arXiv subjects

Pritish Sinha

Publications and source records attributed to Pritish Sinha.

4 recordsLinked to original sources

arXiv2025

Smoothness of Classical Limit in KMOC Formalism

In this paper, we revisit the smoothness of the classical limit of inclusive observables in the formalism developed by Kosower, Maybee and O'Connell (KMOC). Building on the earlier work [1-3], we prove that the classical limit of three classes of inclusive observables, namely scattering angle, radiative field and angular impulse is smooth and does not suffer from any so-called superclassical divergences at all orders in perturbation. We use scalar QED as a model. Our analysis goes some way in showing that KMOC formalism can be used to compute classical radiation by simply focusing on all the terms that scale as $\hbar^{0}$, as all the terms that scale with inverse power of $\hbar$ vanish. Through this analysis, we have successfully isolated the classes of terms that contribute to the classical limit, thereby allowing direct and more efficient computations of physical observables.

hep-th↗

arXiv2024

Level crossing instabilities in inviscid isothermal compressible Couette flow

We study the linear stability of inviscid steady parallel flow of an ideal gas in a channel of finite width. Compressible isothermal two-dimensional monochromatic perturbations are considered. The eigenvalue problem governing density and velocity perturbations is a compressible version of Rayleigh's equation and involves two parameters: a flow Mach number $M$ and the perturbation wavenumber $k$. For an odd background velocity profile, there is a $\mathbb{Z}_2 \times \mathbb{Z}_2$ symmetry and growth rates $γ$ come in symmetrically placed 4-tuples in the complex eigenplane. Specializing to uniform background vorticity Couette flow, we find an infinite tower of noninflectional eigenmodes and derive stability theorems and bounds on growth rates. We show that eigenmodes are neutrally stable for small $k$ and small $M$ but that they otherwise display an infinite sequence of stability transitions with increasing $k$ or $M$. Using a search algorithm based on the Fredholm alternative, we find that the transitions are associated to level crossings between neighboring eigenmodes. Repeated level crossings result in windows of instability. For a given eigenmode, they are arranged in a zebra-like striped pattern on the $k$-$M$ plane. A canonical square-root power law form for $γ(k,M)$ in the vicinity of a stability transition is identified. In addition to the discrete spectrum, we find a continuous spectrum of eigenmodes that are always neutrally stable but fail to be smooth across critical layers.

physics.flu-dyn↗

arXiv2024

Poisson Geometric Formulation of Quantum Mechanics

We study the Poisson geometrical formulation of quantum mechanics for finite dimensional mixed and pure states. Equivalently, we show that quantum mechanics can be understood in the language of classical mechanics. We review the symplectic structure of the Hilbert space and identify its canonical coordinates. We extend the geometric picture to the space of density matrices $D_N^+$. We find it is not symplectic but admits a linear $\mathfrak{su}(N)$ Poisson structure. We identify Casimir surfaces of $D_N^+$ and show that the space of pure states $P_N \equiv \mathbb{C}P^{N-1}$ is one of its symplectic submanifolds which is an intersection of primitive Casimirs. We identify generic symplectic submanifolds of $D_N^+$ and calculate their dimensions. We find that $D_N^+$ is singularly foliated by the symplectic leaves of varying dimensions, also known as coadjoint orbits. We also find an ascending chain of Poisson submanifolds $D_N^M \subset D_N^{M+1}$ for $ 1 \leq M \leq N-1$. Each such Poisson submanifold $D_N^M$ is obtained by tracing out the $\mathbb{C}^M$ states from the bipartite system $\mathbb{C}^N \times \mathbb{C}^M$ and is an intersection of $N-M$ primitive Casimirs of $D_N^+$. Their Poisson structure is induced from the symplectic structure of the bipartite system. We also show their foliations. Finally, we study the positive semi-definite geometry of the symplectic submanifold $E_N^M$ consisting of the mixed states with maximum entropy in $D_N^M$.

quant-ph↗

arXiv2020

Relative entropy in scattering and the S-matrix bootstrap

We consider entanglement measures in 2-2 scattering in quantum field theories, focusing on relative entropy which distinguishes two different density matrices. Relative entropy is investigated in several cases which include $ϕ^4$ theory, chiral perturbation theory ($χPT$) describing pion scattering and dilaton scattering in type II superstring theory. We derive a high energy bound on the relative entropy using known bounds on the elastic differential cross-sections in massive QFTs. In $χPT$, relative entropy close to threshold has simple expressions in terms of ratios of scattering lengths. Definite sign properties are found for the relative entropy which are over and above the usual positivity of relative entropy in certain cases. We then turn to the recent numerical investigations of the S-matrix bootstrap in the context of pion scattering. By imposing these sign constraints and the $ρ$ resonance, we find restrictions on the allowed S-matrices. By performing hypothesis testing using relative entropy, we isolate two sets of S-matrices living on the boundary which give scattering lengths comparable to experiments but one of which is far from the 1-loop $χPT$ Adler zeros. We perform a preliminary analysis to constrain the allowed space further, using ideas involving positivity inside the extended Mandelstam region, and elastic unitarity.

hep-th↗