Speaker SFB/TRR:

"Mathematics of Many-Body Quantum Systems and Their Collective Phenomena"

More information can be found on www.trr352.de.

Curriculum Vitae

CV (PDF, 77 KB)

Research Interests

See full list of Research Interests.

Organization of International Summer Schools

See full list of organized Summer Schools.

Publications

  • The Huang–Yang conjecture for the low-density Fermi gas – Emanuela L. Giacomelli, Christian Hainzl, Phan Thành Nam, Robert Seiringer – 2025 – arXiv:2505.22340
  • The Huang–Yang formula for the low-density Fermi gas: upper bound – Emanuela L. Giacomelli, Christian Hainzl, Phan Thành Nam, Robert Seiringer – 2024 – arXiv:2409.17914
  • Upper Bound for the Free Energy of Dilute Bose Gases at Low Temperature – Florian Haberberger, Christian Hainzl, Benjamin Schlein, Arnaud Triay – 2024 – arXiv:2405.03378
  • The Correlation Energy of the Electron Gas in the Mean-Field Regime – Martin Ravn Christiansen, Christian Hainzl, Phan Thành Nam – 2024 – arXiv:2405.01386
  • Microscopic Derivation of Ginzburg–Landau Theory and the BCS Critical Temperature Shift in General External Fields – Andreas Deuchert, Christian Hainzl, Marcel Maier – 2023 – 10.1007/s00526-023-02539-x
  • The Gell-Mann–Brueckner Formula for the Correlation Energy of the Electron Gas: A Rigorous Upper Bound in the Mean-Field Regime – Martin R. Christiansen, Christian Hainzl, Phan Thành Nam – 2023 – 10.1007/s00220-023-04672-2
  • Obstructions to odd-frequency superconductivity in Eliashberg theory – Edwin Langmann, Christian Hainzl, Robert Seiringer, Alexander V. Balatsky – 2023 – arXiv:2207.01825
  • On the Effective Quasi-Bosonic Hamiltonian of the Electron Gas: Collective Excitations and Plasmon Modes – Martin R. Christiansen, Christian Hainzl, Phan Thành Nam – 2022 – 10.1007/s11005-022-01607-1
  • Bogoliubov Theory in the Gross–Pitaevskii Limit: a Simplified Approach – Christian Hainzl, Benjamin Schlein, Arnaud Triay – 2022 – 10.1017/fms.2022.78
  • Enhanced pairing mechanism in cuprate-type crystals – Maximilian Duell, Christian Hainzl, Eman Hamza – 2022 – 10.1103/PhysRevB.106.054509
  • Microscopic Derivation of Ginzburg–Landau Theory and the BCS Critical Temperature Shift in a Weak Homogeneous Magnetic Field – Andreas Deuchert, Christian Hainzl, Marcel Maier – 2023 – 10.1063/5.0039123
  • Another proof of BEC in the GP-limit – Christian Hainzl – 2021 – 10.1063/5.0039123
  • The dilute Fermi gas via Bogoliubov theory – Marco Falconi, Emanuela L. Giacomelli, Christian Hainzl, Marcello Porta – 2021 – 10.1007/s00023-021-01031-6
  • Lower Bound on the Hartree–Fock Energy of the Electron Gas – David Gontier, Christian Hainzl, Mathieu Lewin – 2019 – 10.1103/PhysRevA.99.052501
  • The BCS critical temperature in a weak external electric field via a linear two-body operator – Rupert L. Frank, Christian Hainzl – 2018 – arXiv:1809.08667
  • On the correlation energy of interacting fermionic systems in the mean-field regime – Christian Hainzl, Marcello Porta, Felix Rexze – 2018 – arXiv:1806.11411
  • The Random Phase Approximation for Interacting Fermi Gases in the Mean-Field Regime – Martin R. Christiansen, Christian Hainzl, Phan Thành Nam – 2022 – Quelle
  • The BCS critical temperature in a weak homogeneous magnetic field – Rupert L. Frank, Christian Hainzl, Edwin Langmann – 2019 – 10.4171/JST/270
  • Persistence of translational symmetry in the BCS model with radial pair interaction – Andreas Deuchert, Alissa Geisinger, Christian Hainzl, Michael Loss – 2018 – 10.1007/s00023-018-0665-7
  • General pairing mechanisms in the BCS-theory of superconductivity – Christian Hainzl, Michael Loss – 2017 – 10.1140/epjb/e2017-70318-3
  • Mixed parity pairing in a dipolar gas – G. M. Bruun, C. Hainzl, M. Laux – 2016 – 10.1080/09500340.2016.1194492
  • Bogoliubov–Hartree–Fock theory for strongly interacting fermions in the low density limit – Gerhard Bräunlich, Christian Hainzl, Robert Seiringer – 2016 – 10.1007/s11040-016-9209-x
  • The BCS functional of superconductivity and its mathematical properties – Christian Hainzl, Robert Seiringer – 2016 – 10.1063/1.4941723
