arXiv subjects

Aritra Ghosh

Publications and source records attributed to Aritra Ghosh.

At least 55 records · Page 3Linked to original sources

arXiv2025

Stochastic thermodynamics and the Ericsson nano engine -- Efficiency from equilibrium results

In this work, we study an Ericsson cycle whose working substance is a charged (quantum) oscillator in a magnetic field that is coupled to a heat bath. The resulting quantum Langevin equations with built-in noise terms encapsulate a thermodynamic structure and allow for the computation of the efficiency of the cycle. We numerically compute the efficiency of the cycle in the quasi-static regime using the steady-state thermodynamic functions of the system. Interestingly, it is found that by increasing the system-bath coupling strength, the efficiency of the cycle can be tuned to a maximum. We also explore the behavior of the efficiency as a function of the pair of magnetic-field values between which the cycle is operated.

cond-mat.mes-hall↗

arXiv2024

Bounds for short character sums for $GL(2) \times GL(3)$ twists

Let $π$ be a $SL(3,\mathbb{Z})$ Hecke Maass-cusp form, $f$ be a $SL(2,\mathbb{Z})$ holomorphic cusp form or Maass-cusp form with normalized Fourier coefficients $λ_π(r,n) \text{ and }λ_{f}(n)$ respectively and $χ$ be any non-trivial character mod $p$ where $p$ is a prime. Then we have $$S_{π,f,χ}(N)\ll_{π, f, ε} N^{3/4}p^{11/16 +{η/4}}(Np)^ε.$$

math.NT↗

arXiv2024

Landauer's principle and black hole area quantization

This article assesses Landauer's principle from information theory in the context of area quantization of the Schwarzschild black hole. Within a quantum-mechanical perspective where Hawking evaporation can be interpreted in terms of transitions between the discrete states of the area (or mass) spectrum, we justify that Landauer's principle holds consistently in the saturated form when the number of microstates of the black hole goes as $2^n$, where $n$ is a large positive integer labeling the levels of the area/mass spectrum in the semiclassical regime. This is equivalent to the area spacing $ΔA = αl_P^2$ (in natural units), where $α= 4 \ln 2$ for which the entropy spacing between consecutive levels in Boltzmann units coincides exactly with one bit of information. We also comment on the situation for other values of $α$ prevalent in the literature.

gr-qc↗

arXiv2024

Exceptional points and quantum phase transition in a fermionic extension of the Swanson oscillator

Motivated by the structure of the Swanson oscillator which is a well-known example of a non-Hermitian quantum system consisting of a general representation of a quadratic Hamiltonian, we propose a fermionic extension of such a scheme which incorporates two fermionic oscillators together with bilinear-coupling terms that do not conserve particle number. We determine the eigenvalues and eigenvectors, and expose the appearance of exceptional points where two of the eigenstates coalesce with the corresponding eigenvectors exhibiting self-orthogonality with respect to the bi-orthogonal inner product. The model admits a quantum phase transition - we discuss the two phases and also demonstrate that the ground-state entanglement entropy exhibits a discontinuous jump indicating the transition between the two phases.

quant-ph↗

arXiv2024

Denser Environments Cultivate Larger Galaxies: A Comprehensive Study beyond the Local Universe with 3 Million Hyper Suprime-Cam Galaxies

The relationship between galaxy size and environment has remained enigmatic, with over a decade of conflicting results. We present one of the first comprehensive studies of the variation of galaxy radius with environment beyond the local Universe and demonstrate that large-scale environmental density is correlated with galaxy radius independent of stellar mass and galaxy morphology. We confirm with $>5σ$ confidence that galaxies in denser environments are up to $\sim25\%$ larger than their equally massive counterparts with similar morphology in less dense regions of the Universe. We achieve this result by correlating projected two-dimensional densities over $\sim360$ deg$^2$ with the structural parameters of $\sim3$ million Hyper Suprime-Cam galaxies at $0.3 \leq z < 0.7$ with $\log M/M_{\odot} \geq 8.9$. Compared to most previous studies, this sample is $\sim100-10,000$ times larger and goes $\sim1$ dex deeper in mass-completeness. We demonstrate that past conflicting results have been driven by small sample sizes and a lack of robust measurement uncertainties. We verify the presence of the above correlation separately for disk-dominated, bulge-dominated, star-forming, and quiescent subpopulations. We find the strength of the correlation to be dependent on redshift, stellar mass, and morphology. The correlation is strongest at lower redshifts and systematically weakens or disappears beyond $z \geq 0.5$. At $z\geq0.5$, more massive galaxies still display a statistically significant correlation. Although some existing theoretical frameworks can be selectively invoked to explain some of the observed correlations, our work demonstrates the need for more comprehensive theoretical investigations of the correlation between galaxy size and environment.

