Andreas Deuchert

I am 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 and a Marie Skłodowska-Curie individual fellowship of the European Union. From October 2016 to September 2019, I was a postdoctoral researcher in the group of Prof. Dr. Robert Seiringer at the Institute of Science and Technology Austria (ISTA). I obtained my doctoral degree in mathematics in 2016 from the University of Tübingen, with a thesis in analysis and mathematical physics under the supervision of Prof. Dr. Christian Hainzl.

My main research interests are mathematical quantum mechanics and quantum statistical mechanics. In my work, I develop analytic, functional-analytic, and probabilistic methods 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. 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

I will give an invited talk at the conference Operator Theory in Quantum Physics – OTQP 2026 that will be held at the Institute of Matematics of the Polish Academy of Sciences in Będlewo, Poland, June 14-19, 2026.

Research Team

My research group currently includes Drake Woosley (PhD student), Amitabha Roy (PhD student), Xuanyu Li (Master’s student), and Benjamin Denson (undergraduate researcher).

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.

Teaching

I am currently teaching Matrix Theory (Math 5524). If you have questions regarding the class please send me an email. Here is a brief description: Topics to be covered in the course include spectral theory for Hermitian matrices, the Jordan normal form, singular value decomposition, variational characterizations of eigenvalues, eigenvalue perturbation theory, nonnegative matrices and Perron–Frobenius theory, functions of matrices, traces of functions of matrices (von Neumann entropy, relative entropy), and trace inequalities. We will also provide a brief introduction to quantum mechanics and illustrate the material with applications to quantum mechanics and quantum information theory. The topics covered in this class are fundamental and therefore relevant for students interested in a variety of areas, such as matrix analysis, numerical analysis, quantum information theory, dynamical systems, and probability theory.

Participants are expected to have an undergraduate-level background in linear algebra and some familiarity with complex numbers.

Published Research Articles and Preprints

1. A new upper bound on the specific free energy of dilute Bose gases
   Giulia Basti, Chiara Boccato, Serena Cenatiempo and Andreas Deuchert,
   arXiv:2507.20877 [math-ph] (2025), 83 pages
2. Dynamics and equilibrium states of infinite systems of lattice bosons
   Andreas Deuchert, Jonas Lampart and Marius Lemm,
   arXiv:2505.13170 [math-ph] (2025), 27 pages
3. A note on spontaneous symmetry breaking in the mean-field Bose gas
   Andreas Deuchert, Phan Thành Nam and Marcin Napiórkowski,
   Letters in Mathematical Physics 115, 111, (2025), 33 pages
   arXiv:2501.19402 [math-ph], doi.org/10.1007/s11005-025-01996-z.
4. The Gibbs state of the mean-field Bose gas
   Andreas Deuchert, Phan Thành Nam and Marcin Napiórkowski,
   arXiv:2501.19396 [math-ph] (2025), 102 pages
5. 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), 61 pages
   arXiv:2310.12314 [math-ph], doi.org/10.1007/s00023-024-01505-3.
6. 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), 50 pages
   arXiv:2305.19173 [math-ph], doi.org/10.1137/23M1580930.
7. 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), 81 pages
   arXiv:2210.09356 [math-ph], doi.org/10.1007/s00526-023-02539-x.
8. 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), 60 pages
   arXiv:2203.17204 [math-ph], doi.org/10.4171/AIHPC/93.
9. 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), 91 pages
   arXiv:2105.05623 [math-ph], doi.org/10.2140/pmp.2023.4.1.
10. 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), 74 pages
    arXiv:2009.00992 [math-ph], doi.org/10.1016/j.jfa.2021.109096.
    
11. 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), 13 pages
    arXiv:1912.02658 [cond-mat.mes-hall], doi.org/10.1063/1.5144759.
12. 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), 74 pages
    arXiv:1910.03372 [math-ph], doi.org/10.1017/fms.2020.17.
13. 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), 55 pages
    arXiv:1901.11363 [math-ph], doi.org/10.1007/s00205-020-01489-4.
    
14. 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), 11 pages
    arXiv:1809.01204 [cond-mat.quant-gas], doi.org/10.1103/PhysRevB.98.224506.
15. 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), 54 pages
    arXiv:1803.05180 [math-ph], doi.org/10.1007/s00220-018-3239-0.
16. Emergence of non-abelian magnetic monopoles in a quantum impurity problem
    Enderalp Yakaboylu, Andreas Deuchert and Mikhail Lemeshko,
    Physical Review Letters 119, 235301 (2017), 6 pages
    arXiv:1705.05162 [cond-mat.quant-gas], doi.org/10.1103,
    
17. A lower bound for the BCS functional with boundary conditions at infinity
    Andreas Deuchert,
    Journal of Mathematical Physics 58, 081901 (2017), 21 pages
    arXiv:1703.04616 [math-ph], doi:10.1063/1.4996580.
18. 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), 21 pages
    arXiv:1612.03303 [math-ph], doi.org/10.1007.
19. Note on a Family of Monotone Quantum Relative Entropies
    Andreas Deuchert, Christian Hainzl and Robert Seiringer,
    Letters in Mathematical Physics 105, 1449 (2015), 18 pages
    arXiv:1502.07205 [math-ph], doi:10.1007/s11005-015-0787-5.
20. 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), 11 pages
    arXiv:1202.4111 [cond-mat.quant-gas], doi:10.1103/PhysRevA.86.013618.

Oberwolfach Reports

Three page summary of publication no. 6.
Three page summary of publication no. 13.

Coverage in public media

Publication no. 16 has been covered e.g. in (english) Gizmodo, Phys.org, (german) Der Standard.

Videos

• Dynamics and equilibrium states of infinite systems of lattics bosons at the Centre International de Rencontre Mathématiques (CIRM) in Luminy (Dec. 2025). Carmin.tv.
  
• Recent developments in the analysis of Bose gases at positive temperature at the Erwin Schrödinger Institute (ESI) in Vienna (Nov. 2025). Youtube.
  
• The Gibbs state of the mean-field Bose gas in the One World Mathematical Physics Seminar of the International Association of Mathematical Physics (IAMP)(April 2025). YouTube.
  
• The Gibbs state of the mean-field Bose gas at the Institute of Pure and Applied Mathematics (IPAM) in Los Angeles (April 2025). Youtube.

Slides

• Dynamics and equilibrium states of infinite systems of lattics bosons 25 min
• Recent developments in the analysis of Bose gases at positive temperature 40 min
• 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 from classes taught at Virginia Tech

• Functional Analysis (Math 6625, Fall term 2025)
• Fourier Series and PDE (Math 4425, Fall term 2024): (1) Introduction, (2) Four important PDEs, (3) Fourier Series, (4) Separation of variables

Lecture notes from classes taught at the University of Zurich

(The lecture notes can be found on the course webpages. Just follow the links.)

• 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)

Organized events

• Together with Guher Camliyurt I organized 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 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).

Contact Information

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