arXiv subjects

Kunal Pal

Publications and source records attributed to Kunal Pal.

31 records · Page 2Linked to original sources

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

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

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

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↗

arXiv2019

The geometry of RN-AdS fluids

We establish the parameter space geometry of a fluid system characterized by two constants, whose equation of state mimics that of the RN-AdS black hole. We call this the RN-AdS fluid. We study the scalar curvature on the parameter space of this system, and show its equivalence with the RN-AdS black hole, in the limit of vanishing specific heat at constant volume. Further, an analytical construction of the Widom line is established. We also numerically study the behavior of geodesics on the parameter space of the fluid, and find a geometric scaling relation near its second order critical point.

hep-th↗

arXiv2019

Collapse in $f(R)$ gravity and the method of $R$ matching

Collapsing solutions in $f(R)$ gravity are restricted due to junction conditions that demand continuity of the Ricci scalar and its normal derivative across the time-like collapsing hypersurface. These are obtained via the method of $R$-matching, which is ubiquitous in $f(R)$ collapse scenarios. In this paper, we study spherically symmetric collapse with the modification term $αR^2$, and use $R$-matching to exemplify a class of new solutions. After discussing some mathematical preliminaries by which we obtain an algebraic relation between the shear and the anisotropy in these theories, we consider two metric ansatzes. In the first, the collapsing metric is considered to be a separable function of the co-moving radius and time, and the collapse is shear-free, and in the second, a non-separable interior solution is considered, that represents gravitational collapse with non-zero shear viscosity. We arrive at novel solutions that indicate the formation of black holes or locally naked singularities, while obeying all the necessary energy conditions. The separable case allows for a simple analytic expression of the energy-momentum tensor, that indicates the positivity of the pressures throughout collapse, and is further used to study the heat flux evolution of the collapsing matter, whose analytic solutions are presented under certain approximations. These clearly highlight the role of modified gravity in the examples that we consider.

gr-qc↗

arXiv2014

Enhanced Multiobjective Evolutionary Algorithm based on Decomposition for Solving the Unit Commitment Problem

The unit commitment (UC) problem is a nonlinear, high-dimensional, highly constrained, mixed-integer power system optimization problem and is generally solved in the literature considering minimizing the system operation cost as the only objective. However, due to increasing environmental concerns, the recent attention has shifted to incorporating emission in the problem formulation. In this paper, a multi-objective evolutionary algorithm based on decomposition (MOEA/D) is proposed to solve the UC problem as a multi-objective optimization problem considering minimizing cost and emission as the multiple objec- tives. Since, UC problem is a mixed-integer optimization problem consisting of binary UC variables and continuous power dispatch variables, a novel hybridization strategy is proposed within the framework of MOEA/D such that genetic algorithm (GA) evolves the binary variables while differential evolution (DE) evolves the continuous variables. Further, a novel non-uniform weight vector distribution strategy is proposed and a parallel island model based on combination of MOEA/D with uniform and non-uniform weight vector distribution strategy is implemented to enhance the performance of the presented algorithm. Extensive case studies are presented on different test systems and the effectiveness of the proposed hybridization strategy, the non-uniform weight vector distribution strategy and parallel island model is verified through stringent simulated results. Further, exhaustive benchmarking against the algorithms proposed in the literature is presented to demonstrate the superiority of the proposed algorithm in obtaining significantly better converged and uniformly distributed trade-off solutions.

cs.NE↗

arXiv2014

Multi-Agent Shape Formation and Tracking Inspired from a Social Foraging Dynamics

Principle of Swarm Intelligence has recently found widespread application in formation control and automated tracking by the automated multi-agent system. This article proposes an elegant and effective method inspired by foraging dynamics to produce geometric-patterns by the search agents. Starting from a random initial orientation, it is investigated how the foraging dynamics can be modified to achieve convergence of the agents on the desired pattern with almost uniform density. Guided through the proposed dynamics, the agents can also track a moving point by continuously circulating around the point. An analytical treatment supported with computer simulation results is provided to better understand the convergence behaviour of the system.

cs.NE↗