## SIG X (Solitons @ Work workshop)

20 June - 01 July 2022

### From classical to quantum Solitons

Lectures on topological solitons, their mathematical properties and physical applications. As always, the aim of this informal workshop is to increase interactions (and possible future collaboration) between topological solitons oriented physicists and mathematicians. So, we are mainly focused on discussion. This year we want once again to discuss problems and open questions related to dynamical aspects of topological solitons, their interactions and quantization. Due to the Russian attack on Ukraine and still unstable COVID situation, the workshop will be held in a hybrid form with all talks avaliable online. However, we do our best to keep the informal spirit of the workshop where the stress is put on the discussion rather than talks. The participation is free and open to everyone. To join the workshop and the workshop mailing list please e-mail Kasia Oles at katarzyna.slawinska [at] uj.edu.pl The first week will have even more informal climate with only one talk a day, also avaliable online. In addition, the talks will have more introduction/overview flavour. Therefore they should be especially interesting for students. In the second week, which is the main week of the workshop, we plan to have (only) 2 online talks every day followed by informal (almost unlimited) discussion sessions. This edition is again organized within the framework Soliton at Work S@W. We acknowledge financial support from:

### Invited speakers and topics

#### The second week

#### The first week

After each talk there will be an informal (unlimited) discussion session. There will be speacial rooms devoted for the discussion, which can be freely enterd and left.

### Program 27 June - 01 July

Monday | Tuesday | Wednesday | Thursday | Friday | |

10.50 | welcome | ||||

11.00 | Nick | Jarah | Peter and Arpad | Patrick and Tom | Bjarke |

15.00 | Zoltan and Marton | Piotr | Jorge/Alberto | Chris | Luiz |

16.30 | closing remarks | ||||

The hours are given for the European time zone. For UK -1 (10 am/14 pm). For China + 6 (5 pm/9 pm). For Brazil -5 (6 am/10 am)

### Program 20 June - 24 June

Monday | Tuesday | Wednesday | Thursday | Friday | |

11.00 | Andrzej | Andy | Miguel / Paul | Martin | Bruno |

16.00 | Dominik | Yasha | Jose | Carlos | |

### Open Problems

We encourage the speakers to propose open problems which may give some inspiration for all participants#### Nick

Both nuclei and Skyrmions are known to spontaneously break rotational symmetry -- i.e. have a shape. This is restored by quantisation, giving definite spins, but the details are different. Nuclear shapes are mainly just ellipsoids or occasionally pear-shapes, though alpha-particle clusters are more subtle. Nuclear vibrations are widespread throughout the nuclear chart too. Skyrmions have (complicated and interesting) shapes arising more naturally. The challenge for Skyrmion theory is to quantatively understand the energy spectra more fundamentally. This includes shapes, vibrational frequencies, moments of inertia. These parameters are largely phenomenological in nuclear theory, e.g. vibrational modes are related to 1p-1h, particle-hole excitations (or better, 2p-2h) but the actual energies (frequencies) are much less than double the nearby shell model gaps. There are many even-even 'spherical' nuclei around B=100 (Ru-104 is a nice example) with clear quadrupole multi-phonons of frequency about 0.5 MeV, and also an octupole 3^- state at about 2 MeV which might be an octupole phonon or a tetrahedral rigid-body state. Can this be understood using Skyrmions? For smaller nuclei like Carbon-12 our work is quite successful, but we are largely playing catch-up with older work going back to Wheeler/Wefelmeier, Bohr/Mottelson and the more recent Bijker/Iachello papers. How can we jump ahead?

Skyrmions spontaneously break isospin symmetry, captured by their 'colouring'. The idea that nuclei spontaneously break isospin symmetry and that collective quantisation restores it is completely revolutionary, and most nuclear physicists don't believe it. Can we find convincing evidence? Some places to look are (i) the correlations between spin and isospin allowed states, (ii) a theory of the strength of spin-orbit coupling, (iii) a collective picture for beta decay as dominated by an isospin raising/lowering transition within an isospin multiplet. We have a few good results on these topics: spin/isospin spectra for B=4,6,7,8,12 not bad, and isospin inertias scale the right way as B increases further (the B=10 spectrum needs a further bending mode). An experimentalist assured me that not seeing the predicted (embarrassing) 0^- state in Lithium-8 (1 second lifetime) is not too surprising -- could be produced through M2 transition from known 2^+ state, but what is rate and could it be observed in radioactive beam? Alternatively, maybe this state disappears through more careful quantisation of two B=8 Skyrmions. Spin-orbit coupling partly understood for N-N and for single Skyrmion coupled to planar layer, but need to deal with single Skyrmion coupled to a (round) cluster with high symmetry -- what orbital angular momenta occur? Can round layer be modelled by rational map?

#### Andrzej

#### Nick and Q-balls

#### Miguel

### Participants (76)

### Advisory board

### Local organizing committee