Christian Hainzl

The Thermodynamic Limit of Quantum Coulomb Systems: A New Approach (2008)

We study the eigenvalues of Schr\"odinger type operators $T + \lambda V$ and their asymptotic behavior in the small coupling limit $\lambda \to 0$, in the case where the symbol of the kinetic energy,...

Hainzl, Christian, Lewin, Mathieu, Solovej, Jan Philip

We present two recent works on the thermodynamic limit of quantum Coulomb systems, in which we provided a general method allowing to show the existence of the limit for many different models.

The Thermodynamic Limit of Quantum Coulomb Systems. Part I. General Theory (2008)

Hainzl, Christian, Lewin, Mathieu, Solovej, Jan Philip

This article is the first in a series dealing with the thermodynamic properties of quantum Coulomb systems. In this first part, we consider a general real-valued function $E$ defined on all bounded...

The Thermodynamic Limit of Quantum Coulomb Systems. Part II. Applications (2008)

Hainzl, Christian, Lewin, Mathieu, Solovej, Jan Philip

In a previous paper, we have developed a general theory of thermodynamic limits. We apply it here to three different Coulomb quantum systems, for which we prove the convergence of the free energy per...

Stellar Collapse in the Time Dependent Hartree-Fock Approximation (2008)

Hainzl, Christian, Schlein, Benjamin

We prove blow-up in finite time for radially symmetric solutions to the pseudo-relativistic Hartree-Fock equation with negative energy. The non-linear Hartree-Fock equation is commonly used in the...

The BCS Critical Temperature for Potentials with Negative Scattering Length (2008)

A Nonlinear Model for Relativistic Electrons at Positive Temperature (2008)

We prove that the critical temperature for the BCS gap equation is given by $T_c = \mu (8/\pi e^{\gamma -2} + o(1)) e^{\pi/(2\sqrt \mu a)}$ in the low density limit $\mu\to 0$. The formula holds for...

Hainzl, Christian, Lewin, Mathieu, Seiringer, Robert

We study the relativistic electron-positron field at positive temperature in the Hartree-Fock-approximation. We consider both the case with and without exchange term, and investigate the existence...

Spectral properties of the BCS gap equation of superfluidity (2008)

Critical Temperature and Energy Gap for the BCS Equation (2008)

We present a review of recent work on the mathematical aspects of the BCS gap equation, covering our results of [arXiv:0801.4159] as well our recent joint work with Hamza and Solovej...

Supported by Federal Ministry of Science and Transport, Austria (2007)

We derive upper and lower bounds on the critical temperature $T_c$ and the energy gap $\Xi$ (at zero temperature) for the BCS gap equation, describing spin 1/2 fermions interacting via a local...

The Erwin, Schrodinger International Boltzmanngasse, Christian Hainzl, Christian Hainzl, Robert Seiringer, Robert Seiringer

A discrete density matrix theory for atoms in strong magnetic elds

2 (2007)

Christian Hainzl, Semjon A. Vugalter

We consider a spinless particle coupled to a photon eld and prove that even if the Schrodinger operator p 2 + V does not have eigenvalues the system can have a ground state. We describe the coupling...

photon (2007)

Christian Hainzl

non-relativistic particle coupled to a

atoms in (2007)

Christian Hainzl, Robert Seiringer

discrete density matrix theory for

2 (2007)

The Erwin, Schrodinger International Boltzmanngasse, Christian Hainzl, Christian Hainzl, Robert Seiringer, Robert Seiringer

Bounds on one-dimensional exchange energies with application to lowest Landau band quantum mechanics

A Minimization Method for Relativistic Electrons in a Mean-Field Approximation of Quantum Electrodynamics (2007)

Hainzl, Christian, Lewin, Mathieu, Sere, Eric, Solovej, Jan Philip

We study a mean-field relativistic model which is able to describe both the behavior of finitely many spin-1/2 particles like electrons and of the Dirac sea which is self-consistently polarized in...

The critical temperature for the BCS equation at weak coupling (2007)

Frank, Rupert L., Hainzl, Christian, Naboko, Serguei, Seiringer, Robert

For the BCS equation with local two-body interaction $\lambda V(x)$, we give a rigorous analysis of the asymptotic behavior of the critical temperature as $\lambda \to 0$. We derive necessary and...

The BCS Functional for General Pair Interactions (2007)

Hainzl, Christian, Hamza, Eman, Seiringer, Robert, Solovej, Jan Philip

The Bardeen-Cooper-Schrieffer (BCS) functional has recently received renewed attention as a description of fermionic gases interacting with local pairwise interactions. We present here a rigorous...

Enhanced binding revisited for a spinless particle in non-relativistic QED (2007)

Catto, Isabelle, Exner, Pavel, Hainzl, Christian

We consider a spinless particle coupled to a quantized Bose field and show that such a system has a ground state for two classes of short-range potentials which are alone too weak to have a...

Existence of Atoms and Molecules in the Mean-Field Approximation of No-Photon Quantum Electrodynamics (2007)

The Mean-Field Approximation in Quantum Electrodynamics. The no-photon case (2007)

The Bogoliubov-Dirac-Fock (BDF) model is the mean-field approximation of no-photon Quantum Electrodynamics. The present paper is devoted to the study of the minimization of the BDF energy functional...