astro-ph.GA↗

arXiv2024

Stripe 82X Data Release 3: Multiwavelength Catalog with New Spectroscopic Redshifts and Black Hole Masses

We present the third catalog release of the wide-area (31.3 deg$^2$) Stripe 82 X-ray survey. This catalog combines previously published X-ray source properties with multiwavelength counterparts and photometric redshifts, presents 343 new spectroscopic redshifts, and provides black hole masses for 1297 Type 1 Active Galactic Nuclei (AGN). With spectroscopic redshifts for 3457 out of 6181 Stripe 82X sources, the survey has a spectroscopic completeness of 56%. This completeness rises to 90% when considering the contiguous portions of the Stripe 82X survey with homogeneous X-ray coverage at an optical magnitude limit of $r<22$. Within that portion of the survey, 23% of AGN can be considered obscured by being either a Type 2 AGN, reddened ($R-K > 4$, Vega), or X-ray obscured with a column density $N_{\rm H} > 10^{22}$ cm$^{-2}$. Unlike other surveys, there is only a 18% overlap between Type 2 and X-ray obscured AGN. We calculated black hole masses for Type 1 AGN that have SDSS spectra using virial mass estimators calibrated on the H$β$,MgII, H$α$, and CIV emission lines. We find wide scatter in these black hole mass estimates, indicating that statiscal analyses should use black hole masses calculated from the same formula to minimize bias. We find that the AGN with the highest X-ray luminosities are accreting at the highest Eddington ratios, consistent with the picture that most black hole mass accretion happens in the phase when the AGN is luminous ($L_{\rm 2-10 keV} > 10^{45}$ erg s$^{-1}$).

astro-ph.HE↗

arXiv2024

Dynamical symmetries of supersymmetric oscillators

In this paper, we describe the dynamical symmetries of classical supersymmetric oscillators in one and two spatial (bosonic) dimensions. Our main ingredient is a generalized Poisson bracket which is defined as a suitable classical counterpart to commutators and anticommutators. In one dimension, i.e., in the presence of one bosonic and one fermionic coordinate, the Hamiltonian admits a $U(1,1)$ symmetry for which we explicitly compute the first integrals. It is found that suitable forms of the supercharges emerge in a natural way as fermionic conserved quantities. Following this, we describe classical supercharge operators based on the generalized Poisson bracket and subsequently define supersymmetry transformations. We perform a straightforward generalization to two spatial dimensions where the Hamiltonian has an overall $U(2,2)$ symmetry. We comment on plausible supersymmetric generalizations of the Pais-Uhlenbeck and isotonic oscillators, and also present the possibility of defining a generalized Nambu bracket within the classical formalism.

math-ph↗

arXiv2024

Weak-coupling limits of the quantum Langevin equation for an oscillator

The quantum Langevin equation as obtained from the independent-oscillator model describes a strong-coupling situation, devoid of the Born-Markov approximation that is employed in the context of the Gorini-Kossakowski-Sudarshan-Lindblad equation. The question we address is what happens when we implement such 'Born-Markov'-like approximations at the level of the quantum Langevin equation for a harmonic oscillator which carries a noise term satisfying a fluctuation-dissipation theorem. In this backdrop, we also comment on the rotating-wave approximation.

quant-ph↗

arXiv2024

Stripe 82-XL: the $\sim$54.8 deg$^2$ and $\sim$18.8 Ms Chandra and XMM-Newton point source catalog and number of counts

