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Aritra Ghosh

Publications and source records attributed to Aritra Ghosh.

At least 37 records · Page 2Linked to original sources
arXiv2026

Twin Hamiltonians, three types of the Dyson maps, and the probabilistic interpretation problem in quasi-Hermitian quantum mechanics

In the framework of the so-called quasi-Hermitian quantum mechanics of stationary unitary systems, bound states are usually constructed as eigenstates $|ψ_n \rangle$ of a Hamiltonian operator $H$ with real spectrum which is non-Hermitian, $H \neq H^\dagger$. One of the ways of the standard probabilistic interpretation of such systems consists in a transformation of $H$ into its isospectral Hermitian ``twin" $\mathfrak{h}= \mathfrak{h}^\dagger$ via one of the so-called Dyson maps $Ω: H \to \mathfrak{h}$. Naturally, the well known ambiguity of these $H-$dependent Dyson-map transformations implies also an ambiguity of the physical, $Ω-$dependent probabilistic and experimental interpretation of the system in question. In the present paper, an exhaustive classification of all of the eligible $H-$dependent Dyson maps $Ω=Ω(H)$ is provided, implying also a systematic framework for a specification of all of the possible probabilistic interpretations of the quantum system characterized by a preselected $H$.

quant-ph↗
arXiv2026

Invariant measures for some dissipative systems from the Jacobi last multiplier

Hamiltonian dynamics describing conservative systems naturally preserves the standard notion of phase-space volume, a result known as the Liouville's theorem which is central to the formulation of classical statistical mechanics. In this paper, we obtain explicit expressions for invariant phase-space measures for certain (generally dissipative) mechanical systems, namely, systems described by conformal vector fields on symplectic manifolds that are cotangent bundles, contact Hamiltonian systems, and systems of the Liénard class. The latter class of systems can be described by certain generalized conformal vector fields on the cotangent bundle of the configuration space. The computation of the invariant measures is achieved by making use of the formalism of Jacobi last multipliers.

math-ph↗
arXiv2026

Generalized virial theorem for contact Hamiltonian systems

We formulate and study a generalized virial theorem for contact Hamiltonian systems. Such systems describe mechanical systems in the presence of simple dissipative forces such as Rayleigh friction, or the vertical motion of a particle falling through a fluid (quadratic drag) under the action of constant gravity. We find a generalized virial theorem for contact Hamiltonian systems which is distinct from that obtained earlier for the symplectic case. The `contact' generalized virial theorem is shown to reduce to the earlier result on symplectic manifolds as a special case. Various examples of dissipative mechanical systems are discussed. We also formulate a generalized virial theorem in the contact Lagrangian framework.

math-ph↗
arXiv2025

Quasi-harmonic spectra from branched Hamiltonians

We revisit the canonical quantization to assess the spectrum of the modified Emden equation $\ddot{x} + kx\dot{x} + ω^2 x + \frac{k^2}{9}x^3 = 0$, which is an isochronous case of the Liénard-Kukles equation. While its classical isochronicity and canonical quantization, leading to polynomial solutions with an exactly-equispaced spectrum have been discussed earlier, including in the recent paper [Int. J. Theor. Phys. 64, 212 (2025)], the present study focuses on the quantization of its branched Hamiltonians. For small $k$, we show numerically that the resulting energy spectrum is no longer perfectly harmonic but only approximately equispaced, exhibiting quasi-harmonic behavior characterized by deviations from uniform spacing. Our numerical results are precisely validated by analytical calculations based on perturbation theory.

