Christian Hainzl

The Critical Temperature for the BCS Equation at Weak Coupling

For the BCS equation with local two-body interaction λV(x), we give a rigorous analysis of the asymptotic behavior of the critical temperature as γ»0. We derive necessary and sufficient conditions onV(x) for the existence of a nontrivial solution for all values of γ>0.

Unconditional Uniqueness for the Cubic Gross‐Pitaevskii Hierarchy via Quantum de Finetti

We present a new, simpler proof of the unconditional uniqueness of solutions to the cubic Gross-Pitaevskii hierarchy in . One of the main tools in our analysis is the quantum de Finetti theorem. Our uniqueness result is equivalent to the one established in the celebrated works of Erdős, Schlein, and Yau.

MICROSCOPIC DERIVATION OF GINZBURG-LANDAU THEORY

We give the first rigorous derivation of the celebrated Ginzburg-Landau (GL) theory, starting from the microscopic Bardeen-Cooper-Schrieffer (BCS) model. Close to the critical temperature, GL arises as an effective theory on the macroscopic scale. The relevant scaling limit is semiclassical in nature, and semiclassical analysis, with minimal regularity assumptions, plays an important part in our proof.

Enhanced Binding in Non-Relativistic QED

Abstract: We consider a spinless particle coupled to a photon field and prove that even if the Schrödinger operator p2+V does not have eigenvalues the system can have a ground state. We describe the coupling by means of the Pauli-Fierz Hamiltonian and our result holds in the case where the coupling constant α is small.

General Decomposition of Radial Functions on Rn and Applications to N-Body Quantum Systems

We present a generalization of the Fefferman–de la Llave decomposition of the Coulomb potential to quite arbitrary radial functions V on Rn going to zero at infinity. This generalized decomposition can be used to extend previous results on N-body quantum systems with Coulomb interaction to a more general class of interactions. As an example of such an application, we derive the high density asymptotics of the ground state energy of jellium with Yukawa interaction in the thermodynamic limit, using a correlation estimate by Graf and Solovej.

Self-energy of one electron in non-relativistic QED

We investigate the self-energy of one electron coupled to a quantized radiation field by extending the ideas developed previously by Hainzl. We fix an arbitrary cutoff parameter

Non-Perturbative Mass and Charge Renormalization in Relativistic No-Photon Quantum Electrodynamics

\Lambda

One Non-Relativistic Particle Coupled to a Photon Field

and recover the

The Bardeen–Cooper–Schrieffer functional of superconductivity and its mathematical properties

\alpha^2

On the Well-Posedness and Scattering for the Gross–Pitaevskii Hierarchy via Quantum de Finetti

-term of the self-energy, where