Thermal Properties of Graphene Via Dirac Oscillator Model Under Doubly Special Relativity Framework

Abstract

This work investigates the electronic and thermodynamic properties of graphene within the framework of Doubly Special Relativity (DSR), emphasizing its role as an effective analog platform for analyzing modified dispersion relations. By incorporating the Dirac oscillator (DO) interaction and utilizing an energy-dependent effective mass for charge carriers in a magnetic field, we analyze how Planck-scale inspired deformations modify the energy spectrum and thermodynamic observables. We compare two structurally distinct DSR implementations: the Amelino–Camelia (AC) and Magueijo–Smolin (MS) models. Our results demonstrate that while the AC framework introduces significant nonlinear corrections and particle–antiparticle branch bifurcation, the MS corrections are strongly suppressed for massless carriers near the Dirac point. We establish a mapping to the Jaynes–Cummings (JC) and anti-Jaynes–Cummings (AJC) models, providing a bridge to quantum optical interpretation and trapped-ion simulations. While direct Planck-scale observations remain beyond current experimental reach, this study provides a controlled sensitivity analysis of how deformed kinematics propagate into solvable Dirac spectra within engineered analog gravity platforms.