论文标题
非铁量子量子模型的准热代表的系统学
Systematics of quasi-Hermitian representations of non-Hermitian quantum models
论文作者
论文摘要
在最近快速开发统一系统量子力学的环境中，使用与时间无关的非富尔顿汉密尔顿$ h $（具有真实的频谱，并定义为在一个非物质但用户友好的希尔伯特空间$ {\ cal r} _n^_n^{（0）} $中，并介绍了构造的元素，并详细介绍了一套构建的元素。 Spaces $ {\ Cal R} _0^{（J）} $。上标$ j $可能从$ j = 0 $到$ j = n $运行。在理论的$ j = 0 $中，该构建目前是众所周知的，仅涉及内部产品度量$θ=θ（h）$。汉密尔顿$ h $本身保持不变。在$ j = n $，内部产品公制仍然很琐碎，只有哈密顿量必须被庇护，$ h \ to \ mathfrak {h} =ω\，h \，h \，ω^{ - 1} = \ mathfrak {h}^\ dagger $。在其余的上标$ j = 1,2，\ ldots，n-1 $，提出了一种新型的混合形式，建造一致的量子模型，需要同时修改公制和汉密尔顿。在应用程序中，预计以示意性三态示例说明的方式，预计对于给定的$ h $来说将是最佳的。
In the recently quickly developing context of quantum mechanics of unitary systems using a time-independent non-Hermitian Hamiltonian $H$ (having real spectrum and defined as acting in an unphysical but user-friendly Hilbert space ${\cal R}_N^{(0)}$), the present paper introduces and describes a set of constructive returns of the description to one of the correct and eligible physical Hilbert spaces ${\cal R}_0^{(j)}$. The superscript $j$ may run from $j=0$ to $j=N$. In the $j=0$ extreme of the theory the construction is currently well known and involves solely the inner product metric $Θ=Θ(H)$. The Hamiltonian $H$ itself remains unchanged. At $j=N$ the inner-product metric remains trivial and only the Hamiltonian must be Hermitized, $H \to \mathfrak{h} = Ω\,H\,Ω^{-1}=\mathfrak{h}^\dagger$. At the remaining superscripts $j=1,2,\ldots, N-1$, a new, hybrid form of the construction of a consistent quantum model is proposed, requiring a simultaneous amendment of both the metric and the Hamiltonian. In applications, one of these options is expected to be optimal for a given $H$ in a way illustrated by a schematic three-state example.
