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 – Calculus of Variations and PDE, 62:203.doi: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 – Communications in Mathematical Physics 398, Nr. 3, S. 1345–1396doi:10.1007/s00220-023-04672-2
  • The Random Phase Approximation for Interacting Fermi Gases in the Mean-Field Regime – Martin R. Christiansen, Christian Hainzl, Phan Thành Nam – 2023 – Forum of Mathematics, Pi., 11, 32.doi:10.1017/fmp.2023.31
  • 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 – Letters in Mathematical Physics 112, 114 doi:10.1007/s11005-022-01607-1
  • Bogoliubov Theory in the Gross–Pitaevskii Limit: a Simplified Approach – Christian Hainzl, Benjamin Schlein, Arnaud Triay – 2022 – Forum of Mathematics, Sigma 10, e90doi:10.1017/fms.2022.78
  • Enhanced pairing mechanism in cuprate-type crystals – Maximilian Duell, Christian Hainzl, Eman Hamza – 2022 – Physical Review B 106, 054509doi: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 – Probability and Mathematical Physics 4, Nr. 1, S. 1–89 doi:10.1063/5.0039123
  • Another proof of BEC in the GP-limit – Christian Hainzl – 2021 – Journal of Mathematical Physics 62, Nr. 5, 051901doi:10.1063/5.0039123
  • The dilute Fermi gas via Bogoliubov theory – Marco Falconi, Emanuela L. Giacomelli, Christian Hainzl, Marcello Porta – 2021 – Annales Henri Poincaré 22, Nr. 5, 1507–1540 doi:10.1007/s00023-021-01031-6
  • Lower Bound on the Hartree–Fock Energy of the Electron Gas – David Gontier, Christian Hainzl, Mathieu Lewin – 2019 – Physical Review A 99, 052501 doi: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 BCS critical temperature in a weak homogeneous magnetic field – Rupert L. Frank, Christian Hainzl, Edwin Langmann – 2019 – Journal of Spectral Theory 9, 1005–1062 doi: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 – Annales Henri Poincaré 19, 1507–1563 doi:10.1007/s00023-018-0665-7
  • General pairing mechanisms in the BCS-theory of superconductivity – Christian Hainzl, Michael Loss – 2017 – European Physical Journal B 90, Nr. 5, 82 doi:10.1140/epjb/e2017-70318-3
  • Mixed parity pairing in a dipolar gas – G. M. Bruun, C. Hainzl, M. Laux – 2016 – Journal of Modern Optics 63, Nr. 17–18, 1693–1703 doi: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 – Mathematical Physics, Analysis and Geometry 19, Art. 13 doi:10.1007/s11040-016-9209-x
  • The BCS functional of superconductivity and its mathematical properties – Christian Hainzl, Robert Seiringer – 2016 – Journal of Mathematical Physics 57, 021101doi: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 – Letters in Mathematical Physics 106, 913–923 doi: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 – European Physical Journal B 89, 196 doi:10.1140/epjb/e2016-60975-y
  • Note on a Family of Monotone Quantum Relative Entropies – Andreas Deuchert, Christian Hainzl, Robert Seiringer – 2015 – Letters in Mathematical Physics 105, 1449–1465 doi: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 – Communications in Mathematical Physics 342, 189–216 doi: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, 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 – Letters in Mathematical Physics 104 (2014), 871–891 doi: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 – Communications on Pure and Applied Mathematics 68, 1845–1884doi:10.1002/cpa.21552
  • Translation-invariant quasi-free states for fermionic systems and the BCS approximation – Gerhard Bräunlich, Christian Hainzl, Robert Seiringer – 2014 – Reviews in Mathematical Physics 26, 1450012 doi:10.1142/S0129055X14500123
  • On contact interactions as limits of short-range potentials – Gerhard Bräunlich, Christian Hainzl, Robert Seiringer – 2013 – Methods of Functional Analysis and Topology 19, 364–375 doi: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 – XVIIth International Congress on Mathematical Physics (Aalborg 2012), World Scientific 2013, 575–583doi:10.1142/9789814449243_0060
