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An algebraic approach to the derivation of effective macroscopic evolution equations

Project description

New mathematical tool connects microscopic theories to macroscopic behaviours

Understanding physical systems involves two perspectives: the microscopic level that focuses on fundamental particles and interactions (e.g. Newtonian mechanics and quantum theory), and the macroscopic level that examines collective system behaviours. While microscopic models are precise, they are computationally complex, making macroscopic descriptions more practical for predictions despite being less accurate. Statistical mechanics aims to explain how macroscopic behaviours emerge from microscopic foundations. With the support of the Marie Skłodowska-Curie Actions programme, the MACROQC project will introduce an approach to derive macroscopic evolution equations using resolvent algebras – a mathematical framework with both classical and quantum applications. Unlike traditional ad hoc methods, this algebraic structure offers an excellent setting to study complex many-body systems.

Objective

Physical systems can be approached at microscopic and macroscopic levels. The former are described in terms of elementary constituents and fundamental interactions, e.g. Newton's theory of classical mechanics, Schrödinger's equation in quantum mechanics and Einstein's general theory of relativity. Although a microscopic description is often very accurate, it is usually not well suited for calculations because of the large number of degrees of freedom. On the other hand, a macroscopic description of the system takes into account only effective interactions, which arise from the collective behaviour of the system and are of interest to the `observer'. Such a description is less accurate, but much more accessible for calculations. Because of the great importance of effective macroscopic theories for making qualitative and quantitative predictions about the behaviour of physical systems, a major goal of statistical mechanics is to understand their emergence from microscopic theories. In this project, we propose a novel approach that generalizes the derivation of macroscopic evolution equations.

The overarching main scientific objective of this project is: to develop a mathematical framework based on resolvent algebras in
which effective macroscopic evolution equations can be rigorously derived.

Despite the fact that many theoretical studies have been devoted to this derivation, most results are based on ad-hoc methods. This project generalizes these by introducing an algebraic setting based on resolvent algebras. These algebras have both a classical and quantum counterpart and form an excellent setting to study many-body interacting systems. Although resolvent algebras have already proved successful in other studies, the new challenge is to exploit their structure to derive effective macroscopic evolution equations.

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HORIZON-TMA-MSCA-PF-EF - HORIZON TMA MSCA Postdoctoral Fellowships - European Fellowships

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Call for proposal

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(opens in new window) HORIZON-MSCA-2024-PF-01

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Coordinator

STICHTING RADBOUD UNIVERSITEIT
Net EU contribution

Net EU financial contribution. The sum of money that the participant receives, deducted by the EU contribution to its linked third party. It considers the distribution of the EU financial contribution between direct beneficiaries of the project and other types of participants, like third-party participants.

€ 232 916,16
Address
HOUTLAAN 4
6525 XZ Nijmegen
Netherlands

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Region
Oost-Nederland Gelderland Arnhem/Nijmegen
Activity type
Higher or Secondary Education Establishments
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Total cost

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