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SUMMARY:Jastrow Factors and Barron Regularity of Electronic Wave Functions
DTSTART:20261008T093000
DTEND:20261008T103000
DTSTAMP:20260916T190553Z
UID:5a58b5b6acacb654ccee6cc25f8aa3179192feae7b6604027d52c2bc
CATEGORIES:Conferences - Seminars
DESCRIPTION:Virginie Ehrlacher (ENPC)\nWave functions describing bound sta
 tes of electronic systems satisfy high-dimensional Schrödinger equations 
 whose potentials exhibit Coulomb singularities at particle-collision confi
 gurations. These singularities generate cusps that limit the global regula
 rity of the wave function in spectral Barron spaces\, which are particular
 ly relevant to the analysis of Fourier-based approximation methods and neu
 ral networks.\nIn this talk\, we study the effect of extracting a truncate
 d Jastrow factor designed to capture the leading coalescence singularities
  while preserving the asymptotic behavior of the wave function at infinity
 . We show that the resulting quotient gains one full order of spectral Bar
 ron regularity: whereas the original wave function typically belongs to sp
 aces of order (s<1)\, the Jastrow quotient belongs to those of order (s<2)
 . An explicit hydrogenic example shows that the threshold (s=2) is natural
 .\nThe proof relies on conjugating the Hamiltonian by the Jastrow factor a
 nd carrying out a global Fourier-space analysis. It combines resolvent est
 imates\, precise control of singular coefficients\, and a fixed-point argu
 ment separating low and high frequencies.\n\n---\nThe electronic structure
  reading group brings together researchers and students interested in math
 ematical aspects of electronic structure problems and adjacent topics\, in
 cluding:\n\n	Density Functional Theory\n	Many-body Schrödinger equation f
 or electrons\n	Born-Oppenheimer Molecular Dynamics\n	Numerical analysis an
 d error control\n\nWebsite: https://matmat.org/readinggroup/\n 
LOCATION:GC B3 31 https://plan.epfl.ch/?room==GC%20B3%2031
STATUS:CANCELLED
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