The quantization of the Rabi Hamiltonian

Abstract

The Bargmann-Fock representation of the Rabi Hamiltonian is expressed by a system of two coupled first-order differential equations in the complex field, which may be rewritten in a canonical form under the Birkhoff transformation. The transformation gives rise to leapfrog recurrence relations, from which the eigenvalues and eigenvectors could be obtained. The interesting feature of this approach is that it generates integer quantum numbers, which relate the solutions to the Juddian baselines. The relationship with Braak's integrability claim [PRL 107, 100401 (2011)] is discussed.

Re-examining Einstein’s B coefficient and rate equations with the Rabi model

“…Before concluding the paper, we take this opportunity to point out that our work opens avenues to many interesting research possibilities: e.g., (i) how to calculate entropy productions of the laser trapped ultra-cold Bose and Fermi systems by generalizing the toy model, (ii) how to generalize our results for degenerate states of a twolevel system, and (iii) how to further generalize our generalized semiclassical results, within the quantum Rabi model (while considering the cavity modes [24,25]) that has attracted both the experimentalists [11,12,31] and the theoreticians [25,[32][33][34] alike in the last few decades.…”

Photophysical Properties of Silver Clusters in Faujasite Zeolites: Does the Crystal Size Matter?

“…Recent progress in controlling the Ag cluster stabilization was obtained by using nanosized zeolites as host materials . Practically, the most demanded feature of the nano-FAUX crystal is its high external surface area that can reach 270 m 2 g –1 , in comparison to 30 m 2 g –1 for the micro-FAUX, opening opportunities for processes taking place specifically on the surface of the zeolite. , With the benefit of the shorter diffusion length through the nanocrystals, the Ag cluster synthesis results in the stabilization of metal nanoparticles with new optical properties . This provides us with the possibility to investigate the interplay and photophysical properties of Ag clusters located specifically at the periphery of the crystal.…”

“…A decrease in the size of crystals was shown to lead to a considerable increase of their external surface and the properties associated with it play an even more significant role: adjustable surface charge, hydrophilicity/hydrophobicity, and surface ion exchange . Hydrophilicity/hydrophobicity and surface ion exchange are unlikely because the sample preserves its emission characteristics in different media . By studying the ionization potential, Fenwick et al reported that the optical properties of silver clusters confined in zeolites depend, besides on the size and geometry of the confined space, also on metal–host electrostatic interactions .…”

Ansatz for the Jahn-Teller triplet instability

“…Application of this transformation greatly enriches our understanding of Jahn-Teller Hamiltonians. It was applied successfully to the single mode Rabi model, and the dual mode E × e Jahn-Teller model [1,5,19,24]. It can be applied as well to the instabilities of the quartet spinor Γ 8 .…”