Lax-Phillips理论与量子演化
Lax-Phillips Theory and Quantum Evolution
摘要：
Lax和Phillips的散射理论主要是为双曲系统设计的，如电磁波或声波。这个理论提供了一个实现的定理Foias和Nagy;有一个子空间的希尔伯特空间中的酉演化系统，限制到这个子空间，实现为一个半群。嵌入的量子理论到这种结构，进行了Flesia和Piron，进行审查。我们展示了如何密度矩阵的一个有效的纯态可以演变成一个有效的混合状态（退相干）在这个框架。给出了半群的生成元的谱与$S$ -矩阵的奇异性（能量表示）之间关系实现的必要条件。结果表明，这些条件在量子演化的刘维尔空间表述和相对论性量子理论的希尔伯特空间中都可以满足。
英文摘要：
The scattering theory of Lax and Phillips, designed primarily for hyperbolic systems, such as electromagnetic or acoustic waves, is described. This theory provides a realization of the theorem of Foias and Nagy; there is a subspace of the Hilbert space in which the unitary evolution of the system, restricted to this subspace, is realized as a semigroup. The embedding of the quantum theory into this structure, carried out by Flesia and Piron, is reviewed. We show how the density matrix for an effectively pure state can evolve to an effectively mixed state (decoherence) in this framework. Necessary conditions are given for the realization of the relation between the spectrum of the generator of the semigroup and the singularities of the $S$-matrix (in energy representation). It is shown that these conditions may be met in the Liouville space formulation of quantum evolution, and in the Hilbert space of relativistic quantum theory.
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