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`

.

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.

**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)**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).**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`

,**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`

.**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`

.**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`

.**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`

.**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`

.**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`

.**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`

.**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`

.**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`

,**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`

.**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`

.**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`

.**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`

.

`Three page summary of publication no. 2`

.

`Three page summary of publication no. 9`

.

Publication no. 12 has been covered e.g. in (english) `Gizmodo`

, `Phys.org`

, (german) `Der Standard`

.

**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`

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.)

`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)

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`

.

**Email:**<`andreas.deuchert@math.uzh.ch`

>**Office:**Y27K44**Postal Address:**Institut für Mathematik, Universität Zürich, Winterthurerstrasse 190, CH-8057 Zürich