Supersymmetry of dissipative Bose-Fermi systems with application to Jaynes-Cummings and Dicke models
Abstract
We demonstrate how supersymmetries of Hamiltonians for coupled Bose-Fermi systems can be used to place the Hamiltonians of the Jaynes-Cummings model and Dicke model under the rotating wave approximation in matrix form and provide explicit analytic solutions for their eigenvalues. We then use this supersymmetry to place the Liouvillians of the associated Markovian open systems in matrix form and provide explicit solutions for their eigenvalues. These results are a consequence of the fact that the Hamiltonian of the Jaynes-Cummings model commutes with the linear Casimir invariant of the superalgebra u(1|1) and that the Hamiltonian of the Dicke model commutes both with the linear invariant of ∑i ui(1|1) and with the invariant of an additional su(2) algebra. Our methods apply to various coupled Bose-Fermi systems with u(1|1) and more generally with u(n|m) dynamical superalgebras, and may provide efficient tools for studying more complicated examples.
Versions
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BibTeX
@misc{coane2026supersymmetry,
title = {{Supersymmetry of dissipative Bose-Fermi systems with application to Jaynes-Cummings and Dicke models}},
author = {Colin V. Coane and Francesco Iachello},
howpublished = {arXiv},
year = {2026},
month = jun,
doi = {10.48550/arxiv.2606.12682},
eprint = {2606.12682},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.12682},
}
RIS
TY - UNPB
TI - Supersymmetry of dissipative Bose-Fermi systems with application to Jaynes-Cummings and Dicke models
AU - Colin V. Coane
AU - Francesco Iachello
PY - 2026
DA - 2026/06/10
PB - arXiv
DO - 10.48550/arxiv.2606.12682
UR - https://arxiv.org/abs/2606.12682
AB - We demonstrate how supersymmetries of Hamiltonians for coupled Bose-Fermi systems can be used to place the Hamiltonians of the Jaynes-Cummings model and Dicke model under the rotating wave approximation in matrix form and provide explicit analytic solutions for their eigenvalues. We then use this supersymmetry to place the Liouvillians of the associated Markovian open systems in matrix form and provide explicit solutions for their eigenvalues. These results are a consequence of the fact that the Hamiltonian of the Jaynes-Cummings model commutes with the linear Casimir invariant of the superalgebra u(1|1) and that the Hamiltonian of the Dicke model commutes both with the linear invariant of ∑_i u_i(1|1) and with the invariant of an additional su(2) algebra. Our methods apply to various coupled Bose-Fermi systems with u(1|1) and more generally with u(n|m) dynamical superalgebras, and may provide efficient tools for studying more complicated examples.
ER -