1-а майстерня "Концепція складних мереж у задачах квантової фізики та космології"

Конференц-зал ІФКС (Львів, вул. Свєнціцького 1), 26 грудня 2017 р., 15:00-18:00

Мета майстерні - презентація спільних досліджень, а також напрямків і методів науковців Лабораторії статистичної фізики складних систем НАН України, кафедри теоретичної фізики  та Астрономічної обсерваторії ЛНУ ім. І. Франка. Семінар проходить в рамках і за підтримки проекту ДФФД №76/105-2017 "Концепція складних мереж у задачах квантової фізики та космології", номер держреєстрації 0117U003869. В рамках проекту заплановано використання  концептуального апарату і методів теорії складних мереж для пояснення і кількісного опису поведінки матерії на різних  просторових і часових масштабах.

Програма:

Analysis of large scale structure of the Universe by methods of complex network theory

M. Tsizh, B. Novosyadlyj, S.Apunevych (Astronomical Observatory of Ivan Franko National University of Lviv)
We investigate the web of halos in N-body simulation by methods of complex network theory. We use the Gadget-2 dark matter only N-body simulation carried by authors of [1], which they use to compare different techniques of defining the space structure, to which halos belong. We calculate various metrics of the network (betweeness centrality, closeness centrality, clustering) and find correlation between them and the type of structure, to which halo belongs (void, filament, sheet or supercluster).
We plan to study also the distributions of galaxies in the VIPERS sky survey [2] using all data about them containing there: space coordinates, redshifts, brightness, colours, morfological types etc. The VIPERS is a completed ESO Large Program that has mapped in detail the spatial distribution of normal galaxies over an unprecedented volume of the Universe. It used the VIMOS spectrograph at Very Large Telescope to measuring of spectra for more than 90,000 galaxies with red magnitude I(AB) brighter than 22.5 over an overall area of nearly 24 square degrees. The VIPERS is exploring the ensemble properties of galaxies with unprecedented statistical accuracy, providing the natural extension back in time the results from the SDSS and COSMOS surveys.
We have explored by complex networks the dataset produced by COSMOS collaboration [3], which aims to identify all possible galaxies on the restricted area of sky, at unprecedented accuracy of photometric measurements. The catalogues provide us with detailed information related to position of a galaxy in space and its photometric properties. Using clustering coefficient we provide the description of topological environment and investigate the association of evolutionary properties of galaxies to environment.
 
1. Libeskind N.I., van de Weygaert R., Cautun M. et al., 2017, arXiv:1705.03021
2. http://vipers.inaf.it
3. http://cosmos.astro.caltech.edu/
 

Time-dependent correlation functions and zeros of partition function of Bose systems

Kh. Gnatenko, V. Tkachuk (Ivan Franko National University of Lviv, Department for Theoretical Physics)
Time-dependent correlation functions of a system of Bose particles  studied. We find relation of zeros of the correlation function  with the Lee-Yang and Fisher zeros of partition functions of the interacting Bose gas [1] and q-deformed Bose gas [2]. The relation gives the possibility to observe the zeros of partition function  experimentally. Particular case of Bose particles on two levels is  examined and zeros of two-time correlation functions and zeros of  partition function of the system are analyzed.
 
[1] Kh. P. Gnatenko, A. Kargol, V. M. Tkachuk. Phys. Rev. E 96, No. 3, 032116 [6 p.] (2017).
[2] Kh. P. Gnatenko, A. Kargol, V. M. Tkachuk.  arXiv:1711.06192.

Ising model with a power-law spin length distribution

M. Krasnytska, Yu. Holovatch (ICMP NAS of Ukraine)
Considering the critical behavior on networks, special attention had been paid to the the case of scale-free networks, which are characterized by a power law decay of the node degree distribution [1]. It is well established by now, that fundamental features of criticality, scaling and universality, have to be reconsidered when a system resides on a scale-free network, see e.g. [2]. In our study we decided to further analyse the combined impact of two power laws present in the system. To this end, we consider the Ising model with power-law spin length distribution on a scale free network. As we show in our study, an interplay of two power laws governing systems statistics leads to rich phase diagram with a variety of phase transitions in different universality classes [3]. We discuss possible applications of the model considered.
 
[1] R. Albert, A.-L. Barab´asi, Rev. Mod. Phys. 74 (2002) 47.
[2] M. Krasnytska, B. Berche,  Yu. Holovatch, R. Kenna,  J. Phys. A 49 (2016) 135001.
[3] B. Berche, Yu. Holovatch, M. Krasnytska.  (unpublished).

Організатори:
Інститут фізики конденсованих систем НАН України
Кафедра теоретичної фізики  ЛНУ ім. І. Франка 
Астрономічна обсерваторія ЛНУ ім. І. Франка