arXiv subjects

Shrohan Mohapatra

Publications and source records attributed to Shrohan Mohapatra.

7 recordsLinked to original sources

arXiv2026

Optical Thermodynamics Beyond the Weak Nonlinearity Limit

Optical thermodynamics has recently emerged as a theoretical framework describing a Rayleigh-Jeans (RJ) modal power distribution of multimoded nonlinear photonic circuits. However, its applicability is constrained to systems exhibiting weak nonlinear mode-mode interactions. Here, by employing a Transfer Integral Operator, we circumvent this limitation and establish a steady-state interacting RJ modal distribution -- referred to as non-ideal RJ (NIRJ) -- with renormalized temperature and optical chemical potential. This also builds a natural bridge with earlier work on grand-canonical statistical-mechanical formulations of discrete nonlinear systems. The theory derives the optical analogue of the compressibility factor, which controls the transition from an ideal, non-interacting equation of state (EoS) to a van der Waals-like interacting EoS.

nlin.PS↗

arXiv2026

Dam breaks in the discrete nonlinear Schrödinger equation

In the present work we study the nucleation of Dispersive shock waves (DSW) in the {defocusing}, discrete nonlinear Schr{ö}dinger equation (DNLS), a model of wide relevance to nonlinear optics and atomic condensates. Here, we study the dynamics of so-called dam break problems with step-initial data characterized by two-parameters, one of which corresponds to the lattice spacing, while the other being the right hydrodynamic background. Our analysis bridges the anti-continuum limit of vanishing coupling strength with the well-established continuum integrable one. To shed light on the transition between the extreme limits, we theoretically deploy Whitham modulation theory, various quasi-continuum asymptotic reductions of the DNLS and existence and stability analysis and connect our findings with systematic numerical computations. Our work unveils a sharp threshold in the discretization across which qualitatively continuum dynamics from the dam breaks are observed. Furthermore, we observe a rich multitude of wave patterns in the small coupling limit including unsteady (and stationary) Whitham shocks, traveling DSWs, discrete NLS kinks and dark solitary waves, among others. Besides, we uncover the phenomena of DSW breakdown and the subsequent formation of multi-phase wavetrains, due to generalized modulational instability of \textit{two-phase} wavetrains. We envision this work as a starting point towards a deeper dive into the apparently rich DSW phenomenology in a wide class of DNLS models across different dimensions and for different nonlinearities.

nlin.PS↗

arXiv2025

The vortex comb: eliminating vortices from Bose-Einstein condensates using optical lattices

In the present work we introduce and explore a technique for the efficient removal of vortices from an atomic Bose-Einstein condensate, through the application and subsequent removal of a one-dimensional optical lattice. We showcase a prototypical experimental realization of the technique that motivates a detailed theoretical study of vortex removal mechanisms. Through simulations of the condensate dynamics during application of the optical lattice, we also discover a vortex removal mechanism that arises in narrow, optical-lattice-induced atomic density channels for which the channel width is on the order of the nominal vortex core size and healing length. This mechanism involves the density profile typically associated with a vortex core spatially separating from the phase singularity associated with the vortex. By analyzing numerical experiments covering a wide range of variations of the optical lattice amplitude and fringe periodicity, we identify the existence of an optimal set of parameters that enables the efficient removal of all vortices from the condensate. This analysis paves the way for further studies aimed at understanding vortex dynamics in narrow channels, and adds to an experimental toolkit for working with vortices and controlling the dynamical states of condensates.

cond-mat.quant-gas↗

arXiv2024

PainleveBacklundCheck: A Sympy-powered Kivy app for the Painlevé property of nonlinear dispersive PDEs and auto-Bäcklund transformations

In the present work we revisit the Painlevé property for partial differential equations. We consider the PDE variant of the relevant algorithm on the basis of the fundamental work of Weiss, Tabor and Carnevale and explore a number of relevant examples. Subsequently, we present an implementation of the relevant algorithm in an open-source platform in Python and discuss the details of a Sympy-powered Kivy app that enables checking of the property and the derivation of associated auto-B{ä}ck{u}nd transform when the property is present. Examples of the relevant code and its implementation are also provided, as well as details of its open access for interested potential users.

nlin.SI↗

arXiv2021

A note on size-momentum correspondence and chaos

The aim of this note is to explore Susskind's proposal [arXiv:1802.01198] on the connection between operator size in chaotic theories and the bulk momentum of a particle falling into black holes (see also [arXiv:1804.04156, 1806.05574, 1904.12819, 1912.05996, 2006.03019] for more recent generalizations), in a broad class of models involving Gauss-Bonnet(GB) and Lifshitz-Hyperscaling violating theories in AdS. For Gauss-Bonnet black holes, the operator size is seen to be suppressed as the coupling constant $λ$ is increased. For the Lifshitz-hyperscaling violating theories characterised by the parameters $z$ and $θ$, the operator size is higher as compared to case $z=1,θ=0$ (Reissner-Nordstrom AdS black holes). In the case of operators with global charge corresponding to charged particles falling into black holes, suppression of chaos is seen in general theories of gravity, in conformity with the original proposal [arXiv:1802.01198] and earlier findings [arXiv:1806.05574].

hep-th↗

arXiv2019

A Note on Circular Geodesics and Phase Transitions of Black Holes

The circular motion of charged test particles in the gravitational field of a Reissner-Nordström black hole in Anti de Sitter space-time is investigated, using a set of independent parameters, such as charge Q, mass M and cosmological constant $Λ= -3/l^2$ of the space-time, and charge to mass ratio $ε=q/m$ of the test particles. Classification of different spatial regions where circular motion is allowed, is presented, showing in particular, the presence of orbits at special limiting values, $M=4/\sqrt{6} Q$ and $l=6 Q$. Thermodynamically, these values are known to occur when the black hole is on the verge of a second order phase transition, there by, giving an interesting connection between thermodynamics and geodesics of black holes. We also comment on the possibility of such a connection for black holes in flat spacetime in a box.

hep-th↗

arXiv2019

A new quadratic-time number-theoretic algorithm to solve matrix multiplication problem

There have been several algorithms designed to optimise matrix multiplication. From schoolbook method with complexity $O(n^3)$ to advanced tensor-based tools with time complexity $O(n^{2.3728639})$ (lowest possible bound achieved), a lot of work has been done to reduce the steps used in the recursive version. Some group-theoretic and computer algebraic estimations also conjecture the existence of an $O(n^2)$ algorithm. This article discusses a quadratic-time number-theoretic approach that converts large vectors in the operands to a single large entity and combines them to make the dot-product. For two $n \times n$ matrices, this dot-product is iteratively used for each such vector. Preprocessing and computation makes it a quadratic time algorithm with a considerable constant of proportionality. Special strategies for integers, floating point numbers and complex numbers are also discussed, with a theoretical estimation of time and space complexity.

cs.DS↗