Language：English   Publishing type：Research paper (scientific journal)   Publisher：Springer Science and Business Media {LLC}  

DOI： 10.1007/s00220-023-04825-3

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：International Press of Boston  

DOI： 10.4310/cntp.2022.v16.n3.a4

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：International Press of Boston  

DOI： 10.4310/atmp.2022.v26.n5.a8

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Authorship：Lead author   Publishing type：Research paper (scientific journal)   Publisher：{IOP} Publishing  

DOI： 10.1088/1751-8121/ac0508

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Publishing type：Research paper (scientific journal)   Publisher：{IOP} Publishing  

DOI： 10.1088/1751-8121/abdca7

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Publisher：Springer Singapore  

<jats:title>Abstract</jats:title><jats:p>The quantum Rabi model (QRM) is widely regarded as one of the fundamental models of quantum optics. One of its generalizations is the asymmetric quantum Rabi model (AQRM), obtained by introducing a symmetry-breaking term depending on a parameter <jats:inline-formula><jats:alternatives><jats:tex-math>$$\varepsilon \in \mathbb {R}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
<mml:mrow>
<mml:mi>ε</mml:mi>
<mml:mo>∈</mml:mo>
<mml:mi>R</mml:mi>
</mml:mrow>
</mml:math></jats:alternatives></jats:inline-formula> to the Hamiltonian of the QRM. The AQRM was shown to possess degeneracies in the spectrum for values <jats:inline-formula><jats:alternatives><jats:tex-math>$$\epsilon \in 1/2\mathbb {Z}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
<mml:mrow>
<mml:mi>ϵ</mml:mi>
<mml:mo>∈</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo>/</mml:mo>
<mml:mn>2</mml:mn>
<mml:mi>Z</mml:mi>
</mml:mrow>
</mml:math></jats:alternatives></jats:inline-formula> via the study of the divisibility of the so-called constraint polynomials. In this article, we aim to provide further insight into the structure of Juddian solutions of the AQRM by extending the divisibility properties and the relations between the constraint polynomials with the solution of the AQRM in the Bargmann space. In particular we discuss a conjecture proposed by Masato Wakayama.</jats:p>

DOI： 10.1007/978-981-15-5191-8_13

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Language：English   Publishing type：Research paper (scientific journal)  

<jats:title>Abstract</jats:title>
<jats:p>The purpose of this paper is to study the exceptional eigenvalues of the asymmetric quantum Rabi models (AQRMs), specifically, to determine the degeneracy of their eigenstates. Here, the Hamiltonian $H_{\textrm{Rabi } }^{\varepsilon }$ of the AQRM is defined by adding the fluctuation term $\varepsilon \sigma _x$, with $\sigma _x$ being the Pauli matrix, to the Hamiltonian of the quantum Rabi model, breaking its $\mathbb{Z}_{2}$-symmetry. The spectrum of $H_{\textrm{Rabi } }^{\varepsilon }$ contains a set of exceptional eigenvalues, considered to be remains of the eigenvalues of the uncoupled bosonic mode, which are further classified in two types: Juddian, associated with polynomial eigensolutions, and non-Juddian exceptional. We explicitly describe the constraint relations for allowing the model to have exceptional eigenvalues. By studying these relations we obtain the proof of the conjecture on constraint polynomials previously proposed by the third author. In fact we prove that the spectrum of the AQRM possesses degeneracies if and only if the parameter $\varepsilon $ is a halfinteger. Moreover, we show that non-Juddian exceptional eigenvalues do not contribute any degeneracy and we characterize exceptional eigenvalues by representations of $\mathfrak{s}\mathfrak{l}_2$. Upon these results, we draw the whole picture of the spectrum of the AQRM. Furthermore, generating functions of constraint polynomials from the viewpoint of confluent Heun equations are also discussed.</jats:p>

DOI： 10.1093/imrn/rnaa034

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Publishing type：Part of collection (book)   Publisher：Springer Singapore  

DOI： 10.1007/978-981-10-5065-7_7

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Publishing type：Research paper (scientific journal)  

DOI： 10.1016/j.laa.2015.09.049

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