论文标题
$ pt $ - 对称的非温和哈密顿量和不变运算符，定期驱动$ su（1,1）$ system
$PT$-symmetric non-Hermitian Hamiltonian and invariant operator in periodically driven $SU(1,1)$ system
论文作者
论文摘要
我们在本文中研究了$ pt $ -smmetric的非温和汉密尔顿的时间演变，该hamiltonian由定期驱动的$ su（1,1）$发电机组成。采用了非热不变的操作员来解决schrödinger方程，因为时间依赖的哈密顿式不再是保守数量。我们提出了一个计划，以构建具有$ pt $ smortric但非自动转换运算符的非热不变的计划。不变及其复杂共轭的特征状态形成了双向异构基础，以制定精确的溶液。我们获得了非绝热浆果阶段，在缓慢的时间变化极限下将其减少到绝热。分析发现了非自动的时间进化运算符。由于非军事的结果，ket（$ |ψ（t）\ rangle $）和胸罩（$ \langleψ（t）| $）状态未彼此归一化。虽然可以在公制运算符的帮助下评估两个状态的内部产品。明确表明该模型可以通过定期驱动的振荡器实现。
We study in this paper the time evolution of $PT$-symmetric non-Hermitian Hamiltonian consisting of periodically driven $SU(1,1)$ generators. A non-Hermitian invariant operator is adopted to solve the Schrödinger equation, since the time-dependent Hamiltonian is no longer a conserved quantity. We propose a scheme to construct the non-Hermitian invariant with a $PT$-symmetric but non-unitary transformation operator. The eigenstates of invariant and its complex conjugate form a bi-orthogonal basis to formulate the exact solution. We obtain the non-adiabatic Berry phase, which reduces to the adiabatic one in the slow time-variation limit. A non-unitary time-evolution operator is found analytically. As an consequence of the non-unitarity the ket ($|ψ(t)\rangle $) and bra ($\langle ψ(t)|$) states are not normalized each other. While the inner product of two states can be evaluated with the help of a metric operator. It is shown explicitly that the model can be realized by a periodically driven oscillator.
