论文标题
实施超出页岩螺旋形条件以外的Bogoliubov转换
Implementing Bogoliubov Transformations Beyond the Shale-Stinespring Condition
论文作者
论文摘要
我们提供了两个密集的Fock空间子空间的扩展，使Bogoliubov转换在它们上可以实现，即使它们违反了页岩刺激条件，因此在Fock空间上无法实现它们。骨骼和费米斯案均被涵盖。陈述并证明了扩展意义上可实施性的条件。从这些情况下，我们得出了二次哈密顿量的条件，可以通过Bogoliubov转换可对角线，从而在扩展意义上实现。三个示例说明了情况，在这种情况下，尽管页岩线弹性条件无法保持，但在扩展意义上实现是可能的。
We provide two extensions of a dense subspace of Fock space, such that Bogoliubov transformations become implementable on them, even though they violate the Shale-Stinespring condition, so they are not implementable on Fock space. Both the bosonic and fermionic case are covered. Conditions for implementability in the extended sense are stated and proved. From these, we derive conditions for a quadratic Hamiltonian to be diagonalizable by a Bogoliubov transformation that is implementable in the extended sense. Three examples illustrate situations, in which an implementation in the extended sense is possible although the Shale-Stinespring condition fails to hold.
