General Information

Symposium

The symposium on advances in semi-classical methods in mathematics and physics will take place on October 19-21 , 2016, at the Van Swinderen Huys in Groningen in the Netherlands.

The symposium is jointly organized by the Johann Bernoulli Institute for Mathematics and Computer Science (JBI) and the Van Swinderen Institute for Particle Physics and Gravity (VSI). The aim of the symposium is to explore the wide range of applications of semi-classical methods in physics and mathematics, in order to stimulate cross-fertilization among the different fields.

Motivation

Many modern applications in physics (e.g., in molecular and nuclear physics and the nano sciences) lie in the transition region of the microscopic world of quantum mechanics and the macroscopic world of classical mechanics. Even with the computer power that we have today, full-fledged ab initio quantum computations are often not feasible. Here semi-classical techniques offer especially powerful alternatives. Formally they can be obtained from asymptotic expansions of quantum mechanics in terms of powers of Planck's constant. Such expansions have not only led to deep conceptual insights but as has been demonstrated in recent years can also be cast into powerful computational tools. In many branches of mathematics and physics semi-classical methods have however been developed independently, and though the underlying ideas have very much in common, there is little interaction between the different communities.

In this 3-day symposium to be held at the University of Groningen from 19 October to 21 October 2016 we wish to explore the wide range of applications of semi-classical methods in physics and mathematics, in order to stimulate cross-fertilization among the different fields. At the symposium we want to address advanced topics from a diverse range of fields. Topics to be discussed include on the more formal side:

• The mathematics of semi-classical approximations and semi-classical time-evolution
• Classical and quantum monodromy
• Quantum normal forms
• Topologically nontrivial solutions: solitons, instantons, etc

and the more applied side, among others:

• The semi-classical limit of quantum mechanics and quantum chaos
• Semi-classical approximations in ultra high energy scattering
• Sphaleron transitions in the early universe
• Excited states and quantum phase transitions
• Applications to transition state theory, molecular reaction rates and spectra

Participation

The program exists of about 20 invited talks of 45 minutes and there is room for a small number (max 10) shorter contributed talks. Requests for a contributed talk may be sent to the organizers.

Organization

The symposium is jointly organized by the Johann Bernoulli Institute for Mathematics and Computer Science (JBI) and the Van Swinderen Institute for Particle Physics and Gravity (VSI). Local organizers are:

Eric Bergshoeff & Daniël Boer, Van Swinderen Institute

Henk W. Broer & Holger Waalkens, Johann Bernoulli Institute

Historical Note

In 2016 it is 70 years ago that Hilbrand Johannes ("Hip") Groenewold (1910–1996) published his seminal paper "On the principles of elementary quantum mechanics", Physica 12 (1946) 405-460. In this paper, published with Groningen affiliation, Groenewold has made major contributions to the understanding of the classical-quantum correspondence. His work comprises a systematic study of how classical phase space functions can be mapped to quantum operators and vice versa. In particular he showed that in order to have an isomorphism between the algebra of phase space functions and the algebra of operators the Poisson bracket needs to be modified. Based on a new so-called star product he introduced a deformed Poisson bracket which later has been named after J. E. Moyal who developed the same theory independently at about the same time and published his work in 1949. The insufficiency of the Poisson bracket for the purpose of quantization has become the content of the well known Groenewold-van Hove theorem. Besides graduating in Groningen, Groenewold later became a professor in theoretical physics in Groningen.

More biographical information about Groenewold can be found here.

Coincidentally, 2016 is also the 90th anniversary of the semi-classical approximation method called WKB by Dutch physicist H.A. Kramers among others.