#### Studies of Wigner Quasi-probability DistributionFunctions

**V. Abgaryan, A. Khvedelidze, I. Rogojin and A. Torosyan**

Laboratory of Information Technologies, JINR, Dubna, Russia

December 4 , 2018

Standard form of the Wigner function; the Stratonovich-Weyl correspondence; constructing the kernel for Wigner distribution; Qubit kernel and the Wigner function; probability of negativity as a measure of non-classicality of space of states

#### Outer Tracker of the BM@N Experiment

**M. Kapishin, V. Lenivenko, V. Palichik, Nikolay Voytishin**

JINR, Dubna

AYSS Prize Competition

December 4 , 2018

The software for the MWPC and DCH detector systems was developed and implemented into the official experiment software and the software for CSC is under development; the spatial resolution for different layers of the DC chambers varies within 150-200 μm; the MWPC and DCH systems give us the possibility to estimate the beam momentum value with a high precision ~2% for the working values of the magnetic field integral; the outer tracker detector systems ( DCH&CSC) provide a high hit efficiency per layer; the first look at CSC spatial hits matching with DCH global tracks shows a good CSC-DCH correlation.

#### How robust is a third family of compact stars against pasta phase eﬀects?

**Alexander Ayriyan**

Laboratory of Information Technologies, JINR, Dubna, Russia

124th session of the Scientiﬁc Council

September 21 , 2018

#### Studies of the Wigner quasiprobability distributions

**V. Abgaryan, A.Khvedelidze, D.Mladenov, I.Rogojin, A.Torosyan **

Laboratory of Information Technologies, JINR, Dubna, Russia

Institute of Quantum Physics and Engineering Technologies, GTU, Tbilisi, Georgia

Theoretical Physics Department, Faculty of Physics, Sofia University “St Kliment Ohridski”, Sofia, Bulgaria

June 14-15 , 2018

A long-standing issue of “quantum analogues” of the statistical dis-tributions of classical mechanics consists in a correct definition ofthe mapping between operators on the Hilbert space of a finite-dimensional quantum system and the so-called quasiprobability dis-tributions [1] defined over the symplectic flag manifold [2, 3].Guiding by the Weyl-Stratonovich correspondence [4, 5], we proposethe construction method of the Wigner function (WF) for anN-levelquantum system. We derive algebraic equations for eigenfunctions ofthe Stratonovich-Weyl (SW) kernel of WF and discuss an arbitrari-ness of its solution. The presentation is exemplified by consideringthe WFs for 2, 3 and 4-dimensional quantum systems. The results ofanalytical and numerical computations of the WF characteristics withvarious SW kernels, including the probability for the WFs from thecorresponding Hilbert-Schmidt ensembles to take negative values will be given.