论文标题
加密 - 热量子哈密顿量的多步墓地化的可行性和方法
Feasibility and method of multi-step Hermitization of crypto-Hermitian quantum Hamiltonians
论文作者
论文摘要
在流行的$ {\ cal pt} - 基于$对称的封闭系统的量子力学的公式中，一个人可以使用非热汉密尔顿人（即$ h \ neq h^\ dagger $）构建统一模型，这是可延性的（因此，可以同时写作，$ h = h = h^\ ddddagger $）。技巧的本质是，参考hilbert space $ \ cal r $（在其中我们使用常规内部产品$ \langleψ_a|ψ_b\ rangle $和写入$ h \ neq h^\ dagger $）被声明为非物理。然后，可以通过单纯的度量介导的修正案$ \langleψ_a|θ|ψ_b\ rangle $来实现哈密顿$ h = h^\ ddagger $的必要墓穴。这将$ \ cal r $转换为正确的物理希尔伯特空间$ \ cal H $。构造的可行性基于分解假设$θ= {\ cal pc} $，通常，$ {\ cal p} $是奇偶校验，而$ {\ cal c} $是充电的。在我们的论文中，我们提出了一个更一般的分解食谱，其中一个人在任何$ n $上构建$θ= z_nz_ {n-1} \ ldots z_1 $，就合适的辅助前固定前运算符$ z_k $而言。
In the popular ${\cal PT}-$symmetry-based formulation of quantum mechanics of closed systems one can build unitary models using non-Hermitian Hamiltonians (i.e., $H \neq H^\dagger$) which are Hermitizable (so that one can write, simultaneously, $H = H^\ddagger$). The essence of the trick is that the reference Hilbert space $\cal R$ (in which we use the conventional inner product $\langle ψ_a|ψ_b\rangle$ and write $H \neq H^\dagger$) is declared unphysical. The necessary Hermiticity of the Hamiltonian $H = H^\ddagger$ can be then achieved by the mere metric-mediated amendment $\langle ψ_a|Θ|ψ_b\rangle$ to the inner product. This converts $\cal R$ into a correct physical Hilbert space $\cal H$. The feasibility of the construction is based on a factorization postulate $Θ={\cal PC}$ where, usually, ${\cal P}$ is parity and ${\cal C}$ is charge. In our paper we propose a more general factorization recipe in which one constructs $Θ=Z_NZ_{N-1}\ldots Z_1$, at any $N$, in terms of suitable auxiliary pre-metric operators $Z_k$.