We present an enhanced version of the publicly-available Stripe 82X catalog (S82-XL), featuring a comprehensive set of 22,737 unique X-ray point sources identified with a significance $\gtrsim 4σ$. This catalog is four times larger than the original Stripe 82X catalog, by including additional archival data from the Chandra and XMM-Newton telescopes. Now covering $\sim54.8$ deg$^2$ of non-overlapping sky area, the S82-XL catalog roughly doubles the area and depth of the original catalog, with limiting fluxes (half-area fluxes) of 3.4$\times 10^{-16}$ (2.4$\times 10^{-15}$), 2.9$\times 10^{-15}$ (1.5$\times 10^{-14}$), and 1.4$\times 10^{-15}$ (9.5$\times 10^{-15}$) erg s$^{-1}$ cm$^{-2}$ across the soft (0.5-2 keV), hard (2-10 keV), and full (0.5-10 keV) bands, respectively. S82-XL occupies a unique region of flux-area parameter space compared to other X-ray surveys, identifying sources with rest-frame luminosities from $1.2\times 10^{38}$ to $1.6\times 10^{47}$ erg s$^{-1}$ in the 2-10 keV band (median X-ray luminosity, $7.2\times 10^{43}$ erg s$^{-1}$), and spectroscopic redshifts up to $z\sim6$. By using hardness ratios, we derived Active Galactic Nuclei (AGNs) obscuration obtaining a median value of $N_H=21.6_{-1.6}^{+1.0}$, and an overall, obscured fraction ($\log N_H/\mathrm{cm^{-2}}>22$) of $\sim 36.9\%$. S82-XL serves as a benchmark in X-ray surveys and, with its extensive multiwavelength data, is especially valuable for comprehensive studies of luminous AGNs.

astro-ph.GA↗

arXiv2024

Independent-oscillator model and the quantum Langevin equation for an oscillator: A review

This review provides a brief and quick introduction to the quantum Langevin equation for an oscillator, while focusing on the steady-state thermodynamic aspects. A derivation of the quantum Langevin equation is carefully outlined based on the microscopic model of the heat bath as a collection of a large number of independent quantum oscillators, the so-called independent-oscillator model. This is followed by a discussion on the relevant `weak-coupling' limit. In the steady state, we analyze the quantum counterpart of energy equipartition theorem which has generated a considerable amount of interest in recent literature. The free energy, entropy, specific heat, and third law of thermodynamics are discussed for one-dimensional quantum Brownian motion in a harmonic well. Following this, we explore some aspects of dissipative diamagnetism in the context of quantum Brownian oscillators, emphasizing upon the role of confining potentials and also upon the environment-induced classical-quantum crossover. We discuss situations where the system-bath coupling is via the momentum variables by focusing on a gauge-invariant model of momentum-momentum coupling in the presence of a vector potential; for this problem, we derive the quantum Langevin equation and discuss quantum thermodynamic functions. Finally, the topic of fluctuation theorems is discussed (albeit, briefly) in the context of classical and quantum cyclotron motion of a particle coupled to a heat bath.

cond-mat.stat-mech↗

arXiv2024

Jacobi last multiplier and two-dimensional superintegrable oscillators

In this paper, we examine the role of the Jacobi last multiplier in the context of two-dimensional oscillators. We first consider two-dimensional unit-mass oscillators admitting a separable Hamiltonian description, i.e., $H = H_1 + H_2$, where $H_1$ and $H_2$ are the Hamiltonians of two one-dimensional unit-mass oscillators; it is shown that there exists a third functionally-independent first integral $Θ$, thereby ensuring superintegrablility. Various examples are explicitly worked out. We then consider position-dependent-mass oscillators and the Bateman pair, where the latter consists of a pair of dissipative linear oscillators. Quite remarkably, the Bateman pair is found to be superintegrable, despite admitting a Hamiltonian which cannot be separated into those of two isolated (non-interacting) one-dimensional oscillators.

nlin.SI↗

arXiv2024

A reappraisal of Lagrangians with non-quadratic velocity dependence and branched Hamiltonians

Time and again, non-conventional forms of Lagrangians with non-quadratic velocity dependence have found attention in the literature. For one thing, such Lagrangians have deep connections with several aspects of nonlinear dynamics including specifically the types of the Liénard class; for another, very often the problem of their quantization opens up multiple branches of the corresponding Hamiltonians, ending up with the presence of singularities in the associated eigenfunctions. In this article, we furnish a brief review of the classical theory of such Lagrangians and the associated branched Hamiltonians, starting with the example of Liénard-type systems. We then take up other cases where the Lagrangians depend upon the velocity with powers greater than two while still having a tractable mathematical structure, while also describing the associated branched Hamiltonians for such systems. For various examples, we emphasize upon the emergence of the notion of momentum-dependent mass in the theory of branched Hamiltonians.

