72 citations · 348 across the 18 of their papers we have counts for
20 papers
Exponential Control of Excitations for Trapped BEC in the Gross-Pitaevskii Regime
Nils Behrmann, Christian Brennecke, Simone Rademacher
We consider trapped Bose gases in three dimensions in the Gross-Pitaevskii regime whose low energy states are well known to exhibit Bose-Einstein condensation. That is, the majorit…
Second Order Expansion of Gibbs State Reduced Density Matrices in the Gross-Pitaevskii Regime
Christian Brennecke, Jinyeop Lee, Phan Thành Nam
We consider a translation-invariant system of bosons in that interact through a repulsive two-body potential with scattering length of order in the li…
Operator Norm Bounds on the Correlation Matrix of the SK Model at High Temperature
Christian Brennecke, Changji Xu, Horng-Tzer Yau
We prove that the two point correlation matrix of the Sherrington-Kirkpatrick model has the p…
The Two Point Function of the SK Model without External Field at High Temperature
Christian Brennecke, Adrien Schertzer, Changji Xu +1
We show that the two point correlation matrix of the Sherrington-Kirkpatrick model with zero external field satisfies \[…
Spectral Gap Estimates for Mixed -Spin Models at High Temperature
Arka Adhikari, Christian Brennecke, Changji Xu +1
We consider general mixed -spin mean field spin glass models and provide a method to prove that the spectral gap of the Dirichlet form associated with the Gibbs measure is of or…
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…
The Replica Symmetric Formula for the SK Model Revisited
Christian Brennecke, Horng-Tzer Yau
We provide a simple extension of Bolthausen's Morita type proof of the replica symmetric formula [E. Bolthausen, Stat. Mech. of Classical and Disordered Systems, pp. 63-93 (2018)]…
Bogoliubov Theory for Trapped Bosons in the Gross-Pitaevskii Regime
Christian Brennecke, Benjamin Schlein, Severin Schraven
We consider systems of bosons in , trapped by an external potential. The interaction is repulsive and has a scattering length of the order (Gross-Pitaevs…
Excitation Spectrum for Bose Gases beyond the Gross-Pitaevskii Regime
Christian Brennecke, Marco Caporaletti, Benjamin Schlein
We consider Bose gases of particles in a box of volume one, interacting through a repulsive potential with scattering length of order , for . Such regimes interp…
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 with Optimal Rate for Trapped Bosons in the Gross-Pitaevskii Regime
Christian Brennecke, Benjamin Schlein, Severin Schraven
We consider a Bose gas consisting of particles in , trapped by an external field and interacting through a two-body potential with scattering length of order $N^{…
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…
Bogoliubov Theory in the Gross-Pitaevskii Limit
Chiara Boccato, Christian Brennecke, Serena Cenatiempo +1
We consider Bose gases consisting of particles trapped in a box with volume one and interacting through a repulsive potential with scattering length of the order (Gross…
Fluctuations of -particle quantum dynamics around the nonlinear Schrödinger equation
Christian Brennecke, Phan Thành Nam, Marcin Napiórkowski +1
We consider a system of bosons interacting through a singular two-body potential scaling with and having the form , for an arbitrary parameter $β\in (0,1…
The excitation spectrum of Bose gases interacting through singular potentials
Chiara Boccato, Christian Brennecke, Serena Cenatiempo +1
We consider systems of bosons in a box with volume one, interacting through a repulsive two-body potential of the form . For all , and for sufficie…
Complete Bose-Einstein condensation in the Gross-Pitaevskii regime
Chiara Boccato, Christian Brennecke, Serena Cenatiempo +1
We consider a gas of bosons in a box with volume one interacting through a two-body potential with scattering length of order (Gross-Pitaevskii limit). Assuming the (u…
Gross-Pitaevskii Dynamics for Bose-Einstein Condensates
Christian Brennecke, Benjamin Schlein
We study the time-evolution of initially trapped Bose-Einstein condensates in the Gross-Pitaevskii regime. Under a physically motivated assumption on the energy of the initial data…