Andreas Deuchert

I am an Assistant Professor of Mathematical Physics at Virginia Tech, Blacksburg, Virginia. Previously I was 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. 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.

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 8th--9th in 2025.
• I will participate as a Senior Fellow in the Spring Program Non-commutaive Optimal Transport to be held at the Institute for Pure and Applied Mathematics (IPAM) for the period March 10th -- June 13 in 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 point of view), I would be happy to hear from you. I also supervise undergraduate research.

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,
   Annales Henri Pincaré (Online first, 2024)
   arXiv:2310.12314 [math-ph], doi.org/10.1007/s00023-024-01505-3
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,
   SIAM Journal on Mathematical Analysis 56, No. 2, 2611 (2024)
   arXiv:2305.19173 [math-ph], doi.org/10.1137/23M1580930.
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, Vol. 41, no. 4, 995 (2024)
   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

• 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.

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