Confining quantum particles with a purely magnetic field

Confining quantum particles with a purely magnetic field
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用纯磁场限制量子粒子

DOI：
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
F. Truc
F. Truc
中科院分区：
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文献类型：
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作者：
Y. D. Verdière;F. Truc

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考虑欧几里得空间中具有紧边界的开域和该域上具有磁场的薛定谔算子。给出了边界附近磁场增长率的充分条件，保证了该算子的本质自伴随性。从物理学的角度来看，这意味着量子粒子被磁场限制在域内。我们在具有光滑边界的多面体和域上构造示例；这些“磁瓶”的例子是托卡马克核聚变过程的高度简化模型。
We consider an open domain with a compact boundary in an Euclidean space and a Schroedinger operator with magnetic field on this domain. We give sufficient conditions on the rate of growth of the magnetic field near the boundary which guarantees essential self-adjointness of this operator. From the physical point of view, it means that the quantum particle is confined in the domain by the magnetic field. We construct examples on polytopes and domains with smooth boundaries; these examples of "magnetic bottles" are highly simplified models of what is done for nuclear fusion in tokamacs.