Andreas Deuchert


Andreas Deuchert portrait

I am an independent research fellow and lecturer at the Institute of Mathematics of the University of Zurich financed by an Ambizione Grant of the Swiss National Science Foundation. In August 2024 I will start as Assistant Professor in Mathematical Physics at Virginia Tech, Blacksburg, USA. My main research interests are mathematical quantum mechanics and quantum statistical mechanics. In my work I develop analytic, functional analytic and probabilistic methods with a strong focus on variational techniques to study mathematical problems originating from solid state physics. Currently, I am mostly interested in developing new mathematical tools to study Bose gases at positive temperature. Another important theme of my work are mathematical aspects of the BCS theory of superconductivity (formulated as a non-commutative variational problem). I have also been interested in the physics of the angulon quasi-particle. For more information see my CV.


Master thesis

If you are interested in writing a Master thesis in quantum statistical mechanics (from a mathematical point of view) I would be happy if you contact me. As prerequiste you need at least one lecture in one of the following topics: Functional Analysis, PDE, Advanced topics in analysis, Mathematical quantum mechanics, Stability of matter in quantum mechanics or something comparable. A certain background in physics or an interest in physics is helpful.


Published Research Articles and Preprints

  1. Upper bound for the grand canonical free energy of the Bose gas in the Gross-Pitaevskii limit for general interaction potentials
    Marco Caporaletti and Andreas Deuchert,
    arXiv:2310.12314 [math-ph] (2023)
  2. Upper bound for the grand canonical free energy of the Bose gas in the Gross-Pitaevskii limit
    Chiara Boccato, Andreas Deuchert and David Stocker,
    Accepted for publication in the SIAM Journal on Mathematical Analysis
    arXiv:2305.19173 [math-ph] (2023).
  3. Microscopic derivation of Ginzburg–Landau theory and the BCS critical temperature shift for general external fields
    Andreas Deuchert, Christian Hainzl and Marcel Oliver Maier,
    Calculus of Variations and PDE 62, 203 (2023)
    arXiv:2210.09356 [math-ph], doi.org/10.1007/s00526-023-02539-x,
  4. Dynamics of mean-field bosons at positive temperature
    Marco Caporaletti, Andreas Deuchert and Benjamin Schlein,
    Annales de l'Institut Henry Poincaré, Analyse Non Linéaire (online first, 2023)
    arXiv:2203.17204 [math-ph], doi.org/10.4171/AIHPC/93.
  5. Microscopic derivation of Ginzburg–Landau theory and the BCS critical temperature shift in a weak homogeneous magnetic field
    Andreas Deuchert, Christian Hainzl and Marcel Oliver Maier,
    Probability and Mathematical Physics 4 (1), 1-89, (2023)
    arXiv:2105.05623 [math-ph], doi.org/10.2140/pmp.2023.4.1.
  6. Semiclassical approximation and critical temperature shift for weakly interacting trapped bosons
    Andreas Deuchert and Robert Seiringer,
    Journal of Functional Analysis 281, Issue 6, 109096 (2021)
    arXiv:2009.00992 [math-ph], doi.org/10.1016/j.jfa.2021.109096.
  7. Intermolecular forces and correlations mediated by a phonon bath
    Xiang Li, Enderalp Yakaboylu, Giacomo Bighin, Richard Schmidt, Mikhail Lemeshko and Andreas Deuchert,
    Journal of Chemical Physics 152, 164302 (2020)
    arXiv:1912.02658 [cond-mat.mes-hall], doi.org/10.1063/1.5144759.
  8. The free energy of the two-dimensional dilute Bose gas. I. Lower bound
    Andreas Deuchert, Simon Mayer and Robert Seiringer,
    Forum of Mathematics, Sigma, Volume 8 (2020)
    arXiv:1910.03372 [math-ph], doi.org/10.1017/fms.2020.17.
  9. Gross-Pitaevskii Limit of a Homogeneous Bose Gas at Positive Temperature
    Andreas Deuchert and Robert Seiringer,
    Archive for Rational Mechanics and Analysis, 236(3), 1217 (2020)
    arXiv:1901.11363 [math-ph], doi.org/10.1007/s00205-020-01489-4.
  10. Theory of the rotating polaron: Spectrum and self-localization
    Enderalp Yakaboylu, Bikashkali Midya, Andreas Deuchert, Nikolai Leopold and Mikhail Lemeshko,
    Physical Review B 98, 224506 (2018)
    arXiv:1809.01204 [cond-mat.quant-gas], doi.org/10.1103/PhysRevB.98.224506.
  11. Bose-Einstein Condensation in a Dilute, Trapped Gas at Positive Temperature
    Andreas Deuchert, Robert Seiringer and Jakob Yngvason,
    Communications in Mathematical Physics 368, 723 (2019)
    arXiv:1803.05180 [math-ph], doi.org/10.1007/s00220-018-3239-0.
  12. Emergence of non-abelian magnetic monopoles in a quantum impurity problem
    Enderalp Yakaboylu, Andreas Deuchert and Mikhail Lemeshko,
    Physical Review Letters 119, 235301 (2017)
    arXiv:1705.05162 [cond-mat.quant-gas], doi.org/10.1103,
  13. A lower bound for the BCS functional with boundary conditions at infinity
    Andreas Deuchert,
    Journal of Mathematical Physics 58, 081901 (2017)
    arXiv:1703.04616 [math-ph], doi:10.1063/1.4996580.
  14. Persistence of translational symmetry in the BCS model with radial pair interaction
    Andreas Deuchert, Alissa Geisinger, Christian Hainzl and Michael Loss,
    Annales Henri Poincaré 19: 1507 (2018)
    arXiv:1612.03303 [math-ph], doi.org/10.1007.
  15. Note on a Family of Monotone Quantum Relative Entropies
    Andreas Deuchert, Christian Hainzl and Robert Seiringer,
    Letters in Mathematical Physics 105, 1449 (2015)
    arXiv:1502.07205 [math-ph], doi:10.1007/s11005-015-0787-5.
  16. Dynamics and symmetries of a repulsively bound atom pair in an infinite optical lattice
    Andreas Deuchert, Kaspar Sakmann, Alexej I. Streltsov, Ofir E. Alon and Lorenz S. Cederbaum,
    Physical Review A 86, 013618 (2012)
    arXiv:1202.4111 [cond-mat.quant-gas], doi:10.1103/PhysRevA.86.013618.

Oberwolfach Reports

Three page summary of publication no. 2.
Three page summary of publication no. 9.


Coverage in public media

Publication no. 12 has been covered e.g. in (english) Gizmodo, Phys.org, (german) Der Standard.


Slides


Lecture notes on mathematical aspects of the BCS theory of superconductivity

In March 2024 I gave a lecture series (4 ×\times 75 min) on mathematical aspects of the BCS theory of superconductivity at the Winter School of the SFB TRR 352 Mathematics of Many-Body Quantum Systems and Their Collective Phenomena that took place in Kochl am See. The lecture notes can be found here: part1, part2.


(Lecture notes can be found on the course webpages.)


Events organised at the University of Zurich

I co-organized the summer school “Current Topics in Mathematical Physics” that took place in Zurich from July 19 to July 23 in 2021 (prior to the International Congress on Mathematical Physics in Geneva). More information can be found here.


Contact Information