1st Workshop "Complex network concept in problems of quantum physics and cosmology"

# 1st Workshop "Complex network concept in problems of quantum physics and cosmology"

### Conference Hall of the ICMP (1 Svientsitskii Str.), 26 December 2017, 15:00-18:00

The task of the Workshop is to present common research as well as the principal research fields of the Laboratory for Statistical Physics of Complex Systems of the ICMP NAS of Ukraine, Astronomical Observatory and Department of Theoretical Physics of the Ivan Franko National University of Lviv. The Workshop is organized in the frames and under support of the Project DFFD №76/105-2017 "* Complex network concept in problems of quantum physics and cosmology*" (0117U003869). Within the project we plan to use the methods of complex network theory for the explanation and quantitative description of behavior of matter on different space and time scales.

## Program:

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*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/

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

*Kh. Gnatenko, V. Tkachuk (**Ivan Franko National University of Lviv, **Department forTheoretical 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.

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*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).

**Organizers:**

Institute for Condensed Matter Physics NAS of Ukraine

Department of Theoretical Physics Ivan Franko National University of Lviv

Astronomical Observatory of Ivan Franko National University of Lviv