  • Incompatibility of time-dependent Bogoliubov–de Gennes and Ginzburg–Landau equations – Rupert L. Frank, Christian Hainzl, Benjamin Schlein, Robert Seiringer – 2016 – 10.1007/s11005-016-0847-5
  • Comparing the full time-dependent Bogoliubov–de Gennes equations to their linear approximation: A numerical investigation – Christian Hainzl, Jonathan Seyrich – 2016 – 10.1140/epjb/e2016-60975-y
  • Note on a Family of Monotone Quantum Relative Entropies – Andreas Deuchert, Christian Hainzl, Robert Seiringer – 2015 – 10.1007/s11005-015-0787-5
  • The external field dependence of the BCS critical temperature – Rupert L. Frank, Christian Hainzl, Robert Seiringer, Jan P. Solovej – 2016 – 10.1007/s00220-015-2526-2
  • On the BCS gap equation for superfluid fermionic gases – Gerhard Bräunlich, Christian Hainzl, Robert Seiringer – 2014 – Proceedings of QMath12 (Acta Mathematica 222, 2019), 219–335
  • On the well-posedness and scattering for the Gross–Pitaevskii hierarchy via quantum de Finetti – Thomas Chen, Christian Hainzl, Nataša Pavlović, Robert Seiringer – 2014 – 10.1007/s11005-014-0693-2
  • Unconditional uniqueness for the cubic Gross–Pitaevskii hierarchy via quantum de Finetti – Thomas Chen, Christian Hainzl, Nataša Pavlović, Robert Seiringer – 2015 – 10.1002/cpa.21552
  • Translation-invariant quasi-free states for fermionic systems and the BCS approximation – Gerhard Bräunlich, Christian Hainzl, Robert Seiringer – 2014 – 10.1142/S0129055X14500123
  • On contact interactions as limits of short-range potentials – Gerhard Bräunlich, Christian Hainzl, Robert Seiringer – 2013 – 10.1007/s00023-004-0194-4
  • Two Hartree–Fock models for the vacuum polarization – Philippe Gravejat, Christian Hainzl, Mathieu Lewin, Éric Séré – 2013 – Conference contribution (Days on PDEs 2012)
  • Microscopic Derivation of the Ginzburg–Landau Model – Rupert L. Frank, Christian Hainzl, Robert Seiringer, Jan P. Solovej – 2013 – 10.1142/9789814449243_0060
  • Construction of the Pauli–Villars–regulated Dirac vacuum in electromagnetic fields – Philippe Gravejat, Christian Hainzl, Mathieu Lewin, Éric Séré – 2012 – 10.1007/s00205-012-0609-1
  • Ground state properties of graphene in Hartree–Fock theory – Christian Hainzl, Mathieu Lewin, Christof Sparber – 2012 – 10.1063/1.4750049
  • Dynamics of Bose–Einstein condensates of fermion pairs in the low density limit of BCS theory – Christian Hainzl, Benjamin Schlein – 2012 – arXiv:1203.2811
  • The BCS gap equation for spin-polarized fermions – Abraham Freiji, Christian Hainzl, Robert Seiringer – 2012 – 10.1063/1.3670747
  • Low Density Limit of BCS Theory and Bose–Einstein Condensation of Fermion Pairs – Christian Hainzl, Robert Seiringer – 2012 – 10.1007/s11005-011-0535-4
  • Derivation of Ginzburg–Landau theory for a one-dimensional system with contact interaction – Rupert L. Frank, Christian Hainzl, Robert Seiringer, Jan P. Solovej – 2011 – arXiv:1103.1866
  • Microscopic Derivation of Ginzburg–Landau Theory – Rupert L. Frank, Christian Hainzl, Robert Seiringer, Jan P. Solovej – 2012 – 10.1090/S0894-0347-2012-00737-9
  • A Spatially Homogeneous and Isotropic Einstein–Dirac Cosmology – Felix Finster, Christian Hainzl – 2011 – 10.1063/1.3567157
  • On Blowup for time-dependent generalized Hartree–Fock equations – Christian Hainzl, Enno Lenzmann, Mathieu Lewin, Benjamin Schlein – 2010 – 10.1007/s00023-010-0054-3
  • Quantum Oscillations Can Prevent the Big Bang Singularity in an Einstein–Dirac Cosmology – Felix Finster, Christian Hainzl – 2010 – 10.1007/s10701-009-9380-z
  • Asymptotic behavior of eigenvalues of Schrödinger-type operators with degenerate kinetic energy – Christian Hainzl, Robert Seiringer – 2010 – Mathematische Nachrichten 283, 489–499
  • The Thermodynamic Limit of Quantum Coulomb Systems: A New Approach – Christian Hainzl, Mathieu Lewin, Jan P. Solovej – 2008 – 10.1142/9789812832382_0008
  • The Thermodynamic Limit of Quantum Coulomb Systems. Part II. Applications – Christian Hainzl, Mathieu Lewin, Jan P. Solovej – 2009 – 10.1016/j.aim.2008.12.003
  • The Thermodynamic Limit of Quantum Coulomb Systems. Part I. General Theory – Christian Hainzl, Mathieu Lewin, Jan P. Solovej – 2009 – 10.1016/j.aim.2008.12.002