quant-ph↗
arXiv2025

REFRAG: Rethinking RAG based Decoding

Large Language Models (LLMs) have demonstrated remarkable capabilities in leveraging extensive external knowledge to enhance responses in multi-turn and agentic applications, such as retrieval-augmented generation (RAG). However, processing long-context inputs introduces significant system latency and demands substantial memory for the key-value cache, resulting in reduced throughput and a fundamental trade-off between knowledge enrichment and system efficiency. While minimizing latency for long-context inputs is a primary objective for LLMs, we contend that RAG require specialized consideration. In RAG, much of the LLM context consists of concatenated passages from retrieval, with only a small subset directly relevant to the query. These passages often exhibit low semantic similarity due to diversity or deduplication during re-ranking, leading to block-diagonal attention patterns that differ from those in standard LLM generation tasks. Based on this observation, we argue that most computations over the RAG context during decoding are unnecessary and can be eliminated with minimal impact on performance. To this end, we propose REFRAG, an efficient decoding framework that compresses, senses, and expands to improve latency in RAG applications. By exploiting the sparsity structure, we demonstrate a 30.85 the time-to-first-token acceleration (3.75 improvement to previous work) without loss in perplexity. In addition, our optimization framework for large context enables REFRAG to extend the context size of LLMs by 16. We provide rigorous validation of REFRAG across diverse long-context tasks, including RAG, multi-turn conversations, and long document summarization, spanning a wide range of datasets. Experimental results confirm that REFRAG delivers substantial speedup with no loss in accuracy compared to LLaMA models and other state-of-the-art baselines across various context sizes.

cs.CL↗
arXiv2025

On novel Hamiltonian descriptions of some three-dimensional non-conservative systems

We present novel Hamiltonian descriptions of some three-dimensional systems including two well-known systems describing the three-wave-interaction problem and some well-known chaotic systems, namely, the Chen, Lü, and Qi systems. We show that all of these systems can be described in a Hamiltonian framework in which the Poisson matrix $\mathcal{J}$ is supplemented by a resistance matrix $\mathcal{R}$. While such resistive-Hamiltonian systems are manifestly non-conservative, we construct higher-degree Poisson matrices via the Jordan product as $\mathcal{N} = \mathcal{J} \mathcal{R} + \mathcal{R} \mathcal{J}$, thereby leading to new bi-Hamiltonian systems. Finally, we discuss conformal Hamiltonian dynamics on Poisson manifolds and demonstrate that by appropriately choosing the underlying parameters, the reduced three-wave-interaction model as well as the Chen and Lü systems can be described in this manner where the concomitant non-conservative part of the dynamics is described with the aid of the Euler vector field.

math-ph↗
arXiv2025

Landau levels of a Dirac electron in graphene from non-uniform magnetic fields

The occurrence of Landau levels in quantum mechanics when a charged particle is subjected to a uniform magnetic field is well known. Considering the recent interest in the electronic properties of graphene, which admits a dispersion relation which is linear in the momentum near the Dirac points, we revisit the problem of Landau levels in the spirit of the Dirac Hamiltonian and ask if there are certain non-uniform magnetic fields which also lead to a spectrum consisting of the Landau levels. The answer, as we show, is in the affirmative. In particular, by considering isospectral deformations of the uniform magnetic field, we present explicit analytical expressions for non-uniform magnetic fields that are strictly isospectral to their uniform counterpart, thus supporting the Landau levels.

cond-mat.mes-hall↗
arXiv2025

Generalized Liénard systems and isochronous connections

In this paper, we explore some classical and quantum aspects of the nonlinear Liénard equation $\ddot{x} + k x \dot{x} + ω^2 x + (k^2/9) x^3 = 0$, where $x=x(t)$ is a real variable and $k, ω\in \mathbb{R}$. We demonstrate that such an equation could be derived from an equation of the Levinson-Smith kind which is of the form $\ddot{z} + J(z) \dot{z}^2 + F(z) \dot{z} + G(z) = 0$, where $z=z(t)$ is a real variable and $\{J(z), F(z), G(z)\}$ are suitable functions to be specified. It can further be mapped to the harmonic oscillator by making use of a nonlocal transformation, establishing its isochronicity. Computations employing the Jacobi last multiplier reveal that the system exhibits a bi-Hamiltonian character, i.e., there are two distinct types of Hamiltonians describing the system. For each of these, we perform a canonical quantization in the momentum representation and explore the possibility of bound states. While one of the Hamiltonians is seen to exhibit an equispaced spectrum with an infinite tower of states, the other one exhibits branching but can be solved exactly in closed form for certain choices of the parameters.

quant-ph↗
arXiv2025

Isochronous oscillator with a singular position-dependent mass and its quantization