Hainzl, Christian, Lewin, Mathieu, Solovej, Jan Philip

We study the mean-field approximation of Quantum Electrodynamics, by means of a thermodynamic limit. The QED Hamiltonian is written in Coulomb gauge and does not contain any normal-ordering or choice...

Existence of Atoms and Molecules in the Mean-Field Approximation of No-Photon Quantum Electrodynamics (2006)

The Mean-Field Approximation in Quantum Electrodynamics. The no-photon case (2005)

The Bogoliubov-Dirac-Fock (BDF) model is the mean-field approximation of no-photon Quantum Electrodynamics. The present paper is devoted to the study of the minimization of the BDF energy functional...

Hainzl, Christian, Lewin, Mathieu, Solovej, Jan Philip

We study the mean-field approximation of Quantum Electrodynamics, by means of a thermodynamic limit. The QED Hamiltonian is written in Coulomb gauge and does not contain any normal-ordering or choice...

Existence of global-in-time solutions to a generalized Dirac-Fock type evolution equation (2004)

Hainzl, Christian, Lewin, Mathieu, Sparber, Christof

We consider a generalized Dirac-Fock type evolution equation deduced from no-photon Quantum Electrodynamics, which describes the self-consistent time-evolution of relativistic electrons, the...

Self-consistent solution for the polarized vacuum in a no-photon QED model (2004)

Enhanced binding revisited for a spinless particle in non-relativistic QED (2004)

We study the Bogoliubov-Dirac-Fock model introduced by Chaix and Iracane ({\it J. Phys. B.}, 22, 3791--3814, 1989) which is a mean-field theory deduced from no-photon QED. The associated functional...

Catto, Isabelle, Exner, Pavel, Hainzl, Christian

We consider a spinless particle coupled to a quantized Bose field and show that such a system has a ground state for two classes of short-range potentials which are alone too weak to have a...

Existence of a stable polarized vacuum in the Bogoliubov-Dirac-Fock approximation (2004)

Binding energy for hydrogen-like atoms in the Nelson model without cutoffs (2003)

According to Dirac's ideas, the vacuum consists of infinitely many virtual electrons which completely fill up the negative part of the spectrum of the free Dirac operator $D^0$. In the presence of an...

Hainzl, Christian, Hirokawa, Masao, Spohn, Herbert

In the Nelson model particles interact through a scalar massless field. For hydrogen-like atoms there is a nucleus of infinite mass and charge $Ze$, $Z > 0$, fixed at the origin and an electron of...

On the Vacuum Polarization Density Caused by an External Field (2003)

Non-Perturbative Mass and Charge Renormalization in Relativistic No-Photon Quantum Electrodynamics (2003)

We consider an external potential, $-\lambda \phi$, due to one or more nuclei. Following the Dirac picture such a potential polarizes the vacuum. The polarization density as derived in physics...

Hainzl, Christian, Siedentop, Heinz

Starting from a formal Hamiltonian as found in the physics literature -- omitting photons -- we define a renormalized Hamiltonian through charge and mass renormalization. We show that the restriction...

Mass Renormalization and Energy Level Shift in Non-Relativistic QED (2002)

Increase of the binding energy of an electron by coupling to a photon field (2002)

Using the Pauli-Fierz model of non-relativistic quantum electrodynamics, we calculate the binding energy of an electron in the field of a nucleus of charge $Z$ and in presence of the quantized...

One non-relativistic particle coupled to a photon field (2002)

We look at an electron in the field of an arbitrary external potential $V$, such that the Schr\"odinger operator $p^2 + V$ has at least one eigenvalue, and show that by coupling to a quantized...

Enhanced Binding in non-relativistic QED (2001)

We investigate the ground state energy of an electron coupled to a photon field. First, we regard the self-energy of a free electron, which we describe by the Pauli-Fierz Hamiltonian. We show that,...

Hainzl, Christian, Vougalter, Vitali, Vugalter, Semjon A.

We consider a spinless particle coupled to a photon field and prove that even if the Schr\"odinger operator $p^2 + V$ does not have eigenvalues the system can have a ground state. We describe the...

General Decomposition of Radial Functions on R^n and Applications to N-Body Quantum Systems (2001)

Semiclassics in the lowest Landau band (2001)

We present a generalization of the Fefferman-de la Llave decomposition of the Coulomb potential to quite arbitrary radial functions $V$ on $R^n$ going to zero at infinity. This generalized...

Bounds on one-dimensional exchange energies with application to lowest Landau band quantum mechanics (2001)

This paper deals with the comparison between the strong Thomas-Fermi theory and the quantum mechanical ground state energy of a large atom confined to lowest Landau band wave functions. Using the...

Bounds on One–Dimensional Exchange Energies with Application to Lowest Landau Band Quantum Mechanics (2001)

By means of a generalization of the Fefferman-de la Llave decomposition we derive a general lower bound on the interaction energy of one-dimensional quantum systems. We apply this result to a...

The Erwin, Schrödinger International Boltzmanngasse, Christian Hainzl, Robert Seiringer, Christian Hainzl, Robert Seiringer

Available via anonymous ftp from FTP.ESI.AC.AT

Gradient corrections for semiclassical theories of atoms in strong magnetic fields (2000)

A discrete density matrix theory for atoms in strong magnetic fields (2000)

This paper is divided into two parts. In the first one the von Weizs\"acker term is introduced to the Magnetic TF theory and the resulting MTFW functional is mathematically analyzed. In particular,...