CORDIS
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CORDIS

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Correlations in Large Quantum Systems

Objective

This project is devoted to the mathematical analysis of important physical properties of many-body quantum systems. We will be interested in properties of the ground state and low-energy excitations but also of non-equilibrium dynamics. We are going to consider systems with different statistics and in different regimes. The questions we are going to address have a common aspect: correlations among particles play a crucial role. Our main goal consists in developing new tools that allow us to correctly describe many-body correlations and to understand their effects. The starting point of our proposal are ideas and techniques that have been introduced in a series of papers establishing the validity of Bogoliubov theory for Bose gases in the Gross-Pitaevskii regime, and in a recent preprint showing how (bosonic) Bogoliubov theory can also be used to study the correlation energy of Fermi gases. In this project, we plan to develop these techniques further and to apply them to new contexts. We believe they have the potential to approach some fundamental open problem in mathematical physics. Among our most ambitious objectives, we include the proof of the Lee-Huang-Yang formula for the energy of dilute Bose gases and of the corresponding Huang-Yang formula for dilute Fermi gases, as well as the derivation of the Gell-Mann--Brueckner expression for the correlation energy of a high density Fermi system. Furthermore, we propose to work on long-term projects (going beyond the duration of the grant) aiming at a rigorous justification of the quantum Boltzmann equation for fermions in the weak coupling limit and at a proof of Bose-Einstein condensation in the thermodynamic limit, two very challenging and important questions in the field.
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Host institution

UNIVERSITAT ZURICH

Address

Ramistrasse 71
8006 Zurich

Switzerland

Activity type

Higher or Secondary Education Establishments

EU Contribution

€ 1 876 050

Beneficiaries (1)

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UNIVERSITAT ZURICH

Switzerland

EU Contribution

€ 1 876 050

Project information

Grant agreement ID: 834782

Status

Ongoing project

  • Start date

    1 September 2019

  • End date

    31 August 2024

Funded under:

H2020-EU.1.1.

  • Overall budget:

    € 1 876 050

  • EU contribution

    € 1 876 050

Hosted by:

UNIVERSITAT ZURICH

Switzerland