ISSN 1064-2269, Journal of Communications Technology and Electronics, 2014, Vol. 59, No. 8, pp. 877–883. © Pleiades Publishing, Inc., 2014. Original Russian Text © V.I. Kanavets, Yu.D. Mozgovoi, S.A. Khritkin, 2014, published in Radiotekhnika i Elektronika, 2014, Vol. 59, No. 8, pp. 836–842. 877 † INTRODUCTION In proceedings of the all-Russia workshops at the Moscow State University in 2006–2009 and in mono- graph [1], V.I. Kanavets formulated the basic ideas on the physical properties of the electron–positron mat- ter (EPM). He suggested a hypothesis on the possibil- ity of long existence of a metastable EPM with unique properties: an extremely high stored energy, which is released in the process of the collective delayed anni- hilation of particles and antiparticles; properties of macroscopic quantum electron–positron superfluids, which are realized in large volumes with effects of superfluidity and superconductivity; and the possibil- ity of resonant self-organization of the EPM with for- mation of macroscopic quantum superplasmoids. The EPM is a combination of three types of funda- mental particles (electrons, positrons, and virtual γ-quanta) self-organizing in one macroscopic quan- tum state. Electron and its antiparticle, positron, are elementary particles whose aggregates are not observed at distances exceeding 10 –16 cm. They are not subject to strong (nuclear) interaction, have a spin of 1/2, and obey the Fermi–Dirac statistics. Elec- tron–positron pairs (e – e + ) have a stored energy of 1.02 MeV = 1.6 × 10 –13 J, which is released during annihilation [1–3]. Gamma-quantum has zero charge, zero mass at rest, and unit spin. Gamma-quanta (photons) obey the Bose–Einstein statistics. At large energy of † Deceased. gamma-quanta (above 10 MeV), conditions for the dominant formation of electron–positron pairs are created [4]. An important role in the theory of the EPM is played by the properties of the collectives of particles. In particular, an individual electron as an elementary particle is not identical to a positron. At the same time, neutrally charged groups of electrons and positrons can be identical. Certain groups of elec- tron–positron pairs can acquire properties of true neutral systems. This is caused by the symmetry with respect to transformation referred to as the charge conjugation [4, 5]. The EPM is created as a result of the Bose–Ein- stein condensation of electrons and positrons at high density of particles and forms a macroscopic elec- tron–positron field with a nonzero mass at rest (the field of matter), in contrast to the electromagnetic field of radiation (the field of γ-quanta). A known example of the EPM are hydrogen-like positronium atoms and positronium molecules [2–5]. For the quantum electron–positron plasma, equa- tions of the hydrodynamic approximation of the clas- sical theory hold true if the spatial variation in the den- sity of charged particles is sufficiently small. In this case, the wave functions of electrons, Ψ e , and positrons, Ψ p , have the form of macroscopic wave functions of the theory of quantum liquids and the theory of superfluidity [6, 7]. In the classical nonlinear theory, interaction pro- cesses in an active medium lead to the phase self- focusing of oscillators, self-excitation of oscillations in Numerical Simulation of Interaction Processes in the Electron–Positron Matter by the Methods of the Classical and Quantum Theories V. I. Kanavets a, † , Yu. D. Mozgovoi b , and S. A. Khritkin b a Moscow State University, Moscow, 119991 Russia b Moscow Institute of Electronics and Mathematics, Higher School of Economics (National Research University), B. Trekhsvyatitel’skii per. 3, Moscow, 109028 Russia e-mail: y.mozgovoy@hse.ru, s.khritkin.hse.ru Received February 12, 2014 Abstract—Numerical simulation of interaction processes in the electron–positron matter (EPM) is numer- ically simulated in the framework of the specific research area, gamma-electronics, which is concerned with the problem of creation and long existence of an EPM with extremely high energy, which is released in the process of delayed annihilation. Interaction processes in the EPM are studied by the methods of the classical large-particle model and a quantum model using macroscopic wave functions of electrons and positrons. In contrast to the point kinematic approach used in quantum electrodynamics, large particles are considered as deformed bunches of charge. DOI: 10.1134/S1064226914080105