math-ph↗

arXiv2024

Morphological Parameters and Associated Uncertainties for 8 Million Galaxies in the Hyper Suprime-Cam Wide Survey

We use the Galaxy Morphology Posterior Estimation Network (GaMPEN) to estimate morphological parameters and associated uncertainties for $\sim 8$ million galaxies in the Hyper Suprime-Cam (HSC) Wide survey with $z \leq 0.75$ and $m \leq 23$. GaMPEN is a machine learning framework that estimates Bayesian posteriors for a galaxy's bulge-to-total light ratio ($L_B/L_T$), effective radius ($R_e$), and flux ($F$). By first training on simulations of galaxies and then applying transfer learning using real data, we trained GaMPEN with $<1\%$ of our dataset. This two-step process will be critical for applying machine learning algorithms to future large imaging surveys, such as the Rubin-Legacy Survey of Space and Time (LSST), the Nancy Grace Roman Space Telescope (NGRST), and Euclid. By comparing our results to those obtained using light-profile fitting, we demonstrate that GaMPEN's predicted posterior distributions are well-calibrated ($\lesssim 5\%$ deviation) and accurate. This represents a significant improvement over light profile fitting algorithms which underestimate uncertainties by as much as $\sim60\%$. For an overlapping sub-sample, we also compare the derived morphological parameters with values in two external catalogs and find that the results agree within the limits of uncertainties predicted by GaMPEN. This step also permits us to define an empirical relationship between the Sérsic index and $L_B/L_T$ that can be used to convert between these two parameters. The catalog presented here represents a significant improvement in size ($\sim10 \times $), depth ($\sim4$ magnitudes), and uncertainty quantification over previous state-of-the-art bulge+disk decomposition catalogs. With this work, we also release GaMPEN's source code and trained models, which can be adapted to other datasets.

astro-ph.GA↗

arXiv2023

Energetics of the dissipative quantum oscillator

In this paper, we discuss some aspects of the energetics of a quantum Brownian particle placed in a harmonic trap, also known as the dissipative quantum oscillator. Based on the fluctuation-dissipation theorem, we analyze two distinct notions of thermally-averaged energy that can be ascribed to the oscillator. These energy functions, respectively dubbed hereafter as the mean energy and the internal energy, are found to be unequal for arbitrary system-bath coupling strength, when the bath spectral function has a finite cutoff frequency, as in the case of a Drude bath. Remarkably, both the energy functions satisfy the quantum counterpart of the energy equipartition theorem, but with different probability distribution functions on the frequency domain of the heat bath. Moreover, the Gibbs approach to thermodynamics provides us with yet another thermally-averaged energy function. In the weak-coupling limit, all the above-mentioned energy expressions reduce to $ε= \frac{\hbar ω_0}{2} \coth \big(\frac{ \hbar ω_0}{2 k_B T}\big)$, which is the familiar result. We generalize our analysis to the case of the three-dimensional dissipative magneto-oscillator, i.e., when a charged dissipative oscillator is placed in a spatially-uniform magnetic field.

quant-ph↗

arXiv2023

The Accretion History of AGN: The Spectral Energy Distributions of X-ray Luminous AGN

