论文标题
具有$ PT $ -SMMETRIC非独立运算符和非甲米型汉密尔顿的经典对应的通用量规变换，以定期驱动的系统
Generalized gauge transformation with $PT$-symmetric non-unitary operator and classical correspondence of non-Hermitian Hamiltonian for a periodically driven system
论文作者
论文摘要
我们在本文中表明，可以通过广义的量规变换从内核汉密尔顿人产生$ pt $ - 符合性的非热汉顿式哈密顿式汉密尔顿。内核汉密尔顿人是隐性和静态的，而时间依赖的转换操作员必须是$ pt $对称性，并且一般而言。本征态的生物表现套件必须是非富米顿汉密尔顿人的结果。我们通过分析获取波函数和相关的非绝热浆果相$γ_{n} $的$ n $ th eigenstate。非热汉密尔顿人的经典版本成为规范变量和时间的复杂功能。相应的内核Hamiltonian在经典仪表转换中以$ PT $对称的规范变量转移得出。此外，随着位置摩托车向角度变量的变化，可以发现非绝热的汉奈的角度$Δθ_{h} $和贝里相确切地满足了量子 - 经典的对应关系，$γ_{n} = $ $（n+1/2）Δθ_{h} $。
We in this paper demonstrate that the $PT$-symmetric non-Hermitian Hamiltonian for a periodically driven system can be generated from a kernel Hamiltonian by a generalized gauge transformation. The kernel Hamiltonian is Hermitian and static, while the time-dependent transformation operator has to be $PT$ symmetric and non-unitary in general. Biorthogonal sets of eigenstates appear necessarily as a consequence of non-Hermitian Hamiltonian. We obtain analytically the wave functions and associated non-adiabatic Berry phase $γ_{n}$ for the $n$th eigenstate. The classical version of the non-Hermitian Hamiltonian becomes a complex function of canonical variables and time. The corresponding kernel Hamiltonian is derived with $PT$ symmetric canonical-variable transfer in the classical gauge transformation. Moreover, with the change of position-momentum to angle-action variables it is revealed that the non-adiabatic Hannay's angle $Δθ_{H}$ and Berry phase satisfy precisely the quantum-classical correspondence,$γ_{n}=$ $(n+1/2)Δθ_{H}$.
