The Hamiltonian for an atom interacting with gravitational waves

• URL: http://arxiv.org/abs/2601.17891v1
• Date: Sun, 25 Jan 2026 16:00:08 GMT
• Title: The Hamiltonian for an atom interacting with gravitational waves
• Authors: Linda M. van Manen, André Grossardt,
• Abstract summary: We build on the relativistic Hamiltonian of Sonnleitner and Barnett arXiv:1806.00234 and its post-Newtonian extensions by Schwartz and Giuilini arXiv:1908.06929.<n>We derive curvature-dependent corrections to both center-of-mass and internal Hamiltonians for atoms interacting with weak gravitational waves.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Building on the relativistic Hamiltonian of Sonnleitner and Barnett arXiv:1806.00234 and its post-Newtonian extensions by Schwartz and Giuilini arXiv:1908.06929, we investigate composite atomic systems in dynamical gravitational backgrounds. Using a local inertial frame and a perturbed Minkowski metric, we derive curvature-dependent corrections to both center-of-mass and internal Hamiltonians for atoms interacting with weak gravitational waves. The resulting Hamiltonian contains distinct curvature couplings modifying the internal potential and affecting the center-of-mass dynamics. These contributions imply that internal-energy variations do not always reduce to mass renormalization and can induce genuine forces due to changes in momentum. The initial research was motivated by anomalous friction-like forces emerging in quantum optics, and clarified that the anomalous forces are mere relativistic corrections from mass-energy equivalence. Our results suggest that, with increasingly sensitive detectors, additional forces from gravitational wave interactions may become visible in future experiments.

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