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 is 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.

Original language	English
Article number	045301
Journal	Journal of Physics A: Mathematical and Theoretical
Volume	47
Issue number	4
DOIs	https://doi.org/10.1088/1751-8113/47/4/045301
Publication status	Published - 31 Jan 2014

Cite this

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title = "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 is 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 = "hybrid mechanical systems, quantum Rabi model",

author = "Honghua Zhong and Qiongtao Xie and Xiwen Guan and Batchelor, {Murray T.} and Kelin Gao and Chaohong Lee",

year = "2014",

month = jan,

day = "31",

doi = "10.1088/1751-8113/47/4/045301",

language = "English",

volume = "47",

journal = "Journal of Physics A: Mathematical and Theoretical",

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publisher = "IOP Publishing Ltd.",

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T1 - Analytical energy spectrum for hybrid mechanical systems

AU - Zhong, Honghua

AU - Xie, Qiongtao

AU - Guan, Xiwen

AU - Batchelor, Murray T.

AU - Gao, Kelin

AU - Lee, Chaohong

PY - 2014/1/31

Y1 - 2014/1/31

N2 - 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 is 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.

AB - 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 is 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.

KW - hybrid mechanical systems

KW - quantum Rabi model

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U2 - 10.1088/1751-8113/47/4/045301

DO - 10.1088/1751-8113/47/4/045301

M3 - Article

SN - 1751-8113

VL - 47

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

IS - 4

M1 - 045301

ER -

Analytical energy spectrum for hybrid mechanical systems

Abstract

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