arXiv subjects

Amit Kumar Jha

Publications and source records attributed to Amit Kumar Jha.

7 recordsLinked to original sources

arXiv2026

Fundamental Limit for One versus Two Point Sources Detection using Direct Imaging

We consider the task of distinguishing between a single weak incoherent optical point source and two weak incoherent optical point sources located symmetrically about the first source. $\theta$ is the separation between the two point sources scaled to the Point Spread Function (PSF) width in the image plane. Using an ideal focal plane array of intensity detectors (ideal direct imaging), we quantify the performance using the Bhattacharyya distance and find the scaling of its leading order term in terms of $\theta$ in the sub-Rayleigh regime. A suite of previous analyses of this problem lacked a comprehensive analysis for when the amplitude spread function (ASF) of the imaging system has zeros and reported a scaling that we find to be incorrect. We complete this analysis by explicitly calculating the leading order term of the Bhattacharyya distance for ideal direct imaging with any ASF, for small $\theta$ and show the difference in scaling based on the presence or absence of zeros in the ASF. This is similar to the ASF dependent performance in the task of estimating the separation between the two point sources and the task of detecting a change to an object. We then apply our results to the specific example of a Gaussian and a Sinc ASF and show good agreement with numerical calculations. Our results allow the accurate comparison of other measurement schemes with ideal direct imaging, and to the quantum limit.

physics.optics↗

arXiv2025

A Stochastic Thermodynamics Approach to Price Impact and Round-Trip Arbitrage: Theory and Empirical Implications

This paper develops a comprehensive theoretical framework that imports concepts from stochastic thermodynamics to model price impact and characterize the feasibility of round-trip arbitrage in financial markets. A trading cycle is treated as a non-equilibrium thermodynamic process, where price impact represents dissipative work and market noise plays the role of thermal fluctuations. The paper proves a Financial Second Law: under general convex impact functionals, any round-trip trading strategy yields non-positive expected profit. This structural constraint is complemented by a fluctuation theorem that bounds the probability of profitable cycles in terms of dissipated work and market volatility. The framework introduces a statistical ensemble of trading strategies governed by a Gibbs measure, leading to a free energy decomposition that connects expected cost, strategy entropy, and a market temperature parameter. The framework provides rigorous, testable inequalities linking microstructural impact to macroscopic no-arbitrage conditions, offering a novel physics-inspired perspective on market efficiency. The paper derives explicit analytical results for prototypical trading strategies and discusses empirical validation protocols.

q-fin.MF↗

arXiv2025

A Sinusoidal Hull-White Model for Interest Rate Dynamics: Capturing Long-Term Periodicity in U.S. Treasury Yields

This study is motivated by empirical observations of periodic fluctuations in interest rates, notably long-term economic cycles spanning decades, which the conventional Hull-White short-rate model fails to adequately capture. To address this limitation, we propose an extension that incorporates a sinusoidal, time-varying mean reversion speed, allowing the model to reflect cyclic interest rate dynamics more effectively. The model is calibrated using a comprehensive dataset of daily U.S. Treasury yield curves obtained from the Federal Reserve Economic Data (FRED) database, covering the period from January 1990 to December 2022. The dataset includes tenors of 1, 2, 3, 5, 7, 10, 20, and 30 years, with the most recent yields ranging from 1.22% (1-year) to 2.36% (30-year). Calibration is performed using the Nelder-Mead optimization algorithm, and Monte Carlo simulations with 200 paths and a time step of 0.05 years. The resulting 30-year zero-coupon bond price under the proposed model is 0.43, compared to 0.47 under the standard Hull-White model. This corresponds to root mean squared errors of 0.12% and 0.14%, respectively, indicating a noticeable improvement in fit, particularly for longer maturities. These results highlight the model's enhanced capability to capture long-term yield dynamics and suggest significant implications for bond pricing, interest rate risk management, and the valuation of interest rate derivatives. The findings also open avenues for further research into stochastic periodicity and alternative interest rate modeling frameworks.

