Andreas Deuchert

I am an Assistant Professor of Mathematical Physics at Virginia Tech in Blacksburg, Virginia. Previously, I was an independent research fellow and lecturer at the Institute of Mathematics, University of Zurich, funded by an Ambizione Grant from the Swiss National Science Foundation.

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 focus on variational techniques, to study mathematical problems arising from solid-state physics. Currently, I am primarily interested in developing new mathematical tools to study bosonic many-particle systems at positive temperature. I have also been interested in mathematical aspects of the BCS theory of superconductivity (formulated as a non-commutative variational problem) and the physics of the angulon quasi-particle.

For more information, see my CV.

Upcoming events

• Together with Guher Camliyurt, I am organizing a session on nonlinear PDEs and their microscopic derivation at the Southeastern Sectional Meeting of the AMS at Clemson University on March 8–9, 2025.
• I will participate as a Senior Fellow in the Spring Program Non-commutative Optimal Transport, to be held at the Institute for Pure and Applied Mathematics (IPAM) from March 10 to June 13, 2025.

Master and PhD thesis

If you are interested in writing a Bachelor's, Master's, or PhD thesis in quantum statistical mechanics from a mathematical perspective, I would be happy to hear from you. I also supervise undergraduate research.

Published Research Articles and Preprints

1. A note on spontaneous symmetry breaking in the mean-field Bose gas
   Andreas Deuchert, Phan Thành Nam and Marcin Napiórkowski,
   arXiv:2501.19402 [math-ph] (2025)
2. The Gibbs state of the mean-field Bose gas
   Andreas Deuchert, Phan Thành Nam and Marcin Napiórkowski,
   arXiv:2501.19396 [math-ph] (2025)
3. 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,
   Annales Henri Poincaré (2024)
   arXiv:2310.12314 [math-ph], doi.org/10.1007/s00023-024-01505-3
4. Upper bound for the grand canonical free energy of the Bose gas in the Gross-Pitaevskii limit
   Chiara Boccato, Andreas Deuchert and David Stocker,
   SIAM Journal on Mathematical Analysis 56, No. 2, 2611-2660 (2024)
   arXiv:2305.19173 [math-ph], doi.org/10.1137/23M1580930.
5. 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,
6. Dynamics of mean-field bosons at positive temperature
   Marco Caporaletti, Andreas Deuchert and Benjamin Schlein,
   Annales de l'Institut Henry Poincaré, Analyse Non Linéaire 41, no. 4, pp. 995 (2024)
   arXiv:2203.17204 [math-ph], doi.org/10.4171/AIHPC/93.
7. 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.
8. 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.
   
9. 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.
10. 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.
11. 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.
    
12. 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.
13. 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.
14. 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,
    
15. 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.
16. 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.
17. 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.
18. 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. 4.
Three page summary of publication no. 11.

Coverage in public media

Publication no. 14 has been covered e.g. in (english) Gizmodo, Phys.org, (german) Der Standard.

Slides

• The Gibbs state of the mean-field Bose gas 50 min
• Upper bound for the grand canonical free energy of the Bose gas in the Gross–Pitaevskii limit for general interaction potentials 50 min
• Upper bound for the grand canonical free energy of the Bose gas in the Gross–Pitaevskii limit 60 min
• Dynamics of mean-field bosons at positive temperature 45 min
• Microscopic derivation of Ginzburg–Landau theory and the BCS critical temperature shift in a weak homogeneous magnetic field 25 min
• Microscopic derivation of Ginzburg–Landau theory and the BCS critical temperature shift in a weak homogeneous magnetic field 50 min
• Semiclassical approximation and critical temperature shift for weakly interacting trapped bosons 50 min
• The free energy of the two-dimensional dilute Bose gas 30 min
• Gross-Pitaevskii limit of a homogeneous Bose gas at positive temperature 20 min
• Gross-Pitaevskii limit of a homogeneous Bose gas at positive temperature 50 min
• Bose-Einstein condensation for a dilute trapped gas at positive temperature 20 min
• Bose-Einstein condensation for a dilute trapped gas at positive temperature 50 min
• Note on a family of monotone quantum relative entropies 20 min

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 for lectures held at Virginia Tech

• Fourier Series and PDE (Math 4425, Fall term 2024): (1) Introduction, (2) Four important PDEs, (3) Fourier Series, (4) Separation of variables

Links to webpages of lectures held at the University of Zurich

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

• Introduction to the statistical mechanics of lattice systems (Summer term 2023)
• Variational methods in analysis (Summer term 2022, joint with Dr. Alessandro Olgiati)
• Advanced topics in analysis (Summer term 2022, joint with Dr. Alessandro Olgiati) (first half of Variational methods in analysis that could be booked independently by Bachelor students)
• Mathematical statistical mechanics (Summer term 2021)
• The mathematics of dilute quantum gases (Summer term 2020)

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

• Email: <andreas.deuchert@vt.edu>
• Office: McBryde 448
• Postal Address: Department of Mathematics, 225 Stanger Street, Blacksburg, VA 24060-1026