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We consider the variety of pre-Lie algebra structures on a given n-dimensional vector space. The group GLn(K) acts on it, and we study the closure of the orbits with respect to the Zariski topology. T...

On geometric perturbations of critical Schrödinger operators with a surface interaction

J. Math. Phys. 50, 112101 (2009); doi:10.1063/1.3243826

Published 3 November 2009

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Pavel Exner1 and Martin Fraas2
1Nuclear Physics Institute, Czech Academy of Sciences, 25068 Řež near Prague, Czech Republic and Doppler Institute, Břehová 7, 11519 Prague, Czech Republic
2Department of Physics, Technion, Haifa 32000, Israel
We study singular Schrödinger operators with an attractive interaction supported by a closed smooth surface [script A][subset or is implied by][openface R]3 and analyze their behavior in the vicinity of the critical situation where such an operator has empty discrete spectrum and a threshold resonance. In particular, we show that if [script A] is a sphere and the critical coupling is constant over it, any sufficiently small smooth area-preserving radial deformation gives rise to isolated eigenvalues. On the other hand, the discrete spectrum may be empty for general deformations. We also derive a related inequality for capacities associated with such surfaces. ©2009 American Institute of Physics
History: Received 11 January 2009; accepted 10 September 2009; published 3 November 2009
Permalink: http://link.aip.org/link/?JMAPAQ/50/112101/1
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KEYWORDS and PACS

Keywords
PACS
  • 03.65.Ge
    Solutions of wave equations: bound states in quantum mechanics
  • 03.65.Db
    Functional analytical methods in quantum mechanics
  • 02.10.Ud
    Linear algebra
  • 03.65.Fd
    Algebraic methods in quantum mechanics
  • 02.30.Tb
    Operator theory
  • 02.40.-k
    Geometry, differential geometry, and topology
  • YEAR: 2009

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PUBLICATION DATA

ISSN:
0022-2488 (print)   1089-7658 (online)
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REFERENCES (11)
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  1. P. Exner, J. Math. Phys. 46, 062105 (2005).
  2. P. Exner, E. M. Harrell, and M. Loss, Lett. Math. Phys. 75, 225 (2006)
    3. 77, 219 (2006).
  3. A. Abrams, J. Cantarella, J. H. G. Fu, M. Ghomi, and R. Howard, Topology 42, 381 (2003).
  4. G. Lükő, Isr. J. Math. 4, 23 (1966).
  5. P. Exner, F. Fraas, and E. M. Harrell, Phys. Lett. A 368, 1 (2007).
  6. J. F. Brasche, P. Exner, Yu. A. Kuperin, and P. Šeba, J. Math. Anal. Appl. 184, 112 (1994).
  7. A. Posilicano, J. Funct. Anal. 183, 109 (2001).
  8. Y. Pinchover, Proc. Symp. Pure Math. 76, 329 (2007).
  9. G. Polya and G. Szegö, Isoperimetric Inequalities in Mathematical Physics, Annals of Mathematics Studies Series No. 27 (Princeton University Press, Princeton, NJ, 1951).
  10. E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Mathematical Series No. 30 (Princeton University Press, Princeton, NJ, 1970.
  11. M. Reed and B. Simon, Analysis of Operators, Methods of Modern Mathematical Physics Vol. IV (Academic, New York, 1978).

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