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SUMMARY:Stability of Nonrelativistic Matter
DTSTART;VALUE=DATE-TIME:20260414T223900Z
DTEND;VALUE=DATE-TIME:20260414T224600Z
DTSTAMP;VALUE=DATE-TIME:20260507T224855Z
UID:indico-contribution-337@fisindico.uniandes.edu.co
DESCRIPTION:Speakers: Juan Felipe Prieto Mateus (Universidad de los Andes)
 \nThe stability of matter is often assumed without question. We typically 
 believe that established physical theories can easily predict that atoms a
 nd molecules will not collapse or that the total energy of matter scales l
 inearly with the number of particles. However\, these questions remained u
 nresolved when quantum theory was first established\, and it actually took
  several decades before any proof was provided. In this talk\, we present 
 Lieb's proof of the stability of non-relativistic matter. By modeling matt
 er as a system of $N$ particles interacting under Coulomb forces\, we show
  how to derive a linear bound for the total energy of the system as a func
 tion of $N$\; that is\, to find a constant $k$ such that $\\mathcal{E}(\\p
 si) > kN $ for every wave function $ \\psi $ of the system. To achieve thi
 s\, we apply the Lieb-Thirring inequalities in the context of Schrödinger
  operators and use a semiclassical approximation of the Coulomb energy. Fi
 nally\, we discuss how this linear bound for the total energy leads to the
  conclusion that matter is extensive and bosonic matter is unstable.\n\nht
 tps://fisindico.uniandes.edu.co/event/23/contributions/337/
LOCATION:Universidad Nacional Edificio 564
URL:https://fisindico.uniandes.edu.co/event/23/contributions/337/
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