Twisted Pseudodifferential Calculus and Application to the Quantum Evolution of Molecules
Twisted Pseudodifferential Calculus and Application to the Quantum Evolution of Molecules
复制标题
扭曲伪微分及其在分子量子演化中的应用
DOI：
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发表时间：
2008
期刊：
影响因子：
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通讯作者：
V. Sordoni
中科院分区：
文献类型：
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作者：
André Martinez;V. Sordoni
我们构造了一种适用于处理库仑型相互作用的带算符值符号的抽象伪微积分，并将其应用于研究在Born-Oppenheimer近似下，当电子哈密顿量的谱中允许局域能隙的情况下分子的量子演化。特别地，我们证明了分子演化可以归结为光滑半经典算子组的演化，其符号可以显式计算。此外，我们还研究了直到Ehrenfest阶长时间值的某些波包的传播。(这项工作已被接受作为美国数学学会回忆录的一部分出版，并将在未来出版一卷。)
We construct an abstract pseudodifferential calculus with operator-valued symbol, adapted to the treatment of Coulomb-type interactions, and we apply it to study the quantum evolution of molecules in the Born-Oppenheimer approximation, in the case where the electronic Hamiltonian admits a local gap in its spectrum. In particular, we show that the molecular evolution can be reduced to the one of a system of smooth semiclassical operators, the symbol of which can be computed explicitely. In addition, we study the propagation of certain wave packets up to long time values of Ehrenfest order. (This work has been accepted for publication as part of the Memoirs of the American Mathematical Society and will be published in a future volume.)