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CORFRONMAT SIGNED

Correlated frontiers of many-body quantum mathematics and condensed matter physics

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EC-Contrib. €

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Partnership

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Project "CORFRONMAT" data sheet

The following table provides information about the project.

Coordinator
CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS 

Organization address
address: RUE MICHEL ANGE 3
city: PARIS
postcode: 75794
website: www.cnrs.fr

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 France [FR]
 Project website https://lpmmc.cnrs.fr/spip.php
 Total cost 1˙056˙664 €
 EC max contribution 1˙056˙664 € (100%)
 Programme 1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
 Code Call ERC-2017-STG
 Funding Scheme ERC-STG
 Starting year 2018
 Duration (year-month-day) from 2018-01-01   to  2022-12-31

 Partnership

Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 
1    CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS FR (PARIS) coordinator 1˙056˙664.00

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 Project objective

One of the main challenges in condensed matter physics is to understand strongly correlated quantum systems. Our purpose is to approach this issue from the point of view of rigorous mathematical analysis. The goals are twofold: develop a mathematical framework applicable to physically relevant scenarii, take inspiration from the physics to introduce new topics in mathematics. The scope of the proposal thus goes from physically oriented questions (theoretical description and modelization of physical systems) to analytical ones (rigorous derivation and analysis of reduced models) in several cases where strong correlations play the key role.

In a first part, we aim at developing mathematical methods of general applicability to go beyond mean-field theory in different contexts. Our long-term goal is to forge new tools to attack important open problems in the field. Particular emphasis will be put on the structural properties of large quantum states as a general tool.

A second part is concerned with so-called fractional quantum Hall states, host of the fractional quantum Hall effect. Despite the appealing structure of their built-in correlations, their mathematical study is in its infancy. They however constitute an excellent testing ground to develop ideas of possible wider applicability. In particular, we introduce and study a new class of many-body variational problems.

In the third part we discuss so-called anyons, exotic quasi-particles thought to emerge as excitations of highly-correlated quantum systems. Their modelization gives rise to rather unusual, strongly interacting, many-body Hamiltonians with a topological content. Mathematical analysis will help us shed light on those, clarifying the characteristic properties that could ultimately be experimentally tested.

 Publications

year authors and title journal last update
List of publications.
2019 Nicolas Rougerie
On the Laughlin state and its perturbations
published pages: , ISSN: , DOI:
2019-09-04
2018 Mathieu Lewin, Phan Thành Nam, Nicolas Rougerie
The interacting 2D Bose gas and nonlinear Gibbs measures
published pages: 8-13, ISSN: , DOI:
Mini-Workshop: Gibbs Measures for Nonlinear Dispersive Equations Report No. 18/2018 2019-06-27
2018 Mathieu Lewin, Phan Thành Nam, Nicolas Rougerie
Classical field theory limit of 2D many-body quantum Gibbs states
published pages: , ISSN: , DOI:
2019-08-05
2019 Mathieu Lewin, Phan Thành Nam, Nicolas Rougerie
Derivation of renormalized Gibbs measures from equilibrium many-body quantum Bose gases
published pages: , ISSN: , DOI:
2019-08-05
2019 Alessandro Olgiati, Nicolas Rougerie
Stability of the Laughlin phase against long-range interactions
published pages: , ISSN: , DOI:
2019-08-05
2018 Nicolas Rougerie
Limites de champ moyen bosoniques à température positive
published pages: , ISSN: , DOI:
2019-08-05
2019 Rougerie , Nicolas
Non linear Schrödinger limit of bosonic ground states, again
published pages: , ISSN: , DOI:
https://hal.archives-ouvertes.fr/hal-01994870 3 2019-08-05

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The information about "CORFRONMAT" are provided by the European Opendata Portal: CORDIS opendata.

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