78 citations · 1k across the 73 of their papers we have counts for
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A simple derivation of the zero-temperature BCS functional from the reduced BCS Hamiltonian
Christian Hainzl, Riccardo Panza
We consider a grand-canonical reduced BCS Hamiltonian on the full fermionic Fock space with an attractive pairing interaction supported in an energy shell around the Fermi surface.…
The Huang--Yang formula for a two-dimensional Fermi gas: upper bound
Christian Hainzl, Fabian Saxler, Robert Seiringer
We compute an upper bound on the ground state energy of a dilute two-dimensional Fermi gas with repulsive short-range interactions. Our bound can be viewed as the two-dimensional a…
The Huang-Yang conjecture for the low-density Fermi gas
Emanuela L. Giacomelli, Christian Hainzl, Phan Thành Nam +1
Our work establishes a three-term asymptotic expansion of the ground state energy of a dilute gas of spin fermions with repulsive short-range interactions, validating a formu…
The Huang-Yang formula for the low-density Fermi gas: upper bound
Emanuela L. Giacomelli, Christian Hainzl, Phan Thành Nam +1
We study the ground state energy of a gas of spin fermions with repulsive short-range interactions. We derive an upper bound that agrees, at low density , with the Huang-Y…
Upper Bound for the Free Energy of Dilute Bose Gases at Low Temperature
Florian Haberberger, Christian Hainzl, Benjamin Schlein +1
We consider a Bose gas at density , interacting through a repulsive potential with scattering length . We prove an upper bound fo…
The Correlation Energy of the Electron Gas in the Mean-Field Regime
Martin Ravn Christiansen, Christian Hainzl, Phan Thành Nam
We prove a rigorous lower bound on the correlation energy of interacting fermions in the mean-field regime for a wide class of singular interactions, including the Coulomb potentia…
The free energy of dilute Bose gases at low temperatures
Florian Haberberger, Christian Hainzl, Phan Thành Nam +2
We consider a low density Bose gas interacting through a repulsive potential in the thermodynamic limit. We justify, as a rigorous lower bound, a Lee--Huang--Yang type formula for…
Microscopic Derivation of Ginzburg-Landau Theory and the BCS Critical Temperature Shift in General External Fields
Andreas Deuchert, Christian Hainzl, Marcel Maier
We consider the Bardeen-Cooper-Schrieffer (BCS) free energy functional with weak and macroscopic external electric and magnetic fields and derive the Ginzburg-Landau functional. We…
The Gell-MannBrueckner Formula for the Correlation Energy of the Electron Gas: A Rigorous Upper Bound in the Mean-Field Regime
Martin Ravn Christiansen, Christian Hainzl, Phan Thành Nam
We prove a rigorous upper bound on the correlation energy of interacting fermions in the mean-field regime for a wide class of interaction potentials. Our result covers the Coulomb…
On the Effective Quasi-Bosonic Hamiltonian of the Electron Gas: Collective Excitations and Plasmon Modes
Martin Ravn Christiansen, Christian Hainzl, Phan Thành Nam
We consider an effective quasi-bosonic Hamiltonian of the electron gas which emerges naturally from the random phase approximation and describes the collective excitations of the g…
Bogoliubov Theory in the Gross-Pitaevskii Limit: a Simplified Approach
Christian Hainzl, Benjamin Schlein, Arnaud Triay
We show that Bogoliubov theory correctly predicts the low-energy spectral properties of Bose gases in the Gross-Pitaevskii regime. We recover recent results from \cite{BBCS,BBCS4}.…
Boundary Superconductivity in the BCS Model
Christian Hainzl, Barbara Roos, Robert Seiringer
We consider the linear BCS equation, determining the BCS critical temperature, in the presence of a boundary, where Dirichlet boundary conditions are imposed. In the one-dimensiona…
The Random Phase Approximation for Interacting Fermi Gases in the Mean-Field Regime
Martin Ravn Christiansen, Christian Hainzl, Phan Thành Nam
We present a general approach to justify the random phase approximation for the homogeneous Fermi gas in three dimensions in the mean-field scaling regime. We consider a system of…
Microscopic Derivation of Ginzburg-Landau Theory and the BCS Critical Temperature Shift in a Weak Homogeneous Magnetic Field
Andreas Deuchert, Christian Hainzl, Marcel Maier
Starting from the Bardeen-Cooper-Schrieffer (BCS) free energy functional, we derive the Ginzburg-Landau functional in the presence of a weak homogeneous magnetic field. We also pro…
Another proof of BEC in the GP-limit
Christian Hainzl
We present a fresh look at the methods introduced by Boccato, Brennecke, Cenatiempo, and Schlein concerning the trapped Bose gas and give a conceptually very simple and concise pro…
The dilute Fermi gas via Bogoliubov theory
Marco Falconi, Emanuela L. Giacomelli, Christian Hainzl +1
We study the ground state properties of interacting Fermi gases in the dilute regime, in three dimensions. We compute the ground state energy of the system, for positive interactio…
The BCS critical temperature in a weak external electric field via a linear two-body operator
Rupert L. Frank, Christian Hainzl
We study the critical temperature of a superconductive material in a weak external electric potential via a linear approximation of the BCS functional. We reproduce a similar resul…
On the correlation energy of interacting fermionic systems in the mean-field regime
Christian Hainzl, Marcello Porta, Felix Rexze
We consider a system of interacting fermionic particles in three dimensions, confined in a periodic box of volume , in the mean-field scaling. We assume that the intera…
The BCS critical temperature in a weak homogeneous magnetic field
Rupert L. Frank, Christian Hainzl, Edwin Langmann
We show that, within a linear approximation of BCS theory, a weak homogeneous magnetic field lowers the critical temperature by an explicit constant times the field strength, up to…
Persistence of translational symmetry in the BCS model with radial pair interaction
Andreas Deuchert, Alissa Geisinger, Christian Hainzl +1
We consider the two-dimensional BCS functional with a radial pair interaction. We show that the translational symmetry is not broken in a certain temperature interval below the cri…
Bogolubov-Hartree-Fock theory for strongly interacting fermions in the low density limit
Gerhard Bräunlich, Christian Hainzl, Robert Seiringer
We consider the Bogolubov-Hartree-Fock functional for a fermionic many-body system with two-body interactions. For suitable interaction potentials that have a strong enough attract…
The BCS functional of superconductivity and its mathematical properties
Christian Hainzl, Robert Seiringer
We review recent results concerning the mathematical properties of the Bardeen-Cooper-Schrieffer (BCS) functional of superconductivity, which were obtained in a series of papers pa…
Incompatibility of time-dependent Bogoliubov--de-Gennes and Ginzburg--Landau equations
Rupert L. Frank, Christian Hainzl, Benjamin Schlein +1
We study the time-dependent Bogoliubov--de-Gennes equations for generic translation-invariant fermionic many-body systems. For initial states that are close to thermal equilibrium…
Comparing the full time-dependent Bogoliubov--de-Gennes equations to their linear approximation: A numerical investigation
Christian Hainzl, Jonathan Seyrich
In this paper we report on the results of a numerical study of the nonlinear time-dependent Bardeen--Cooper--Schrieffer (BCS) equations, often also denoted as Bogoliubov--de--Genne…