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Universal upper bound for the tunneling rate of a large quantum spin. (English) Zbl 0699.46058

Summary: An upper bound is derived for the tunneling rate of a spin with large spin quantum number S. The bound is universal in the sense that it does not depend on the specific form of the anisotropy (i.e., the potential barrier). The method of proof relies on the exponential localization theorem of Fröhlich and Lieb and lends precise support to a rather suggestive interpretation put forth in a WKB analysis of the first author and Sütö. The resulting bound agrees with their expression for the tunneling rate in the limit of large S.

MSC:

46N99 Miscellaneous applications of functional analysis
47A10 Spectrum, resolvent
47A55 Perturbation theory of linear operators
81Q99 General mathematical topics and methods in quantum theory
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