Spectral energy distributions (SEDs) from X-ray to far-infrared (FIR) wavelengths are presented for a sample of 1246 X-ray luminous active galactic nuclei (AGN; $L_{0.5-10\rm{keV}}>10^{43}$ erg s$^{-1}$), with $z_{\rm{spec}}<1.2$, selected from Stripe 82X, COSMOS, and GOODS-N/S. The rest-frame SEDs show a wide spread ($\sim2.5$ dex) in the relative strengths of broad continuum features at X-ray, ultraviolet (UV), mid-infrared (MIR), and FIR wavelengths. A linear correlation (log-log slope of 0.7$\pm0.04$) is found between $L_{\rm{MIR}}$ and $L_{\rm{X}}$. There is significant scatter in the relation between the $L_{\rm{UV}}$ and $L_{\rm{X}}$ due to heavy obscuration, however the most luminous and unobscured AGN show a linear correlation (log-log slope of 0.8$\pm0.06$) in the relation above this scatter. The relation between $L_{\rm{FIR}}$ and $L_{\rm{X}}$ is predominantly flat, but with decreasing dispersion at $L_{\rm{X}}>10^{44}$ erg s$^{-1}$. The ratio between the "galaxy subtracted" bolometric luminosity and the intrinsic $L_{\rm{X}}$ increases from a factor of $\sim$$10-70$ from log $L_{\rm{bol}}/{\rm(erg\; s}^{-1})=44.5-46.5$. Characteristic SED shapes have been determined by grouping AGN based on relative strengths of the UV and MIR emission. The average $L_{1μ\rm{m}}$ is constant for the majority of these SED shapes, while AGN with the strongest UV and MIR emission have elevated $L_{1μ\rm{m}}$, consistent with the AGN emission dominating their SEDs at optical and NIR wavelengths. A strong correlation is found between the SED shape and both the $L_{\rm{X}}$ and $L_{\rm{bol}}$, such that $L_{\rm{bol}}/L_{\rm{X}}=20.4\pm1.8$, independent of the SED shape. This is consistent with an evolutionary scenario of increasing $L_{\rm{bol}}$ with decreasing obscuration as the AGN blows away circumnuclear gas.

astro-ph.GA↗

arXiv2023

A Conceptual Model for End-to-End Causal Discovery in Knowledge Tracing

In this paper, we take a preliminary step towards solving the problem of causal discovery in knowledge tracing, i.e., finding the underlying causal relationship among different skills from real-world student response data. This problem is important since it can potentially help us understand the causal relationship between different skills without extensive A/B testing, which can potentially help educators to design better curricula according to skill prerequisite information. Specifically, we propose a conceptual solution, a novel causal gated recurrent unit (GRU) module in a modified deep knowledge tracing model, which uses i) a learnable permutation matrix for causal ordering among skills and ii) an optionally learnable lower-triangular matrix for causal structure among skills. We also detail how to learn the model parameters in an end-to-end, differentiable way. Our solution placed among the top entries in Task 3 of the NeurIPS 2022 Challenge on Causal Insights for Learning Paths in Education. We detail preliminary experiments as evaluated on the challenge's public leaderboard since the ground truth causal structure has not been publicly released, making detailed local evaluation impossible.

cs.LG↗

arXiv2023

Partition of kinetic energy and magnetic moment in dissipative diamagnetism

In this paper, we analyze dissipative diamagnetism, arising due to dissipative cyclotron motion in two dimensions, in the light of the quantum counterpart of energy equipartition theorem. We consider a charged quantum particle moving in a harmonic well, in the presence of a uniform magnetic field, and coupled to a quantum heat bath which is taken to be composed of an infinite number of independent quantum oscillators. The quantum counterpart of energy equipartition theorem tells us that it is possible to express the mean kinetic energy of the dissipative oscillator as a two-fold average, where, the first averaging is performed over the Gibbs canonical state of the heat bath while the second one is governed by a probability distribution function $P_k(ω)$. We analyze this result further, and also demonstrate its consistency in the weak-coupling limit. Following this, we compute the equilibrium magnetic moment of the system, and reveal an interesting connection with the quantum counterpart of energy equipartition theorem. The expressions for kinetic energy and magnetic moment are reformulated in the context of superstatistics, i.e. the superposition of two statistics. A comparative study of the present results with those obtained from the more traditional Gibbs approach is performed and a perfect agreement is obtained.

cond-mat.stat-mech↗

arXiv2023

Quantum dissipation and the virial theorem

In this note, we study the celebrated virial theorem for dissipative systems, both classical and quantum. The classical formulation is discussed and an intriguing effect of the random force (noise) is made explicit in the context of the virial theorem. Subsequently, we derive a generalized virial theorem for a dissipative quantum oscillator, i.e. a quantum oscillator coupled with a quantum heat bath. Such a heat bath is modeled as an infinite collection of independent quantum oscillators with a certain distribution of initial conditions. In this situation, the non-Markovian nature of the quantum noise leads to novel bath-induced terms in the virial theorem. We also consider the case of an electrical circuit with thermal noise and analyze the role of non-Markovian noise in the context of the virial theorem.

quant-ph↗