7 papers
The Low Energy Spectrum of Trapped Bosons in the Gross-Pitaevskii Regime
Christian Brennecke
Bogoliubov Theory provides important predictions for the low energy properties of the weakly interacting Bose gas. Recently, Bogoliubov's predictions could be justified rigorously…
On the mean-field equations for ferromagnetic spin systems
Christian Brennecke, Per von Soosten
We derive mean-field equations for a general class of ferromagnetic spin systems with an explicit error bound in finite volumes. The proof is based on a link between the mean-field…
Dynamical Approach to the TAP Equations for the Sherrington-Kirkpatrick Model
Arka Adhikari, Christian Brennecke, Per von Soosten +1
We present a new dynamical proof of the Thouless-Anderson-Palmer (TAP) equations for the classical Sherrington-Kirkpatrick spin glass at sufficiently high temperature. In our deriv…
Bose-Einstein Condensation Beyond the Gross-Pitaevskii Regime
Arka Adhikari, Christian Brennecke, Benjamin Schlein
We consider N bosons in a box with volume one, interacting through a two-body potential with scattering length of the order , for . Assuming that , we…
Free Energy of the Quantum Sherrington-Kirkpatrick Spin-Glass Model with Transverse Field
Arka Adhikari, Christian Brennecke
We consider the quantum Sherrington-Kirkpatrick (SK) spin-glass model with transverse field and provide a formula for its free energy in the thermodynamic limit, valid for all inve…
Optimal Rate for Bose-Einstein Condensation in the Gross-Pitaevskii Regime
Chiara Boccato, Christian Brennecke, Serena Cenatiempo +1
We consider systems of bosons trapped in a box, in the Gross-Pitaevskii regime. We show that low-energy states exhibit complete Bose-Einstein condensation with an optimal bound on…