Abstract
As a toy model for the microscopic description of matter in de Sitter space, we consider a Hamiltonian acting on the spin-j representation of SU(2). This is a model with a finite-dimensional Hilbert space, from which quasinormal modes emerge in the large-spin limit. The path integral over coherent spin states can be evaluated at the semiclassical level and from it we find the single-particle de Sitter density of states, including 1/j corrections. Along the way, we discuss the use of quasinormal modes in quantum mechanics, starting from the paradigmatic upside-down harmonic oscillator.
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Acknowledgments
I wish to thank Frederik Denef for initial collaboration, and many helpful discussions. I am also grateful to Dio Anninos for insightful suggestions, to Ruben Monten, Zimo Sun and Herman Verlinde for useful comments on the draft, to the other participants of the DAMTP workshop “Quantum de Sitter Universe” and PCTS workshop “Towards the Beginning of Time” for stimulating interactions, and finally, to Ana Asenjo-Garcia and Stuart Masson for bringing to my attention the quantum optics literature on the two-axis twisting Hamiltonian. This work was supported in part by the US DOE (DE-SC011941).
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Parmentier, K. Coherent spin states and emergent de Sitter quasinormal modes. J. High Energ. Phys. 2024, 109 (2024). https://doi.org/10.1007/JHEP06(2024)109
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DOI: https://doi.org/10.1007/JHEP06(2024)109