  • Construction of the Pauli–Villars–regulated Dirac vacuum in electromagnetic fields – Philippe Gravejat, Christian Hainzl, Mathieu Lewin, Éric Séré – 2012 – Archive for Rational Mechanics and Analysis 208, 603–665
    doi:10.1007/s00205-012-0609-1
  • Ground state properties of graphene in Hartree–Fock theory – Christian Hainzl, Mathieu Lewin, Christof Sparber – 2012 – Journal of Mathematical Physics 53, 012101 doi: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 – Journal of Mathematical Physics 53, 012101 doi:10.1063/1.3670747
  • Low Density Limit of BCS Theory and Bose–Einstein Condensation of Fermion Pairs – Christian Hainzl, Robert Seiringer – 2012 – Letters in Mathematical Physics 100, 119–131doi: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 – Journal of the American Mathematical Society 25, 667–713doi:10.1090/S0894-0347-2012-00737-9
  • A Spatially Homogeneous and Isotropic Einstein–Dirac Cosmology – Felix Finster, Christian Hainzl – 2011 – Journal of Mathematical Physics 52, 042501 doi:10.1063/1.3567157
  • On Blowup for time-dependent generalized Hartree–Fock equations – Christian Hainzl, Enno Lenzmann, Mathieu Lewin, Benjamin Schlein – 2010 – Annales Henri Poincaré 11, Nr. 6, 1023–1052 doi:10.1007/s00023-010-0054-3
  • Quantum Oscillations Can Prevent the Big Bang Singularity in an Einstein–Dirac Cosmology – Felix Finster, Christian Hainzl – 2010 – Foundations of Physics 40, 116–124 doi: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 – in QMath10, Quantum Mathematics (Cambridge Univ. Press), S. 925–955 doi:10.1142/9789812832382_0008
  • The Thermodynamic Limit of Quantum Coulomb Systems. Part II. Applications – Christian Hainzl, Mathieu Lewin, Jan P. Solovej – 2009 – Advances in Mathematics 221, Nr. 2, 454–487 doi: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 – Advances in Mathematics 221, Nr. 2, 460–492doi:10.1016/j.aim.2008.12.002
  • Stellar Collapse in the Time-Dependent Hartree–Fock Approximation – Christian Hainzl, Benjamin Schlein – 2009 – Communications in Mathematical Physics 287, 705–717 doi: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 – Reviews in Mathematical Physics 20 (2008), 1283–1307 doi:10.1142/S0129055X08003547
  • Spectral properties of the BCS gap equation of superfluidity – Christian Hainzl, Robert Seiringer – 2010 – in Mathematical Results in Quantum Mechanics, World Scientific, S. 117–136doi:10.1142/9789812832382_0009
  • Critical Temperature and Energy Gap for the BCS Equation – Christian Hainzl, Robert Seiringer – 2008 – Physical Review B 77, 184517 doi: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 – Physical Review A 76, 052104doi: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 – Journal of Geometry and Analysis 17, 559–568 doi:10.1007/s11854-007-0036-5
  • The BCS Functional for General Pair Interactions – Christian Hainzl, Eman Hamza, Robert Seiringer, Jan P. Solovej – 2008 – Communications in Mathematical Physics 281, 349–367 doi: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 – Archive for Rational Mechanics and Analysis 192, Nr. 3, 453–499 doi: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 – Communications on Pure and Applied Mathematics 60, 1466–1482 doi: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 – Letters in Mathematical Physics 72, 99–113 doi: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 – Journal of Physics A: Mathematical and General 38, 4483–4494 doi: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 – Journal of Mathematical Physics 45, 4174–4185 doi:10.1063/1.1793329
  • Existence of a stable polarized vacuum in the Bogoliubov–Dirac–Fock approximation – Christian Hainzl, Mathieu Lewin, Éric Séré – 2005 – Communications in Mathematical Physics 257, 515–562 doi: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 – Journal of Mathematical Physics 42, 5596–5625 doi:10.1063/1.1415744
  • A discrete density matrix theory for atoms in strong magnetic fields – Christian Hainzl, Robert Seiringer – 2001 – Communications in Mathematical Physics 217, 229–244 doi:10.1007/s002200100373