q-fin.ST↗

arXiv2023

Beyond VaR and CVaR: Topological Risk Measures in Financial Markets

This paper introduces a novel approach to financial risk assessment by incorporating topological data analysis (TDA), specifically cohomology groups, into the evaluation of equities portfolios. The study aims to go beyond traditional risk measures like Value at Risk (VaR) and Conditional Value at Risk (CVaR), offering a more nuanced understanding of market complexities. Using last one year daily real-world closing price return data for three equities Apple, Microsoft and Google , we developed a new topological riskmeasure, termed Topological VaR Distance (TVaRD). Preliminary results indicate a significant change in the density of the point cloud representing the financial time series during stress conditions, suggesting that TVaRD may offer additional insights into portfolio risk and has the potential to complement existing risk management tools.

q-fin.RM↗

arXiv2021

Demonstration of magnetic and light-controlled actuation of a photomagnetically actuated deformable mirror for wavefront control

Deformable Mirrors (DMs) have wide applications ranging from astronomical imaging to laser communications and vision science. However, they often require bulky multi-channel cables for delivering high power to their drive actuators. A low powered DM which is driven in a contactless fashion could provide a possible alternative to this problem.Here, we present a photo-magnetically actuated deformable mirror (PMADM) concept which is actuated in a contactless fashion by a permanent magnet and low power laser heating source. This paper presents the laboratory demonstration of prototype optical surface quality, magnetic control of focus, and COMSOL simulations of its precise photo-control. The PMADM prototype is made of a magnetic composite (polydimethylsiloxane [PDMS] + ferromagnetic $\text{CrO}_\text{2}$) and an optical-quality substrate layer and is 30.48 mm $\times$ 30.48 mm $\times$ 175 $μ$ m in dimension with an optical pupil diameter of 8 mm. It deforms to 5.76 $μ$ m when subjected to a 0.12 T magnetic flux density and relaxes to 3.76 $μ$ m when illuminated by a 50 mW laser. A maximum stroke of 8.78 $μ$ m before failure is also estimated considering a 3x safety factor. This works also includes simulation of astigmatism generation with the PMADM, a first step in demonstrating control of higher order modes. A fully developed PMADM can have potential application for wavefront corrections in vacuum and space environments.

astro-ph.IM↗

arXiv2020

Fractal dimension analysis of spatio-temporal patterns using image processing and nonlinear time-series analysis

This article deals with the estimation of fractal dimension of spatio-temporal patterns that are generated by numerically solving the Swift Hohenberg (SH) equation. The patterns were converted into a spatial series (analogous to time series) which were shown to be chaotic by evaluating the largest Lyapunov exponent. We have applied several nonlinear time-series analysis techniques like Detrended fluctuation and Rescaled range on these spatial data to obtain Hurst exponent values that reveal spatial series data to be long range correlated. We have estimated fractal dimension from the Hurst and power law exponent and found the value lying between 1 and 2. The novelty of our approach lies in estimating fractal dimension using image to data conversion and spatial series analysis techniques, crucial for experimentally obtained images.

nlin.PS↗

arXiv2020

Modeling light-controlled actuation of flexible magnetic composite structures using the finite element method (FEM)

Photoactive materials hold great promise for a variety of applications. We present a finite element model of light-controlled flexible magnetic composite structure composed of 33.3% Chromium dioxide (CrO2) and 66.7% Polydimethylsiloxane (PDMS) by weight. The structure has a dimension of 8 mm x 2 mm x 100 um and has been previously experimentally studied. Due to the low Curie temperature, the structure acts as an actuator, shows significant deflection under the external magnetic field and relaxation due to laser heating. Thermal and magnetic deflection analysis has been performed using the FEM model. The simulation results show a maximum structural deflection of 6.08 mm (76% of the length of the structure) when subjected to 30 mT magnetic flux density and 160 mW laser power at 303 K (room temperature). We will present the results of the simulation model and comparison to experimental data reproducing the previously observed motion of the (CrO2+PDMS). This model will enable future fracture and fatigue analysis as well as extension to new photoactive geometries.

physics.app-ph↗