arXiv subjects

Yogesh Dandekar

Publications and source records attributed to Yogesh Dandekar.

11 recordsLinked to original sources

arXiv2026

Planar Three-Body Problem: theoretical predictions and simulation results

We investigate the statistical properties of the non-hierarchical planar three-body problem, relevant to astrophysical systems with nearly planar dynamics, including protoplanetary disks and AGN disks. Using the Flux-based statistical theory of the three-body problem, previously studied in three dimensions, we derive theoretical predictions for several statistical observables in the planar case. Focusing on ergodic disintegration outcomes, we compare these predictions directly with numerical simulations and contrast the results with the corresponding unconstrained three-dimensional case. Our analysis is based on one million simulations for each of eight distinct mass sets. We examine escape probabilities, properties of marginal escape events, eccentricity distributions, lifetime distributions, and relative prevalence of prograde and retrograde escapes. While several of the theoretical predictions are in good agreement with the simulations, others exhibit unexpected discrepancies. We discuss possible explanations for these deviations.

astro-ph.EP↗

arXiv2026

Quantum Sensing of Birefringence Beyond the Classical Limit with a Hyper-Squeezed SU(1,1) Interferometer

Quantum interferometric sensing plays a crucial role in a wide range of applications, including quantum metrology, quantum imaging, and quantum lithography, where minute phase shifts carry valuable physical information. The strength of quantum sensing lies in surpassing classical sensitivity limits, particularly through the use of quantum correlations and squeezing to suppress optical shot noise. Birefringence sensing is crucial for various applications, as it provides detailed information about the material's structure, stress, composition, and environmental conditions. We present an interferometric scheme for detecting unknown small birefringence beyond the shot-noise limit of sensitivity that leverages the hyper-squeezing (squeezed in both number-phase and polarization correlations) within a pair of polarized nonlinear SU(1,1) interferometers, coupled by the birefringence. Specifically, two pairs of crossed-polarization nonlinear media, both generate and measure two-mode quantum light that is squeezed and polarization-entangled. We present a complete theoretical analysis of the interferometer's sensitivity to small birefringence under realistic conditions of gain and internal loss, illuminating the potential for enhancement of the sensitivity by 3-15dB in practical, real-world experiments (the exact achievable enhancement is governed solely by the loss).

quant-ph↗

arXiv2025

Distribution of regularized three-body phase-volume

The micro-canonical phase-space volume for the three-body problem is a topic of intrinsic interest. Within the flux-based statistical theory, it provides a means to predict the scale of disintegration times for non-hierarchical systems. While the bare phase-volume diverges, arXiv:2205.04294 (Paper I) showed that a regularized version can be defined. Building on Paper I, which determined the regularized phase-volume for a given energy $\barσ(E)$, this paper extends the analysis to its distribution over angular momentum, $\barσ(E,L)$. Through analytical integrations, we reduce the problem to a 3d numerical integration, a step up in complexity from the 2d integration required for $\barσ(E)$. We provide regularized phase-volume values for several mass sets across a range of $E$ and $L$, validated through an $L$-integration test. Notably, the values remain positive for all tested parameters, lending further support to the validity of the chosen regularization procedure. For high values of $L$ at fixed masses and $E$, we observe a strong suppression of $\barσ(E,L)$.

astro-ph.EP↗

arXiv2022

Regularized phase-space volume for the three-body problem

The micro-canonical phase-space volume for the three-body problem is an elementary quantity of intrinsic interest, and within the flux-based statistical theory, it sets the scale of the disintegration time. While the bare phase-volume diverges, we show that a regularized version can be defined by subtracting a reference phase-volume, which is associated with hierarchical configurations. The reference quantity, also known as a counter-term, can be chosen from a 1-parameter class. The regularized phase-volume of a given (negative) total energy, $\barσ(E)$, is evaluated. First, it is reduced to a function of the masses only, which is sensitive to the choice of a regularization scheme only through an additive constant. Then, analytic integration is used to reduce the integration to a sphere, known as shape sphere. Finally, the remaining integral is evaluated numerically, and presented by a contour plot in parameter space. Regularized phase-volumes are presented for both the planar three-body system and the full 3d system. In the test mass limit, the regularized phase-volume is found to become negative, thereby signalling the breakdown of the non-hierarchical statistical theory. This work opens the road to the evaluation of $\barσ(E,L)$, where $L$ is the total angular momentum, and it turn, to comparison with simulation determined disintegration times.

astro-ph.EP↗

arXiv2019

Large D membrane for Higher Derivative Gravity and Black Hole Second Law

We derive the effective equations of the membranes dual to black holes in a particular theory of higher derivative gravity namely Einstein-Gauss-Bonnet (EGB) gravity at sub-leading order in $1/D$ upto linear order in the Gauss-Bonnet (GB) parameter $β$. We find an expression for an entropy current which satisfies a local version of second law onshell in this regime. We also derive the membrane equations upto leading order in $1/D$ but non-perturbatively in $β$ for EGB gravity. In this regime we write down an expression for a world-volume stress tensor of the membrane and also work out the effective membrane equation for stationary black holes.

