QUANTUM MODELLING

New computational tools for the modelling of correlations in quantum systems

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 Obiettivo del progetto (Objective)

'The aim of this project is to use insights from exactly solvable models in order to improve the accuracy of quantum Monte Carlo methods for the modelling of correlated quantum systems such as ultracold atomic gases, nuclear matter and non-conventional superconductors. This will lead to a more precise understanding of the quantum correlations that exist in such systems and will allow to extend these insights to nuclear matter, neutron-rich atomic nuclei or neutron stars. The project also aims to clarify the relation between these systems and recent experiments on ultracold atomic gases. Through the development of new numerical simulation techniques the project will have considerable impact on the fields of nanotechnology (high-Tc superconductors, carbon nanotubes), quantum computing, nuclear waste transmutation and nuclear energy production.'

Introduzione (Teaser)

Many standard models for describing quantum phenomena only approximate reality while exactly solvable models are accurate but cumbersome. An EU-funded open source project developed a solution to this dilemma.

Descrizione progetto (Article)

The quantum world is a bizarre place that often exhibits phenomena that are counter intuitive. Superconductivity, when certain materials possess exactly zero electrical resistance below certain temperatures, is a prime example of such peculiar behaviour.

Understanding and describing phenomena at the quantum level requires sophisticated mathematical models and complex equations. However, many of these, such as the Bardeen-Cooper-Schrieffer (BCS) mean field theory of superconductivity, provide only approximations of reality. BCS describes superconductivity as a microscopic effect caused by a 'condensation' of pairs of electrons into a boson-like state.

To study more complicated quantum correlations, researchers must resort to methods that go beyond the mean field. One promising candidate is the Richardson-Gaudin (RG) models, which provides mathematical equations that can be solved exactly. However, this is a cumbersome process due to the resulting singularities that occur and explains why the RG models have failed to attract the attention they deserve.

The 'New computational tools for the modelling of correlations in quantum systems' (Quantum Modelling) project sought to use insights from exactly solvable models, such as RG, to improve the accuracy of quantum Monte Carlo (QMC) methods for the modelling of correlated quantum systems. These include ultra-cold atomic gases, nuclear matter and non-conventional superconductors.

Named after the famous casino, QMC is a large class of computer algorithms that simulate quantum systems in order to solve the quantum many-body problem.

One of the project's main breakthroughs was the development of a computer code that can solve the RG equations efficiently even for thousands of particles. This paved the way for the use of RG models to analyse correlations in quantum systems, particularly ultra-small metallic grains, atomic nuclei and p-wave superconductors.

The RG equations describe quantum correlations under the ideal condition of zero absolute temperature. They also describe pair correlations in atomic nuclei.

In order to maximise Quantum Modelling's scientific utility and impact, the researchers involved also planned to release the computer code under an open source licence.