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Quantum few-body systems : proceedings of the Joint Physics/Mathematics Workshop on Quantum Few-Body Systems, Aarhus, Denmark, 19-20 March 2007

Joint Physics, Jacob Schach Møller, Dmitiri Fedorov

Published Jan 1, 2008• 0 citations
OpenAlex

Abstract

All papers have been peer-reviewed. The purpose of the workshop was to bring together and promote cooperation between theoretical physicists and mathematicians. Half of the talks were presented by mathematicians, the other half by physicists with the unifying theme being the field of Quantum few-body systems. The field is conceptually understood as applications of rigorous ab-initio methods to quantum systems consisting of a relatively small number of well-defined constituents and is of interest for both mathematicians and physicists.

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All papers have been peer-reviewed. The purpose of the workshop was to bring together and promote cooperation between theoretical physicists and mathematicians. Half of the talks were presented by mathematicians, the other half by physicists with the unifying theme being the field of Quantum few-body systems. The field is conceptually understood as applications of rigorous ab-initio methods to quantum systems consisting of a relatively small number of well-defined constituents and is of interest for both mathematicians and physicists.
In the last years, substantial progress has been made in many areas of mathematical physics. The goal of this workshop was to bring together researchers working on analytic and probabilistic aspects of many-body quantum systems and quantum statistical mechanics, to discuss recent developments, exchange ideas and propose new challenges and research directions. Among the questions addressed during the workshop were the derivation of effective equations, the analysis of physically interesting nonlinear partial differential equations emerging from microscopic theories, the study of open quantum systems in and out of equilibrium, and the investigation of the ground state properties and of the dynamics of quantum spin systems.
The mathematical study of quantum many-body physics has seen significant breakthroughs in the past 15–20 years. Mathematical physicists have approached these systems from different perspectives with different methods. The mini-workshop aimed to connect two rapidly growing fields: the mathematical analysis of many-body systems in scaling regimes (which has led to precise asymptotic formulas of the ground state energy and time evolution, e.g., of Bose gases) and the study of strongly correlated quantum systems via Lieb-Robinson bounds (which provide fundamental insights into the spreading of quantum information).
The mathematical study of quantum many-body physics has seen significant breakthroughs in the past 15–20 years. Mathematical physicists have approached these systems from different perspectives with different methods. The mini-workshop aimed to connect two rapidly growing fields: the mathematical analysis of many-body systems in scaling regimes (which has led to precise asymptotic formulas of the ground state energy and time evolution, e.g., of Bose gases) and the study of strongly correlated quantum systems via Lieb-Robinson bounds (which provide fundamental insights into the spreading of quantum information).
The purpose of the conference (the fourth in the series of Vaxjo conferences) was to bring together scientists (physicists, mathematicians and philosophers) who are interested in foundations of quantum physics. An emphasis was made on both theory and experiment, the underlying objective being to offer to the physical, mathematical and philosophic communities a truly interdisciplinary conference as a privileged place for a scientific interaction. Due to the actual increased role of foundations in the development of quantum information theory as well as the necessity to reconsider foundations at the beginning of the new millennium, the organizers of the conference decided that it was just the right time for taking the scientific risk of trying this.
The field of quantum chemistry is concerned with the modelling and simulation of the behaviour of molecular systems on the basis of the fundamental equations of quantum mechanics. Since these equations exhibit an extreme case of the curse of dimensionality (the Schrödinger equation for N electrons being a partial differential equation on \mathbb R^{3N} ), the quantum-chemical simulation of even moderate-size molecules already requires highly sophisticated model-reduction, approximation, and simulation techniques. The workshop brought together selected quantum chemists and physicists, and the growing community of mathematicians working in the area, to report and discuss recent advances on topics such as coupled-cluster theory, direct approximation schemes in full configuration-interaction (FCI) theory, interacting Green’s functions, foundations and computational aspects of density-functional theory (DFT), low-rank tensor methods, quantum chemistry in the presence of a strong magnetic field, and multiscale coupling of quantum simulations.