hep-th↗

arXiv2018

An Action for and Hydrodynamics from the improved Large D membrane

It has recently been demonstrated that black hole dynamics at large D is dual to the motion of a probe membrane propagating in the background of a spacetime that solves Einstein's equations. The equation of motion of this membrane is determined by the membrane stress tensor. In this paper we `improve' the membrane stress tensor derived in earlier work to ensure that it defines consistent probe membrane dynamics even at finite $D$ while reducing to previous results at large D. Our improved stress tensor is the sum of a Brown York term and a fluid energy momentum tensor. The fluid has an unusual equation of state; its pressure is nontrivial but its energy density vanishes. We demonstrate that all stationary solutions of our membrane equations are produced by the extremisation of an action functional of the membrane shape. Our action is an offshell generalization of the membrane's thermodynamical partition function. We demonstrate that the thermodynamics of static spherical membranes in flat space and global AdS space exactly reproduces the thermodynamics of the dual Schwarzschild black holes even at finite D. We study the long wavelength dynamics of membranes in AdS space, and demonstrate that the boundary `shadow' of this membrane dynamics is boundary hydrodynamics with with a definite constitutive relation. We determine the explicit form of shadow dual boundary stress tensor upto second order in derivatives of the boundary temperature and velocity, and verify that this stress tensor agrees exactly with the fluid gravity stress tensor to first order in derivatives, but deviates from the later at second order and finite D.

hep-th↗

arXiv2018

Black holes in presence of cosmological constant: Second order in 1/D

We have extended the results of arXiv:1704.06076 upto second subleading order in an expansion around large dimension D. Unlike the previous case, there are non-trivial metric corrections at this order. Due to our `background-covariant' formalism, the dependence on Ricci and the Riemann curvature tensor of the background is manifest here. The gravity system is dual to a dynamical membrane coupled with a velocity field. The dual membrane is embedded in some smooth background geometry that also satisfies the Einstein equation in presence of cosmological constant. We explicitly computed the corrections to the equation governing the membrane-dynamics. Our results match with earlier derivations in appropriate limits. We calculated the spectrum of QNM from our membrane equations and matched them against similar results derived from gravity.

hep-th↗

arXiv2018

The large D black hole dynamics in AdS/dS backgrounds

We have constructed a class of perturbative dynamical black hole solutions in presence of cosmological constant. We have done our calculation in large number of dimensions. The inverse power of dimension has been used as the perturbation parameter and our calculation is valid upto the first subleading order. The solutions are in one to one correspondence with a dynamical membrane and a velocity field embedded in the asymptotic geometry. Our method is manifestly covariant with respect to the asymptotic geometry. One single calculation and the same universal result works for both dS and AdS geometry or in case of AdS for both global AdS and Poincare patch. We have checked our final answer with various known exact solutions and the known spectrum of Quasi Normal modes in AdS/dS.

hep-th↗

arXiv2016

Unstable `black branes' from scaled membranes at large $D$

It has recently been demonstrated that the dynamics of black holes at large $D$ can be recast as a set of non gravitational membrane equations. These membrane equations admit a simple static solution with shape $S^{D-p-2} \times R^{p,1}$. In this note we study the equations for small fluctuations about this solution in a limit in which amplitude and length scale of the fluctuations are simultaneously scaled to zero as $D$ is taken to infinity. We demonstrate that the resultant nonlinear equations, which capture the Gregory- Laflamme instability and its end point, exactly agree with the effective dynamical `black brane' equations of Emparan Suzuki and Tanabe. Our results thus identify the `black brane' equations as a special limit of the membrane equations and so unify these approaches to large $D$ black hole dynamics.

hep-th↗

arXiv2016

The large D black hole Membrane Paradigm at first subleading order

In the large D limit, and under certain circumstances, it has recently been demonstrated that black hole dynamics in asymptotically flat spacetime reduces to the dynamics of a non gravitational membrane propagating in flat D dimensional spacetime. We demonstrate that this correspondence extends to all orders in a 1/D expansion and outline a systematic method for deriving the corrected membrane equation in a power series expansion in 1/D. As an illustration of our method we determine the first subleading corrections to the membrane equations of motion. A qualitatively new effect at this order is that the divergence of the membrane velocity is nonzero and proportional to the square of the shear tensor reminiscent of the entropy current of hydrodynamics. As a test, we use our modified membrane equations to compute the corrections to frequencies of light quasinormal modes about the Schwarzschild black hole and find a perfect match with earlier computations performed directly in the gravitational bulk.

hep-th↗

arXiv2015

Poles in the $S$-Matrix of Relativistic Chern-Simons Matter theories from Quantum Mechanics

An all orders formula for the $S$-matrix for 2 $\rightarrow$ 2 scattering in large N Chern-Simons theory coupled to a fundamental scalar has recently been conjectured. We find a scaling limit of the theory in which the pole in this $S$-matrix is near threshold. We argue that the theory must be well described by non-relativistic quantum mechanics in this limit, and determine the relevant Schroedinger equation. We demonstrate that the $S$-matrix obtained from this Schroedinger equation agrees perfectly with this scaling limit of the relativistic $S$-matrix; in particular the pole structures match exactly. We view this matching as a nontrivial consistency check of the conjectured field theory $S$-matrix.

hep-th↗