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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.

Field of science

  • /engineering and technology/environmental engineering/energy and fuels/fossil energy/gas
  • /natural sciences/mathematics/pure mathematics/mathematical analysis
  • /natural sciences/physical sciences/theoretical physics/particles
  • /natural sciences/physical sciences/condensed matter physics/bose-einstein condensates
  • /natural sciences/physical sciences/theoretical physics/particles/fermion
  • /natural sciences/mathematics/applied mathematics/mathematical physics

Call for proposal

ERC-2018-ADG
See other projects for this call

Funding Scheme

ERC-ADG - Advanced Grant

Host institution

UNIVERSITAT ZURICH
Address
Ramistrasse 71
8006 Zurich
Switzerland
Activity type
Higher or Secondary Education Establishments
EU contribution
€ 1 876 050

Beneficiaries (1)

UNIVERSITAT ZURICH
Switzerland
EU contribution
€ 1 876 050
Address
Ramistrasse 71
8006 Zurich
Activity type
Higher or Secondary Education Establishments