用线性量子变换对角化二次型哈密顿量(英文)

Diagonalization of Quadratic Hamiltonian by the Linear Quantum Transformation

借助线性量子变换（ＬＱＴ）理论，对ｎ模玻色和费米子的二次型哈密顿量，我们给出了简洁的对角化形式．并且指出，对于ｎ模玻色子耦合二次型哈密顿量，通过一个负幺正矩阵（它是复辛群ＳＰ（２ｎ，ｃ）的元素）可以把它对角化；对ｎ模费米子耦合二次型哈密顿量，通过一个幺正矩阵（它是复费米群Ｆ（２ｎ，ｃ）的元素）可以把它对角化．

By the aid of the linear quantum transformation (LQT) theory, we give a concise diagonalization for n-mode boson and fermion of quadratic Hamiltonian. It is also pointed out that an n-mode boson coupled quadratic Hamiltonian can be diagonalized by a 'negative unitary' matrix which is an element of complex symplectic group SP(2n, c), and an n-mode fermion coupled quadratic Hamiltonian can be diagonalized by a unitary matrix which is an element of complex fermion group F(2n, c).