The Mathematics of the Structure of Matter

Objectif

"The objective of the proposed research in mathematical physics is to study the quantum theory of matter from a mathematical perspective. We will consider systems ranging from the tiny scale of atoms over macroscopic everyday matter to the gigantic scale of stars. Despite the range in scale, these systems may all be described by many-body quantum physics. Our aim is to rigorously understand their stability and structure, in particular, exotic phenomena such as Bose-Einstein condensation, superconductivity, superfluidity, and special low-dimensional behavior. The ultimate goal is to understand the full many-body theory but we will also investigate simpler approximate models such as Bogolubov’s model for superfluidity, Bardeen-Cooper-Schrieffer (BCS) and Ginzburg-Landau (GL) models of superconductivity, and the Hartree-Fock model of atoms and molecules. The role of such models is two-fold. On one hand they are of independent interest. On the other hand and more importantly they may give information about the many-body theory. This is true to the extent we can estimate the degree to which they approximate in appropriate limits.
From a mathematical point of view our approach is variational. All the theories we consider are formulated in terms of energy functionals. The full many-body theories are linear but due to the essentially uncontrolled number of variables they are extremely complicated. The approximate models are non-linear. Surprisingly they are nevertheless significantly simpler due to the reduction in degrees of freedom. Often the limits correspond to semiclassical limits for spectral problems.
Examples of specific goals that we will pursue are
*Establish the thermodynamic properties of matter coupled to electromagnetic fields
*Derive GL theory as a limit of BCS theory
*Estimate ionization energies of large atoms and molecules
*Derive spectral estimates of Lieb-Thirring type for 2D anyons
*Derive semiclassical expansions for problems with low regularity"

Champ scientifique

Régime de financement

ERC-AG - ERC Advanced Grant

Institution d’accueil

KOBENHAVNS UNIVERSITET

Contribution de l’UE

€ 1 465 016,00

Adresse

NORREGADE 10
1165 Kobenhavn
Danemark

Région

Danmark Hovedstaden Byen København

Type d’activité

Higher or Secondary Education Establishments

Chercheur principal

Jan Philip Solovej (Prof.)

Contact administratif

Ivan Kristoffersen (Mr.)

Liens

Contacter l’organisation Site web

Coût total

Aucune donnée

Bénéficiaires (1)