论文标题
时间依赖的c仪，作为非休富师理论中的刘易斯·里森菲尔德不变式
Time-dependent C-operators as Lewis-Riesenfeld invariants in non-Hermitian theories
论文作者
论文摘要
$ {\ cal c} $ - 运营商被引入非涉及时间的涉及操作员，这些经营者与时间无关的汉密尔顿人和奇偶校验/时间逆转操作员通勤。在这里，我们提出了一个与时间相关的$ {\ cal c}（t）$ - 运算符的定义，并证明，对于特定的签名，它们可能会根据时间依赖于时间依赖的生物表达的左右特征向后进行扩展。在时间依赖性方案中，$ {\ cal c} $ - 运算符和哈密顿量之间的消失的换向关系被刘易斯·里森菲尔德方程所取代。因此，$ {\ cal c}（t）$ - 运算符始终是刘易斯·里森菲尔德不变的，而逆向仅在某些情况下是正确的。我们证明了非高级两级矩阵哈密顿的一般性工作。我们表明，$ {\ cal c}（t）$的解决方案可能会发现与时间相关的度量运算符，这些解决方案可以在所有三个$ {\ cal pt} $ - 机制中，即$ {\ cal pt} $ - 机制，自发损坏的$ {\ cal pt} $ - pt} $ - 政权和异常点。
${\cal C}$-operators were introduced as involution operators in non-Hermitian theories that commute with the time-independent Hamiltonians and the parity/time-reversal operator. Here we propose a definition for time-dependent ${\cal C}(t)$-operators and demonstrate that for a particular signature they may be expanded in terms of time-dependent biorthonormal left and right eigenvectors of Lewis-Riesenfeld invariants. The vanishing commutation relation between the ${\cal C}$-operator and the Hamiltonian in the time-independent case is replaced by the Lewis-Riesenfeld equation in the time-dependent scenario. Thus, ${\cal C}(t)$-operators are always Lewis-Riesenfeld invariants, whereas the inverse is only true in certain circumstances. We demonstrate the working of the generalities for a non-Hermitian two-level matrix Hamiltonian. We show that solutions for ${\cal C}(t)$ and the time-dependent metric operator may be found that hold in all three ${\cal PT}$-regimes, i.e., the ${\cal PT}$-regime, the spontaneously broken ${\cal PT}$-regime and at the exceptional point.
