Analytical energy spectrum for hybrid mechanical systems
Abstract
We investigate the energy spectrum for hybrid mechanical systems described by non-parity-symmetric quantum Rabi models. A set of analytical solutions in terms of the confluent Heun functions and their analytical energy spectrum are obtained. The analytical energy spectrum includes regular and exceptional parts, which are both confirmed by direct numerical simulation. The regular part is determined by the zeros of the Wronskian for a pair of analytical solutions. The exceptional part is relevant to the isolated exact solutions and its energy eigenvalues are obtained by analyzing the truncation conditions for the confluent Heun functions. By analyzing the energy eigenvalues for exceptional points, we obtain the analytical conditions for the energy-level-crossings, which correspond to two-fold energy degeneracy.
Keywords
Cite
@article{arxiv.1311.1588,
title = {Analytical energy spectrum for hybrid mechanical systems},
author = {Honghua Zhong and Qiongtao Xie and Xiwen Guan and Murray T. Batchelor and Kelin Gao and Chaohong Lee},
journal= {arXiv preprint arXiv:1311.1588},
year = {2014}
}
Comments
17 pages, 2 figures