In this paper, we present an analysis of the equation $\ddot{x} - (1/2x) \dot{x}^2 + 2 ω^2 x - 1/8x = 0$, where $ω> 0$ and $x = x(t)$ is a real-valued variable. We first discuss the appearance of this equation from a position-dependent-mass scenario in which the mass profile goes inversely with $x$, admitting a singularity at $x = 0$. The associated potential is also singular at $x = 0$, splitting the real axis into two halves, i.e., $x > 0$ and $x < 0$. The dynamics is exactly solvable for both the branches and so for definiteness, we stick to the $x > 0$ branch. Performing a canonical quantization in the position representation and upon employing the ordering strategy of the kinetic-energy operator due to von Roos, we show that the problem is isospectral to the isotonic oscillator. Thus, the quantum spectrum consists of an infinite number of equispaced levels. The spacing between the energy levels is found to be insensitive to the specific choices of the ambiguity parameters that are employed for ordering the kinetic-energy operator à la von Roos.

quant-ph↗
arXiv2025

Cavity Optomechanical Quantum Memory for Twisted Photons Using a Ring BEC

We theoretically propose a photonic orbital angular momentum (OAM) quantum memory platform based on an atomic Bose-Einstein condensate confined in a ring trap and placed inside a Fabry-Perot cavity driven by Laguerre-Gaussian beams. In contrast to electromagnetically induced transparency-based protocols, our memory does not require change of internal atomic levels. The optical states are instead stored in the large Hilbert space of topologically protected and long-lived motional states (persistent currents) of the condensate, yielding a storage time three orders of magnitude better than presently available. Further, the use of a cavity provides orders of magnitude more resonances, and hence bandwidth, for reading and writing than internal atomic transitions. Finally, the analogy to cavity optomechanics suggests a natural path to wavelength conversion, OAM transduction, and nondestructive readout of the memory.

quant-ph↗
arXiv2025

Dirac-isotonic oscillators in (1 + 1) and (2 + 1) dimensions

We discuss the Dirac oscillator in $(1+1)$ and $(2+1)$ dimensions and generalize it in the spirit of the isotonic oscillator using supersymmetric quantum mechanics. In $(1+1)$ dimensions, the Dirac oscillator returns to the quantum harmonic oscillator in the non-relativistic limit, while its generalization maps to the isotonic oscillator. We describe exact solutions of these generalized systems and also present their non-relativistic limits. Finally, based on supersymmetric quantum mechanics, we show that a generalized Dirac oscillator in $(2+1)$ dimensions can be mapped to an anti-Jaynes-Cummings-like Hamiltonian in which the spin operators couple with the supercharges.

quant-ph↗
arXiv2025

Quantized Area of the Schwarzschild Black Hole: A non-Hermitian Perspective

In this work, our aim is to link Bekenstein's quantized form of the area of the event horizon to the Hamiltonian of the non-Hermitian Swanson oscillator which is known to be $\mathbb{PT}$-symmetric. We achieve this by employing a similarity transformation that maps the non-Hermitian quantum system to a scaled harmonic oscillator. Our procedure is standard and well known. We, first of all, consider the unconstrained reduced Hamiltonian which is directly expressed in terms of the Schwarzschild mass and implies a periodic character for the conjugate momentum (which represents the asymptotic time coordinate), the period being the inverse Hawking temperature. This leads to the quantization of the event-horizon area in terms of the harmonic-oscillator levels. Within the framework of the Swanson oscillator, we proceed to derive novel expressions for the Hawking temperature and the black hole entropy. Notably, the logarithmic area-correction term -(1/2)$\ln$(area) is consistent with our results whereas -(3/2) $\ln$(area) is not.

gr-qc↗
arXiv2025

Automatic Machine Learning Framework to Study Morphological Parameters of AGN Host Galaxies within $z < 1.4$ in the Hyper Supreme-Cam Wide Survey

