Diamagnetic behavior of sums Dirichlet eigenvalues

László Erdös; Michael Loss; Vitali Vougalter

Annales de l'institut Fourier (2000)

  • Volume: 50, Issue: 3, page 891-907
  • ISSN: 0373-0956

Abstract

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The Li-Yau semiclassical lower bound for the sum of the first N eigenvalues of the Dirichlet–Laplacian is extended to Dirichlet– Laplacians with constant magnetic fields. Our method involves a new diamagnetic inequality for constant magnetic fields.

How to cite

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Erdös, László, Loss, Michael, and Vougalter, Vitali. "Diamagnetic behavior of sums Dirichlet eigenvalues." Annales de l'institut Fourier 50.3 (2000): 891-907. <http://eudml.org/doc/75442>.

@article{Erdös2000,
abstract = {The Li-Yau semiclassical lower bound for the sum of the first $N$ eigenvalues of the Dirichlet–Laplacian is extended to Dirichlet– Laplacians with constant magnetic fields. Our method involves a new diamagnetic inequality for constant magnetic fields.},
author = {Erdös, László, Loss, Michael, Vougalter, Vitali},
journal = {Annales de l'institut Fourier},
keywords = {magnetic laplacian; diamagnetic inequality; semiclassical bound},
language = {eng},
number = {3},
pages = {891-907},
publisher = {Association des Annales de l'Institut Fourier},
title = {Diamagnetic behavior of sums Dirichlet eigenvalues},
url = {http://eudml.org/doc/75442},
volume = {50},
year = {2000},
}

TY - JOUR
AU - Erdös, László
AU - Loss, Michael
AU - Vougalter, Vitali
TI - Diamagnetic behavior of sums Dirichlet eigenvalues
JO - Annales de l'institut Fourier
PY - 2000
PB - Association des Annales de l'Institut Fourier
VL - 50
IS - 3
SP - 891
EP - 907
AB - The Li-Yau semiclassical lower bound for the sum of the first $N$ eigenvalues of the Dirichlet–Laplacian is extended to Dirichlet– Laplacians with constant magnetic fields. Our method involves a new diamagnetic inequality for constant magnetic fields.
LA - eng
KW - magnetic laplacian; diamagnetic inequality; semiclassical bound
UR - http://eudml.org/doc/75442
ER -

References

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  8. [LL97] E.H. LIEB, M. LOSS, Analysis, Graduate Studies in Mathematics, Volume 14, American Mathematical Society (1997). Zbl0873.26002MR98b:00004
  9. [LT75] E.H. LIEB, W. THIRRING, Bound for the kinetic energy of fermions which proves the stability of matter, Phys. Rev. Lett., 35 (1975), 687. 
  10. [LT76] E.H. LIEB, W. THIRRING, Inequalities for the moments of the eigenvalues of the Schrödinger Hamiltonian and their relation to Sobolev inequalities, Studies in Math. Phys., Essays in Honor of Valentine Bargmann., Princeton (1976). Zbl0342.35044
  11. [LW99] A. LAPTEV, T. WEIDL, Sharp Lieb-Thirring inequalities in high dimensions, to appear in Acta Math. Zbl1142.35531
  12. [LY83] P. LI, S.-T. YAU, On the Schrödinger equation and the eigenvalue problem, Comm. Math. Phys., 88 (1983), 309-318. Zbl0554.35029MR84k:58225
  13. [RS79] M. REED, B. SIMON, Methods of Modern Mathematical Physics, III. Scattering Theory, Academic Press, 1979. Zbl0405.47007MR80m:81085
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  15. [S77, 79] B. SIMON, An abstract Kato inequality for generators of positivity preserving semigroups, Ind. Math. J., 26 (1977), 1067-1073. Kato's inequality and the comparison of semigroups, J. Funct. Anal., 32 (1979), 97-101. Zbl0389.47021MR57 #1194

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