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UID:5735@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20230214T110000
DTEND;TZID=Europe/Paris:20230214T120000
DTSTAMP:20241120T200202Z
URL:https://www.i2m.univ-amu.fr/evenements/continuum-limits-for-lattice-sc
 hrodinger-equations/
SUMMARY:Hiroshi Isozaki (University of Tsukuba): Continuum limits for latti
 ce Schrödinger equations
DESCRIPTION:Hiroshi Isozaki: We consider the behavior of solutions of the H
 elmholtz equation\n$(- \\Delta_{disc\,h} - E)u_h = f_h$ for a continuous s
 pectrum $E$ on a periodic lattice as the mesh size $h$ tends to 0. For the
  case of the hexagonal and related lattices\, in a suitable energy region\
 , it converges to that for the Dirac equation. For the case of the square 
 lattice\, triangular lattice\, hexagonal lattice (in another energy region
 ) and subdivision of a square lattice\, one can add a scalar potential\, a
 nd the solution of the lattice Schr{\\"o}dinger equation $( - \\Delta_{dis
 c\,h} +V_{disc\,h} - E)u_h = f_h$ converges to that of the continuum Schr
 ödinger equation $(P(D_x) + V(x) -E)u = f$. This is a joint work with A. 
 Jensen.\n[su_spacer size="10"]\nhttps://arxiv.org/abs/2006.00854\n\n&nbsp\
 ;
ATTACH;FMTTYPE=image/jpeg:https://www.i2m.univ-amu.fr/wp-content/uploads/2
 023/01/image-seminar_AA-arxiv.2006.00854-Graphite-fig.4-Jensen-Hisozaki.pn
 g
CATEGORIES:Séminaire,Analyse Appliquée
LOCATION:I2M Chateau-Gombert - CMI\, Salle de Séminaire R164 (1er étage)\
 , 39 Rue Joliot Curie\, 13013 Marseille\, France\, Campus Château-Gombert
 \, 
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  Marseille\, France\, Campus Château-Gombert\, ;X-APPLE-RADIUS=100;X-TITL
 E=I2M Chateau-Gombert - CMI\, Salle de Séminaire R164 (1er étage):geo:0,
 0
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