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Analysis of quantum many-body systems

Total Cost €


EC-Contrib. €






Project "AQUAMS" data sheet

The following table provides information about the project.


Organization address
address: Am Campus 1
postcode: 3400

contact info
title: n.a.
name: n.a.
surname: n.a.
function: n.a.
email: n.a.
telephone: n.a.
fax: n.a.

 Coordinator Country Austria [AT]
 Project website
 Total cost 1˙497˙755 €
 EC max contribution 1˙497˙755 € (100%)
 Programme 1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
 Code Call ERC-2015-AdG
 Funding Scheme ERC-ADG
 Starting year 2016
 Duration (year-month-day) from 2016-10-01   to  2021-09-30


Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 


 Project objective

The main focus of this project is the mathematical analysis of many-body quantum systems, in particular, interacting quantum gases at low temperature. The recent experimental advances in studying ultra-cold atomic gases have led to renewed interest in these systems. They display a rich variety of quantum phenomena, including, e.g., Bose–Einstein condensation and superfluidity, which makes them interesting both from a physical and a mathematical point of view. The goal of this project is the development of new mathematical tools for dealing with complex problems in many-body quantum systems. New mathematical methods lead to different points of view and thus increase our understanding of physical systems. From the point of view of mathematical physics, there has been significant progress in the last few years in understanding the interesting phenomena occurring in quantum gases, and the goal of this project is to investigate some of the key issues that remain unsolved. Due to the complex nature of the problems, new mathematical ideas and methods will have to be developed for this purpose. One of the main question addressed in this proposal is the validity of the Bogoliubov approximation for the excitation spectrum of many-body quantum systems. While its accuracy has been successfully shown for the ground state energy of various models, its predictions concerning the excitation spectrum have so far only been verified in the Hartree limit, an extreme form of a mean-field limit where the interaction among the particles is very weak and ranges over the whole system. The central part of this project is concerned with the extension of these results to the case of short-range interactions. Apart from being mathematically much more challenging, the short-range case is the one most relevant for the description of actual physical systems. Hence progress along these lines can be expected to yield valuable insight into the complex behavior of these many-body quantum systems.


year authors and title journal last update
List of publications.
2019 Mathieu Lewin, Elliott H. Lieb, Robert Seiringer
Floating Wigner crystal with no boundary charge fluctuations
published pages: , ISSN: 2469-9950, DOI: 10.1103/physrevb.100.035127
Physical Review B 100/3 2020-03-20
2018 Mathieu Lewin, Elliott H. Lieb, Robert Seiringer
Statistical mechanics of the uniform electron gas
published pages: 79-116, ISSN: 2270-518X, DOI: 10.5802/jep.64
Journal de l’École polytechnique — Mathématiques 5 2020-03-20
2017 Thomas Moser, Robert Seiringer
Stability of a Fermionic N + 1 Particle System with Point Interactions
published pages: 329-355, ISSN: 0010-3616, DOI: 10.1007/s00220-017-2980-0
Communications in Mathematical Physics 356/1 2020-03-20
2018 Douglas Lundholm, Robert Seiringer
Fermionic behavior of ideal anyons
published pages: 2523-2541, ISSN: 0377-9017, DOI: 10.1007/s11005-018-1091-y
Letters in Mathematical Physics 108/11 2020-03-20
2019 Andreas Deuchert, Robert Seiringer, Jakob Yngvason
Bose–Einstein Condensation in a Dilute, Trapped Gas at Positive Temperature
published pages: 723-776, ISSN: 0010-3616, DOI: 10.1007/s00220-018-3239-0
Communications in Mathematical Physics 368/2 2020-03-20
2017 Andreas Deuchert
A lower bound for the BCS functional with boundary conditions at infinity
published pages: 81901, ISSN: 0022-2488, DOI: 10.1063/1.4996580
Journal of Mathematical Physics 58/8 2020-03-20
2018 Andreas Deuchert, Alissa Geisinger, Christian Hainzl, Michael Loss
Persistence of Translational Symmetry in the BCS Model with Radial Pair Interaction
published pages: 1507-1527, ISSN: 1424-0637, DOI: 10.1007/s00023-018-0665-7
Annales Henri Poincaré 19/5 2020-03-20
2019 Thomas Moser, Robert Seiringer
Energy Contribution of a Point-Interacting Impurity in a Fermi Gas
published pages: 1325-1365, ISSN: 1424-0637, DOI: 10.1007/s00023-018-00757-0
Annales Henri Poincaré 20/4 2020-03-20
2017 Xiang Li, Robert Seiringer, Mikhail Lemeshko
Angular self-localization of impurities rotating in a bosonic bath
published pages: , ISSN: 2469-9926, DOI: 10.1103/physreva.95.033608
Physical Review A 95/3 2020-03-20
2017 E. Yakaboylu, A. Deuchert, M. Lemeshko
Emergence of Non-Abelian Magnetic Monopoles in a Quantum Impurity Problem
published pages: , ISSN: 0031-9007, DOI: 10.1103/physrevlett.119.235301
Physical Review Letters 119/23 2020-03-20
2018 Thomas Moser, Robert Seiringer
Stability of the 2 + 2 Fermionic System with Point Interactions
published pages: , ISSN: 1385-0172, DOI: 10.1007/s11040-018-9275-3
Mathematical Physics, Analysis and Geometry 21/3 2020-03-20
2018 Enderalp Yakaboylu, Bikashkali Midya, Andreas Deuchert, Nikolai Leopold, Mikhail Lemeshko
Theory of the rotating polaron: Spectrum and self-localization
published pages: , ISSN: 2469-9950, DOI: 10.1103/physrevb.98.224506
Physical Review B 98/22 2020-03-20

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