论文标题
量子狂犬病模型II的热核：繁殖和光谱决定因素
Heat kernel for the quantum Rabi model II: propagators and spectral determinants
论文作者
论文摘要
量子兔模型（QRM）被广泛认为是量子系统中的重要模型，尤其是在量子光学中。众所周知，Hamiltonian $ h _ {\ text {rabi}} $具有均等分解$ h _ {\ text {rabi}} = h _ {+} \ oplus h _ { - { - } $。在本文中，我们为schrödinger方程（时代进化运算符的积分内核）的繁殖器提供了明确的公式，该公式为哈密顿式$ h _ {\ text {\ text {rabi}} $和$ h _ {\ h _ {\ h _ {\ pm} $ by wick rotation（meromorphic continuation conteriating the Cooples the Sepureting Heaters of Seporsing Heaters of Seleting Heaters of Temering the kernels serlels sernels。此外，与QRM的全哈密顿量一样，我们表明，对于hamiltonians $ h _ {\ pm} $，频谱决定因素是，与braak $ g $ function（每一个parity）相当的不变整个功能都可以使用QRM的集成性。为此，我们显示了汉密尔顿人$ h _ {\ pm} $的光谱Zeta功能的Meromorphic延续，并提供了一些基本属性。
The quantum Rabi model (QRM) is widely recognized as an important model in quantum systems, particularly in quantum optics. The Hamiltonian $H_{\text{Rabi}}$ is known to have a parity decomposition $H_{\text{Rabi}} = H_{+} \oplus H_{-}$. In this paper, we give the explicit formulas for the propagator of the Schrödinger equation (integral kernel of the time evolution operator) for the Hamiltonian $H_{\text{Rabi}}$ and $H_{\pm}$ by the Wick rotation (meromorphic continuation) of the corresponding heat kernels. In addition, as in the case of the full Hamiltonian of the QRM, we show that for the Hamiltonians $H_{\pm}$, the spectral determinant is, up to a non-vanishing entire function, equal to the Braak $G$-function (for each parity) used to prove the integrability of the QRM. To do this, we show the meromorphic continuation of the spectral zeta function of the Hamiltonians $H_{\pm}$ and give some of its basic properties.
