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“Machine learning and AI for the sciences -- towards understanding”
Thursday, 08. June 2017
Video-Recording for any system with MP4-support
- Video.mp4 (ca.330 Mb)
15:15 – 16:15
The seemingly chaotic world around us often exhibits remarkable regularities and
repetitive patterns, suggesting a simple origin. That in turn can point to the relevance
of symmetries in nature, often reflecting a geometric underpinning.
Mathematically, the exploitation of symmetries frequently involves algebraic techniques.
In atomic nuclei, the use of structural symmetries or algebraic approaches is one of the
most important tools for the study and understanding of nuclear structure. An example
is the Wigner supermultiplet symmetry SU(4) or the symmetry SU(3), pioneered by Elliott
in the 1950’s to study deformed light mass nuclei in the s-d shell. In heavy nuclei, this
symmetry breaks but a well-known approximate symmetry, pseudo- SU(3), has been
actively studied for many years. Since the 1970’s, the interacting boson model – based on
an algebraic group theoretical foundation – and its offshoots and extensions, has provided
a very successful approach to understanding the structure of myriads of medium mass and
heavy nuclei. Algebraic methods often provide simple, analytic, and parameter-efficient
approaches to the structure of many-body systems.
This talk will provide a selected perspective on some of these and then turn to a new entry
in this field, an approximate symmetry called proxy-SU(3).
Proxy-SU(3) is motivated by a consideration of the spatial overlaps of certain nucleon
wave functions, in particular for deformed nuclei. Like pseudo-SU(3), it exploits a specific
orbit substitution to attain a space that can be described by an SU(3) symmetry.
This in turn allows a number of parameter-free predictions of the structure of heavy
deformed nuclei using the simplest analytic expressions. We will introduce this symmetry,
show the nature and impact of the approximations involved, and outline how its irreps
can be used to make specific predictions of the deformation variables and , of prolate
dominance in deformed nuclei, and of the locus of the prolate-oblate transition region.
Overall, the agreement is good, but, at the same time, specific classes of discrepancies point
to the need for improvements to the model that take into account missing ingredients.
The future colloquium program can be found at:
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