arXiv subjects

Avinandan Mondal

Publications and source records attributed to Avinandan Mondal.

4 recordsLinked to original sources

arXiv2026

Estimating the asymptotics of integer partitions in intermediate dimensions ($d = 3,4,5,6$)

It was recently shown by Yeliussizov \cite{Yeliussizov} that integer partitions in dimensions $d \geq 7$ asymptotically grow strictly faster than MacMahon numbers. As MacMahon numbers match with integer partitions in dimensions $d = 1,2$, the comparison of asymptotics of integer partitions with MacMahon numbers in intermediate dimensions ($d = 3,4,5,6$) is an open question. In this work, we perform Markov chain Monte Carlo (MCMC) simulations till $N=15000$ by using adaptive weight learning followed by conventional MCMC steps to numerically estimate the asymptotics of integer partitions in these intermediate dimensions. We numerically establish that in these intermediate dimensions, partitions asymptotically grow faster than MacMahon numbers. More specifically, assuming that the limits exist, we show: $\lim_{n\to\infty}n^{-3/4}\log p_3(n) = 1.8196 \pm 0.0019$, $\lim_{n\to\infty}n^{-4/5}\log p_4(n) = 1.7215 \pm 0.0045$, $\lim_{n\to\infty}n^{-5/6}\log p_5(n) = 1.6521 \pm 0.0059$, and $\lim_{n\to\infty}\log n^{-6/7}p_6(n) = 1.652 \pm 0.021$ for partitions in dimensions $d=3,4,5,$ and $6$ respectively. These numbers are all larger than MacMahon leading order asymptotic coefficients of $1.7898, 1.6614, 1.5737,$ and $1.509$ respectively. Additionally, we also find estimates for some of the sub-leading asymptotic terms in $\log p_d(n)$ in each of the dimensions.

math-ph↗

arXiv2026

Holography in the linearized quantum gravity regime and modular crossed product

Within the semi-classical regime of AdS/CFT correspondence, we consider the limit where the bulk dynamical field is linearized metric perturbations satisfying linearized Einstein equations over background pure AdS spacetime. AdS/CFT correspondence gives us a holographic map, which is an isometric embedding map of the GNS Hilbert space of linearized gravity in the bulk (w.r.t. the AdS-invariant vacuum) to the GNS Hilbert space of CFT in the boundary (w.r.t. the Minkowski-invariant vacuum). We assume that the map takes AdS-vacuum in the bulk to CFT-vacuum in the boundary and that it allows AdS-Rindler wedge reconstruction. Then using this map, we show that for a given ball-shaped region in the boundary $A$, the relative entropy of a bulk state w.r.t. the AdS vacuum in the algebra of causal wedge associated to $A$ matches with the relative entropy of the dual CFT state w.r.t. the CFT vacuum in the algebra of CFT observables in $A$ in the code subspace, which is known as Jafferis-Lewkowycz-Maldacena-Suh (JLMS) condition. Furthermore, for localized semi-classical coherent excitations in the causal wedge associated to $A$ which corresponds to perturbed bulk geometry, we show rigorously using modular crossed product construction that the state-dependent part of entropy of the dual CFT state in the dressed Type-II algebra associated to $A$ satisfies vacuum subtracted Hubeney-Rangamani-Takayanagi (HRT) formula.

hep-th↗

arXiv2026

Microcanonical Phase Space and Entropy in Curved Spacetime

We discuss the structure of microcanonical ensembles in inertial and non-inertial frames attached to a confined system of positive energy particles in curved spacetime. Under certain physically reasonable assumptions that ensure the existence of such ensembles, we obtain, for microcanonical ensembles, exact analytical results in certain stationary spacetimes such as Rindler, Schwarzschild, and de Sitter along with leading curvature corrections in arbitrary curved spacetimes. For de Sitter, the exact results have interesting limits when the size of the system is comparable to $Λ^{-1/2}$. We further highlight two generic characteristics of the leading curvature corrections for a point particle system confined to a spherical or cubical box: (1) they are characterized by Ricci and Einstein tensors, and (2) their contribution is proportional to the bounding area. We argue that the area scaling in (2) does not hold for arbitrary box geometries. We also present a general argument to highlight two distinct sources of divergences in the phase space volume, coming from redshift and spatial geometry, and illustrate this by comparing and contrasting the results for (i) geodesic box in de Sitter, (ii) geodesic box in Schwarzschild, and (iii) uniformly accelerated box in Minkowski. Finally, we extend these results to $N$ particle systems in the restricted case of massless (ultra-relativistic) limit for static spacetimes, for which the results follow very simply from single particle results. Furthermore, we show that the ultra-relativistic expression for equipartition of energy in flat spacetimes continues to hold in static spacetimes.

gr-qc↗

arXiv2026

Perturbative semiclassical entropy of dynamical black holes

We consider perturbative quantum gravity as a quantum field theory of linearized metric perturbation on an asymptotically flat spacetime with a bifurcate Killing horizon. We include the perturbative gravitational constraints into the algebra of observables restricted to the right half of the future horizon of the spacetime. We use the boundary charge, associated to the horizon Killing field, as an auxiliary "observer" degree of freedom. The observables "dressed" with the additional charge are invariant under the Killing symmetry and generate a Type-$\text{II}_{\infty}$ von Neumann factor. We compute the von Neumann entropy of the reduced density matrix of a classical-quantum coherent state constructed from the metric perturbations and the "observer wavefunction". This von Neumann entropy satisfies an analogue of the first law of thermodynamics. We further show that this entropy is related to Hollands-Wald-Zhang entropy of the (second order) perturbed dynamical black hole through the flux of perturbations through the horizon and future null infinity.

hep-th↗