We present a composite machine learning framework to estimate posterior probability distributions of bulge-to-total light ratio, half-light radius, and flux for Active Galactic Nucleus (AGN) host galaxies within $z<1.4$ and $m<23$ in the Hyper Supreme-Cam Wide survey. We divide the data into five redshift bins: low ($0<z<0.25$), mid ($0.25<z<0.5$), high ($0.5<z<0.9$), extra ($0.9<z<1.1$) and extreme ($1.1<z<1.4$), and train our models independently in each bin. We use PSFGAN to decompose the AGN point source light from its host galaxy, and invoke the Galaxy Morphology Posterior Estimation Network (GaMPEN) to estimate morphological parameters of the recovered host galaxy. We first trained our models on simulated data, and then fine-tuned our algorithm via transfer learning using labeled real data. To create training labels for transfer learning, we used GALFIT to fit $\sim 20,000$ real HSC galaxies in each redshift bin. We comprehensively examined that the predicted values from our final models agree well with the GALFIT values for the vast majority of cases. Our PSFGAN + GaMPEN framework runs at least three orders of magnitude faster than traditional light-profile fitting methods, and can be easily retrained for other morphological parameters or on other datasets with diverse ranges of resolutions, seeing conditions, and signal-to-noise ratios, making it an ideal tool for analyzing AGN host galaxies from large surveys coming soon from the Rubin-LSST, Euclid, and Roman telescopes.

astro-ph.GA↗
arXiv2025

Subconvexity for $GL(1)$ twists of Rankin-Selberg $L$-functions

Let $f$ and $g$ be two holomorphic or Hecke-Maass primitive cusp forms for $SL(2,\mathbb{Z})$ and $χ$ be a primitive Dirichlet character of modulus $p$, an odd prime. A subconvex bound for the central values of the Rankin-Selberg $L$-functions is $L(s, f \otimes g \otimes χ)$ is given by $$L(\frac{1}{2}, f \otimes g \otimes χ) \ll_{f,g,ε}p^{\frac{27}{28}+ε} ,$$ for any $ε> 0$, where the implied constant depends only on the forms $f,g$ and $ε$. Here the convexity bound has exponent $1+ε$, which was improved to $1-\frac{1}{1324}$ (see \cite{HM}). Our bound reduces it further to $1- \frac{1}{28}$. The main ingredients is to reduce the original problem to a $GL(2) \times GL(2)$ shifted convolution sum problem.

math.NT↗
arXiv2025

Subconvex bound for Rankin-Selberg $L$-functions in prime power level

Let $f$ be a $p$-primitive cusp form of level $p^{4r}$, where local representation of $f$ be supercuspidal at $p$, $p$ being an odd prime, $r\geq 1$ and $g$ be a Hecke-Maass or holomorphic primitive cusp form for $\mathrm{SL}(2,\mathbb{Z})$. A subconvex bound for the central values of the Rankin-Selberg $L$-functions $L(s, f \otimes g )$ is given by $$ L (\frac{1}{2}, f \otimes g ) \ll_{g,ε}p^{\frac{23r}{12} +ε}.$$

math.NT↗
arXiv2025

First integrals of some two-dimensional integrable Hamiltonian systems

In this paper, we discuss some results on integrable Hamiltonian systems with two degrees of freedom. We revisit the much-studied problem of the two-dimensional harmonic oscillator and discuss its (super)integrability in the light of a canonical transformation which can map the anisotropic oscillator to a corresponding isotropic one. Following this, we discuss the computation of first integrals for integrable two-dimensional systems using the framework of the Jacobi last multiplier. Using the latter, we describe some novel physical examples, namely, the classical Landau problem with a scalar-potential-induced hyperbolic mode, the two-dimensional Kepler problem, and a problem involving a linear curl force.

nlin.SI↗
arXiv2025

Pseudo-Hermitian extensions of the harmonic and isotonic oscillators

In this work, we describe certain pseudo-Hermitian extensions of the harmonic and isotonic oscillators, both of which are exactly-solvable models in quantum mechanics. By coupling the dynamics of a particle moving in a one-dimensional potential to an imaginary-valued gauge field, it is possible to obtain certain pseudo-Hermitian extensions of the original (Hermitian) problem. In particular, it is pointed out that the Swanson oscillator arises as such an extension of the quantum harmonic oscillator. For the pseudo-Hermitian extensions of the harmonic and isotonic oscillators, we explicitly solve for the wavefunctions in the position representation and also explore their intertwining relations.

quant-ph↗