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3 papersUpdated Jun 12, 11:00 AM
⚛️ PhysicsHigh ImpactQuantum Mechanics23h ago

Effective Geometry and Position-Dependent Mass in Dual-$q$ Quantum Mechanics

A. Boumali,A. Makhlouf

💡 New method simplifies quantum mechanics

This work investigates the deformed-derivative formalism introduced by Borges, with emphasis on the relation between the linear operator $D_{(q)}$ and its nonlinear dual counterpart $D^{(q)}$. Directly inserting the dual derivative into the kinetic term leads to a nonlinear Schrodinger equation and obscures the usual interpretation of superposition and probability. We show that this nonlinearity can be removed by a simultaneous transformation of the coordinate and of the wave function. The transformed problem is an ordinary linear Schrodinger equation in a deformed coordinate, and its representation in the physical coordinate is equivalent to a Hermitian position-dependent-mass (PDM) Hamiltonian. In this formulation, the deformation parameter $q$ determines both the effective mass profile and the associated metric. The formalism is appl

🔬 The Research·

Quantum mechanics and deformed derivatives

arXiv PDF
🧬 BiologyHigh ImpactQuantitative Biology23h ago

Implementation of Linear Regression and Linear Interpolation using Reaction Networks

Aryan Kumar,Amey Choudhary,Jiaxin Jin

💡 Scientists use reaction networks for linear regression and interpolation.

Performing statistical inference is an essential component of data science. Our focus in this work is on two inference techniques, viz. regression and interpolation. We propose a reaction network based approach that can implement linear regression (both univariate and multivariate) and linear interpolation. We do this by encoding the steady state concentration of species as the output of these inference techniques. Towards this, we use a novel generalized division module that can handle division of negative numbers. We verify our results by comparing them with in-silico implementation on standard synthetic datasets.

🔬 The Research·

Studies reaction networks for statistical inference

arXiv PDF
🚀 SpaceHigh ImpactAstrophysics23h ago

Multifractal Signatures of Hamiltonian Chaos in Hyperion's Rotational Dynamics

null·S. Jaroszewicz,N. Mendez,Maria P. Beccar-Varela

💡 Scientists found a new way to detect chaos in the rotation of Saturn's moon Hyperion using a novel analysis technique.

The chaotic rotation of Saturn's moon Hyperion is a paradigmatic example of Hamiltonian chaos in a natural system. Although its tumbling motion is well established theoretically, identifying a robust observational signature of chaos from sparse and noisy astronomical time series remains a major challenge, making phase-space reconstruction techniques impractical under realistic conditions. In this work, we show that multifractal detrended fluctuation analysis (MFDFA) provides an effective alternative for detecting chaotic dynamics directly from photometric observations. Using historical ground-based light curves and synthetic datasets, we demonstrate that the intermittency associated with chaotic tumbling produces a broad multifractal singularity spectrum. While multifractality is a known feature of Hamiltonian chaos, we show that it can ser

🔬 The Research·

Investigates the chaotic rotation of Saturn's moon Hyperion using multifractal analysis.

arXiv PDF