Gravitational Influence on the Quantum Speed Limit in Flavor Oscillations of Neutrino-Antineutrino System

• URL: http://arxiv.org/abs/2411.18604v1
• Date: Wed, 27 Nov 2024 18:48:39 GMT
• Title: Gravitational Influence on the Quantum Speed Limit in Flavor Oscillations of Neutrino-Antineutrino System
• Authors: Abhishek Kumar Jha, Banibrata Mukhopadhyay, Mriganka Dutta, Mayank Pathak, Subhashish Banerjee,
• Abstract summary: We derive an analytical expression for the four-vector gravitational potential in the underlying Hermitian Dirac Hamiltonian. This gravitational potential leads to an axial vector term in the Dirac equation in curved spacetime, contributing to the effective mass matrix of the neutrino-antineutrino systems. Our findings indicate that the gravitational field, expressed in BL coordinates, significantly influences the transition probabilities in two-flavor oscillations of the neutrino-antineutrino system.
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• Abstract: We investigate the quantum speed limit (QSL) during the time evolution of neutrino-antineutrino system under the influence of the gravitational field of a spinning primordial black hole (PBH). We derive an analytical expression for the four-vector gravitational potential in the underlying Hermitian Dirac Hamiltonian using the Boyer-Lindquist (BL) coordinates. This gravitational potential leads to an axial vector term in the Dirac equation in curved spacetime, contributing to the effective mass matrix of the neutrino-antineutrino systems. Our findings indicate that the gravitational field, expressed in BL coordinates, significantly influences the transition probabilities in two-flavor oscillations of the neutrino-antineutrino system. We then apply the expression for transition probabilities between states to analyze the Bures angle, which quantifies the closeness between the initial and final states of the time-evolved flavor state. We use this concept to probe the QSL for the time evolution of the initial flavor neutrino state.

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