Andreas Deuchert

Andreas Deuchert portrait

I am currently an independent research fellow and lecturer at the Institute of Mathematics of the University of Zurich financed by an Ambizione Fellowship of the Swiss National Science Foundation. My main research interests are mathematical quantum mechanics and quantum statistical mechanics. More specifically I am applying techniques from Analysis, Functional Analysis and Probability to problems coming from condensed matter and cold atom physics. Currently I am mostly interested in the mathematics of Bose gases at positive temperature. Two other important themes of my work are mathematical aspects of the BCS theory of superconductivity and the physics of the angulon quasi-particle. For more information see my CV.

Introduction to the statistical mechanics of lattice systems

In the spring term 2023 I give a lecture with the title "Introduction to the statistical mechanics of lattice systems" (2 hrs lecture + 2 hrs exercise group, 6 ECTS) at the Institute of Mathematics of the University of Zurich (UZH). The lecture is indended for Bachelor and Master students in mathematics and physics at UZH and ETH Zurich. As prerequisite you need the basic courses in analysis and linear algebra. An introduction to probability theory is helpful but not required. For more information, please see the course website.

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.

Publications and Preprints

  1. Microscopic derivation of Ginzburg–Landau theory and the BCS critical temperature shift for general external fields
    Andreas Deuchert, Christian Hainzl and Marcel Schaub,
    arXiv:2210.09356 [math-ph] (2022)
  2. Dynamics of mean-field bosons at positive temperature
    Marco Caporaletti, Andreas Deuchert and Benjamin Schlein,
    arXiv:2203.17204 [math-ph]
  3. Microscopic derivation of Ginzburg–Landau theory and the BCS critical temperature shift in a weak homogeneous magnetic field
    Andreas Deuchert, Christian Hainzl and Marcel Schaub,
    arXiv:2105.05623 [math-ph] (2021), (Accepted for publication in Probability and Mathematical Physics)
  4. 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.
  5. 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.
  6. 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.
  7. 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.
    Oberwolfach Report (three page summary).
  8. Theory of the rotating polaron: Spectrum and self-localization
    Enderalp Yakaboylu, Bikashkali Midya, Andreas Deuchert, Nikolai Leopold and Mikhail Lemeshko,
    Phys. Rev. B 98, 224506 (2018)
    arXiv:1809.01204 [cond-mat.quant-gas], doi.org/10.1103/PhysRevB.98.224506.
  9. Bose-Einstein Condensation in a Dilute, Trapped Gas at Positive Temperature
    Andreas Deuchert, Robert Seiringer and Jakob Yngvason,
    Commun. Math. Phys. 368, 723 (2019)
    arXiv:1803.05180 [math-ph], doi.org/10.1007/s00220-018-3239-0.
  10. Emergence of non-abelian magnetic monopoles in a quantum impurity problem
    Enderalp Yakaboylu, Andreas Deuchert and Mikhail Lemeshko,
    Phys. Rev. Lett. 119, 235301 (2017)
    arXiv:1705.05162 [cond-mat.quant-gas], doi.org/10.1103,
    Coverage in public media (english) Gizmodo, Phys.org, (german) Der Standard, ProPhysik.
  11. 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.
  12. Persistence of translational symmetry in the BCS model with radial pair interaction
    Andreas Deuchert, Alissa Geisinger, Christian Hainzl and Michael Loss,
    Ann. Henri Poincaré 19: 1507 (2018)
    arXiv:1612.03303 [math-ph], doi.org/10.1007.
  13. Note on a Family of Monotone Quantum Relative Entropies
    Andreas Deuchert, Christian Hainzl and Robert Seiringer,
    Lett. Math. Phys. 105, 1449 (2015)
    arXiv:1502.07205 [math-ph], doi:10.1007/s11005-015-0787-5.
  14. 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,
    Phys. Rev. A 86, 013618 (2012)
    arXiv:1202.4111 [cond-mat.quant-gas], doi:10.1103/PhysRevA.86.013618.

Slides

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