  • Stellar Collapse in the Time-Dependent Hartree–Fock Approximation – Christian Hainzl, Benjamin Schlein – 2009 – 10.1007/s00220-008-0668-1
  • The BCS Critical Temperature for Potentials with Negative Scattering Length – Christian Hainzl, Robert Seiringer – 2008 – Letters in Mathematical Physics 84, 99–107
  • A Nonlinear Model for Relativistic Electrons at Positive Temperature – Christian Hainzl, Mathieu Lewin, Robert Seiringer – 2008 – 10.1142/S0129055X08003547
  • Spectral properties of the BCS gap equation of superfluidity – Christian Hainzl, Robert Seiringer – 2010 – 10.1142/9789812832382_0009
  • Critical Temperature and Energy Gap for the BCS Equation – Christian Hainzl, Robert Seiringer – 2008 – 10.1103/PhysRevB.77.184517
  • A Minimization Method for Relativistic Electrons in a Mean-Field Approximation of Quantum Electrodynamics – Christian Hainzl, Mathieu Lewin, Éric Séré, Jan P. Solovej – 2007 – 10.1103/PhysRevA.76.052104
  • The critical temperature for the BCS equation at weak coupling – Rupert L. Frank, Christian Hainzl, Serguei Naboko, Robert Seiringer – 2007 – 10.1007/s11854-007-0036-5
  • The BCS Functional for General Pair Interactions – Christian Hainzl, Eman Hamza, Robert Seiringer, Jan P. Solovej – 2008 – 10.1007/s00220-008-0489-2
  • Existence of Atoms and Molecules in the Mean-Field Approximation of No-Photon Quantum Electrodynamics – Christian Hainzl, Mathieu Lewin, Éric Séré – 2009 – 10.1007/s00205-008-0144-2
  • The Mean-Field Approximation in Quantum Electrodynamics: The no-photon case – Christian Hainzl, Mathieu Lewin, Jan P. Solovej – 2007 – 10.1002/cpa.20153
  • Existence of global-in-time solutions to a generalized Dirac–Fock type evolution equation – Christian Hainzl, Mathieu Lewin, Christof Sparber – 2005 – 10.1007/s11005-005-4377-9
  • Self-consistent solution for the polarized vacuum in a no-photon QED model – Christian Hainzl, Mathieu Lewin, Éric Séré – 2005 – 10.1088/0305-4470/38/20/014
  • Enhanced binding revisited for a spinless particle in non-relativistic QED – Isabelle Catto, Pavel Exner, Christian Hainzl – 2004 – 10.1063/1.1793329
  • Existence of a stable polarized vacuum in the Bogoliubov–Dirac–Fock approximation – Christian Hainzl, Mathieu Lewin, Éric Séré – 2005 – 10.1007/s00220-005-1343-4
  • Binding energy for hydrogen-like atoms in the Nelson model without cutoffs – Christian Hainzl, Masao Hirokawa, Herbert Spohn – 2005 – Journal of Functional Analysis 220, 424–459
  • On the Vacuum Polarization Density Caused by an External Field – Christian Hainzl – 2004 – Annales Henri Poincaré 5, 1137–1157
  • Non-perturbative mass and charge renormalization in relativistic no-photon QED – Christian Hainzl, Heinz Siedentop – 2003 – Communications in Mathematical Physics 243, 241–260
  • Self-energy of one electron in non-relativistic QED – Isabelle Catto, Christian Hainzl – 2002 – arXiv:math-ph/0207036
  • Mass Renormalization and Energy Level Shift in Non-Relativistic QED – Christian Hainzl, Robert Seiringer – 2003 – Advances in Theoretical and Mathematical Physics 6, 847–861
  • Increase of the binding energy of an electron by coupling to a photon field – Christian Hainzl – 2003 – Annales Henri Poincaré 4, 217–237
  • Enhanced Binding in non-relativistic QED – Christian Hainzl, Vitali Vougalter, Semjon A. Vugalter – 2003 – Communications in Mathematical Physics 233, 13–26
  • General Decomposition of Radial Functions on ℝ^n and Applications to N-Body Quantum Systems – Christian Hainzl, Robert Seiringer – 2002 – Letters in Mathematical Physics 61, 75–84
  • Semiclassics in the lowest Landau band – Christian Hainzl – 2001 – arXiv:math-ph/0103009
  • Bounds on one-dimensional exchange energies with application to lowest Landau band quantum mechanics – Christian Hainzl, Robert Seiringer – 2001 – Letters in Mathematical Physics 55, 133–142
  • Gradient corrections for semiclassical theories of atoms in strong magnetic fields – Christian Hainzl – 2001 – 10.1063/1.1415744
  • A discrete density matrix theory for atoms in strong magnetic fields – Christian Hainzl, Robert Seiringer – 2001 – 10.1007/s002200100373