论文标题
混合状态的自动墓穴
Automatic hermiticity for mixed states
论文作者
论文摘要
我们先前提出了一种机制，可以在长期发展后有效地获得Hamiltonian是Hermitian，该机制是关于修改后的内部产品$ I_Q $，它通过使用适当选择的Hermitian操作员$ Q $来使给定的非正常的Hamiltonian正常。我们为纯状态研究了它。在这封信中，我们表明，一种类似的机制也通过引入密度矩阵来描述它们并在未来不包含和未来的理论中明确调查其性质，也适用于混合状态。 In particular, in the latter, where not only a past state at the initial time $T_A$ but also a future state at the final time $T_B$ is given, we study a couple of candidates for it, and introduce a ``skew density matrix'' composed of both ensembles of the future and past states such that the trace of the product of it and an operator ${\cal O}$ matches a normalized matrix element of $ {\ cal o} $。我们认为，当前时间用$ i_q $定义的偏差密度矩阵$ t $ $ t_b-t $和大的$ t-t_a $大约对应于另一个仅限过去状态组成的密度矩阵，并由另一个内在产品$ i_ {Q_j} $定义为大型$ t-t_a $。
We previously proposed a mechanism to effectively obtain, after a long time development, a Hamiltonian being Hermitian with regard to a modified inner product $I_Q$ that makes a given non-normal Hamiltonian normal by using an appropriately chosen Hermitian operator $Q$. We studied it for pure states. In this letter we show that a similar mechanism also works for mixed states by introducing density matrices to describe them and investigating their properties explicitly both in the future-not-included and future-included theories. In particular, in the latter, where not only a past state at the initial time $T_A$ but also a future state at the final time $T_B$ is given, we study a couple of candidates for it, and introduce a ``skew density matrix'' composed of both ensembles of the future and past states such that the trace of the product of it and an operator ${\cal O}$ matches a normalized matrix element of ${\cal O}$. We argue that the skew density matrix defined with $I_Q$ at the present time $t$ for large $T_B-t$ and large $t-T_A$ approximately corresponds to another density matrix composed of only an ensemble of past states and defined with another inner product $I_{Q_J}$ for large $t-T_A$.
