论文标题
关于派生的存在，作为状态对称量子马尔可夫半群的发电机的平方根
On the existence of derivations as square roots of generators of state-symmetric quantum Markov semigroups
论文作者
论文摘要
Cipriani和Sauvageot表明，对于任何$ l^2 $的生机$ l^{（2）} $，在C*-Algebra $ \ Mathcal {A a}上的特殊对称的量子Markov Semigroup在$ \ Mathcal $ the $ from $ \ natercal $ the c $ the c $ the c $ from c $ \ m m ni} a} a} a} a} a} a} a} a} a} a} a} a} a}均存在$ l^{（2）} =δ^*\ circ \overlineδ$。在这里，我们表明，这种推导的构建通常不能推广到相对于非停留状态的对称的量子马尔可夫半群。特别是我们表明，可以假定对希尔伯特双模模的所有派生都具有混凝土形式，然后我们使用此形式来表明，在有限维情况下，这种推导的存在等同于存在线性方程系统的阳性基质解决方案。我们使用Mathematica来求解该线性方程式的混凝土示例，以完成证明。
Cipriani and Sauvageot have shown that for any $L^2$-generator $L^{(2)}$ of a tracially symmetric quantum Markov semigroup on a C*-algebra $\mathcal{A}$ there exists a densely defined derivation $δ$ from $\mathcal{A}$ to a Hilbert bimodule $H$ such that $L^{(2)}=δ^*\circ \overlineδ$. Here we show that this construction of a derivation can in general not be generalised to quantum Markov semigroups that are symmetric with respect to a non-tracial state. In particular we show that all derivations to Hilbert bimodules can be assumed to have a concrete form, and then we use this form to show that in the finite-dimensional case the existence of such a derivation is equivalent to the existence of a positive matrix solution of a system of linear equations. We solve this system of linear equations for concrete examples using Mathematica to complete the proof.
