing parameters of the one-axis twisted Hamiltonians in a transverse field, thus indicating its relation with pairwise entanglement. We further point out the difficulty with this approach for the Lipkin-Meshkov-Glick model, and resolve the problem by computing the complexity in the Tait-Bryan parametrisation.

quant-ph↗

arXiv2021

Quantum potential in dust collapse with a negative cosmological constant

In the functional Schrodinger formalism, we obtain the wave function describing collapsing dust in an anti-de Sitter background, as seen by a co-moving observer, by mapping the resulting variable mass Schrodinger equation to that of the quantum isotonic oscillator. Using this wave function, we perform a causal de Broglie-Bohm analysis, and obtain the corresponding quantum potential. We construct a bouncing geometry via a disformal transformation, incorporating quantum effects. We derive the external solution that matches with this smoothly, and is also quantum corrected. Due to a pressure term originating from the quantum potential, an initially collapsing solution with a negative cosmological constant bounces back after reaching a minimum radius, and thereby avoids the classical singularity predicted by general relativity.

gr-qc↗

arXiv2021

Geometry of AdS black hole thermodynamics in extended phase space

We consider the geometry of anti-de-Sitter (AdS) black hole thermodynamics in four dimensions, where the equation of state in the extended phase space formalism allows explicit comparison with normal fluid systems. We show that for the two-dimensional parameter manifolds considered here, the scalar curvature is proportional to the thermodynamic volume. This allows us to critically examine the applicability of geometric methods in black hole thermodynamics in extended phase space. We show how several standard features that are expected to hold in normal fluid systems impose severe restrictions on the black hole parameters, leading to the fact that several results in the current literature on the geometry of thermodynamics in extended phase space may be physically invalid. These are true for both charged and rotating AdS black holes. As a by-product of our analysis, we examine a conjecture regarding the equality of the correlation lengths of co-existing phases near criticality, in charged AdS black hole backgrounds, and find reasonable validity.

hep-th↗

arXiv2021

Shadows and thin accretion disk images of the $γ$-metric

The $γ$-metric is a static, axially-symmetric singular solution of the vacuum Einstein's equations without an event horizon. This is a two-parameter family of solutions, generic values of one of which (called $γ$) measure the deviation from spherical symmetry. Here, we first study the shadow cast by this geometry, in order to constrain the $γ$-metric from observations. We find that for $γ< 1/2$, there are, in principle, no shadows cast. On the other hand, shadows cast for all values of $γ\geq 1/2$ are consistent with observations of M$87^*$ by the Event Horizon Telescope. We also study images of thin accretion disks in the $γ$-metric background. In situations where the $γ$-metric possesses light rings, these qualitatively mimic Schwarzschild black holes with the same ADM mass, while in the absence of such rings, they are drastically different from the black hole case.

gr-qc↗

arXiv2021

A stellar constraint on Eddington-inspired Born-Infeld gravity from cataclysmic variable binaries

Eddington-inspired Born-Infeld gravity is an important modification of Einstein's general relativity, which can give rise to non-singular cosmologies at the classical level, and avoid the end-stage singularity in a gravitational collapse process. In the Newtonian limit, this theory gives rise to a modified Poisson's equation, as a consequence of which stellar observables acquire model dependent corrections, compared to the ones computed in the low energy limit of general relativity. This can in turn be used to establish astrophysical constraints on the theory. Here, we obtain such a constraint using observational data from cataclysmic variable binaries. In particular, we consider the tidal disruption limit of the secondary star by a white dwarf primary. The Roche lobe filling condition of this secondary star is used to compute stellar observables in the modified gravity theory in a numerical scheme. These are then contrasted with the values obtained by using available data on these objects, via a Monte Carlo error progression method. This way, we are able to constrain the theory within $5σ$ confidence level.

gr-qc↗

arXiv2021

Constraining alternatives to the Kerr black hole

The recent observation of the shadow of the supermassive compact object M87$^*$ by the Event Horizon Telescope (EHT) collaboration has opened up a new window to probe the strong gravity regime. In this paper, we study shadows cast by two viable alternatives to the Kerr black hole, and compare them with the shadow of M87$^{*}$. The first alternative is a horizonless compact object (HCO) having radius $r_0$ and exterior Kerr geometry. The second one is a rotating generalisation of the recently obtained one parameter ($r_0$) static metric by Simpson and Visser. This latter metric, constructed by using the Newman-Janis algorithm, is a special case of a parametrised rotating non-Kerr geometry obtained by Johannsen. Here, we constrain the parameter $r_0$ of these alternatives using the results from M87$^{*}$ observation. We find that, for the mass, inclination angle and the angular diameter of the shadow of M87$^{*}$ reported by the EHT collaboration, the maximum value of the parameter $r_0$ must be in the range $2.54r_{+}\leq r_{0,max}\leq 3.51r_{+}$ for the dimensionless spin range $0.5\leq a_{*}\leq 0.94$, with $r_{+}$ being the outer horizon radius of the Kerr black hole at the corresponding spin value. We conclude that these black hole alternatives having $r_0$ below this maximum range (i.e. $r_0\leq r_{0,max}$) is consistent with the size and deviation from circularity of the observed shadow of M87$^{*}$.

gr-qc↗

arXiv2021

Disformal transformations and the motion of a particle in semi-classical gravity

The approach to incorporate quantum effects in gravity by replacing free particle geodesics with Bohmian non-geodesic trajectories has an equivalent description in terms of a conformally related geometry, where the motion is force free, with the quantum effects inside the conformal factor, i.e., in the geometry itself. For more general disformal transformations relating gravitational and physical geometries, we show how to establish this equivalence by taking the quantum effects inside the disformal degrees of freedom. We also show how one can solve the usual problems associated with the conformal version, namely the wrong continuity equation, indefiniteness of the quantum mass, and wrong description of massless particles in the singularity resolution argument, by using appropriate disformal transformations.

gr-qc↗