论文标题
量子动力学的非线性扩展
Nonlinear extension of the quantum dynamical semigroup
论文作者
论文摘要
在本文中，我们考虑确定性的非线性时间演变满足所谓的cenvex准线性条件。这种演变保留了合奏的等效性，因此没有信号传导问题。我们表明，如果线性非痕迹保留地图家族满足Semigroup属性，那么生成的凸形质量线性操作家族也具有Semigroup属性。接下来，我们将Gorini-Kossakowski-Sudarshan-Lindblad类型方程式概括为所考虑的进化。作为示例，我们讨论了我们的模型中的一般量子进化以及Jaynes-Cummings模型的扩展。我们将形式主义应用于电磁场中移动的带电粒子的旋转密度矩阵，并调味太阳中微子的演变。
In this paper we consider deterministic nonlinear time evolutions satisfying so called convex quasi-linearity condition. Such evolutions preserve the equivalence of ensembles and therefore are free from problems with signaling. We show that if family of linear non-trace-preserving maps satisfies the semigroup property then the generated family of convex quasi-linear operations also possesses the semigroup property. Next we generalize the Gorini-Kossakowski-Sudarshan-Lindblad type equation for the considered evolution. As examples we discuss the general qubit evolution in our model as well as an extension of the Jaynes-Cummings model. We apply our formalism to spin density matrix of a charged particle moving in the electromagnetic field as well as to flavor evolution of solar neutrinos.
