Van Hemmen, J. L.; Wreszinski, W. F. Universal upper bound for the tunneling rate of a large quantum spin. (English) Zbl 0699.46058 Commun. Math. Phys. 119, No. 2, 213-219 (1988). 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. Cited in 1 Document 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 Keywords:universal upper bound; large quantum spin; tunneling rate; spin with large spin quantum number; potential barrier; exponential localization theorem; WKB analysis PDFBibTeX XMLCite \textit{J. L. Van Hemmen} and \textit{W. F. Wreszinski}, Commun. Math. Phys. 119, No. 2, 213--219 (1988; Zbl 0699.46058) Full Text: DOI References: [1] Leggett, A. J., Chakravarty, S., Dorsey, A. T., Fisher, M. P. A., Garg, A., Zwerger, W.: Rev. Mod. Phys.59, 1 (1987) · doi:10.1103/RevModPhys.59.1 [2] Vourdas, A., Bishop, R. F.: J. Phys.G11, 95 (1985) [3] van Hemmen, J. L., S?t?, A.: Europhys. Lett.1, 481 (1986) · doi:10.1209/0295-5075/1/10/001 [4] van Hemmen, J. L., S?t?, A.: Physica141B, 37 (1986) [5] Enz, M., Schilling, R.: J. Phys.C19, 1765 (1986) [6] Scharf, G., Wreszinski, W. F., van Hemmen, J. L.: J. Phys.A20, 4309 (1987) [7] van Hemmen, J. L., S?t?, A.: Z. Phys.B61, 263 (1985) [8] Chudnowsky, E. M., Gunther, L.: Quantum tunneling of magnetization in small ferromagnetic particles, Phys. Rev. Lett.60, 661 (1988) · doi:10.1103/PhysRevLett.60.661 [9] Kirsch, W., Simon, B.: Universal lower bounds on eigenvalue splittings for one-dimensional Schr?dinger operators. Commun. Math. Phys.97, 453 (1985), and references therein · Zbl 0579.34014 · doi:10.1007/BF01213408 [10] Fr?hlich, J., Lieb, E. H.: Phase transitions in anisotropic lattice spin systems. Commun. Math. Phys.60, 233 (1978) · doi:10.1007/BF01612891 [11] Kato, T.: Perturbation theory for linear operators. Berlin, Heidelberg, New York: Springer Verlag 1966, Chap II · Zbl 0148.12601 [12] Brink, D. M., Satchler, G. R.: Angular momentum, 2nd ed. Oxford: Oxford University Press 1968, Eqs. (2.15), (2.17), and (2.18) · Zbl 0137.45403 [13] Harrell, E. M.: Double wells. Commun. Math. Phys.75, 239 (1980) · Zbl 0445.35036 · doi:10.1007/BF01212711 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.