In order to construct time-dependent pseudo-bosonic coherent states, first, we extend the non-Hermitian integrals of motion method to cases where the quantum systems are described by time-dependent non-Hermitian Hamiltonians; second, we introduce a pseudo-bosonic annihilation operator defined as a time-dependent non-Hermitian linear invariant. The pseudo-bosons operators are a pseudo-Hermitian extension of usual boson operators. In fact, they are obtained from the modification of usual boson commutation relations where the annihilation and creation operators are related to their adjoint operators via the bounded Hermitian invertible operator or metric operator. Thus, the pseudo-bosonic coherent states are just obtained as eigenstates of the pseudo-bosonic annihilation operator. As an illustration, we study the time-dependent non-Hermitian Swanson Hamiltonian and we compare the obtained results with those in the literature (Swanson model but time-independent).

中文翻译：

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时间相关的伪玻色相干态

为了构造时间相关的伪玻色相干态，首先，我们将非厄米运动积分方法扩展到量子系统由时间相关的非厄米哈密顿量描述的情况；其次，我们引入了一个伪玻色子湮灭算子，定义为时间相关的非厄米线性不变量。伪玻色子算子是普通玻色子算子的伪厄米扩展。事实上，它们是从通常的玻色子对易关系的修改中获得的，其中湮灭和创造算子通过有界厄米可逆算子或度量算子与其伴随算子相关。因此，伪玻色子相干态只是作为伪玻色子湮灭算符的本征态而获得的。作为例证，