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Your search keyword '"A.E. Rassadin"' showing total 6 results
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6 results on '"A.E. Rassadin"'

1. Fractional Laplasians and propagation of waves in three-dimensional space as quantum process

Author

A.A. Potapov and A.E. Rassadin

Subjects
quasiparticle, pauli matrix, fractal tree, green’s matrix, generalized henon map, peano curve, hamiltonian, quantized field, renormalization, fock space, Physics, QC1-999, Electronics, TK7800-8360
Abstract

In this paper it is shown that in the whole range of problems of waves propagation there is hidden feynmanon. We call by feynmanon the quantum object moving along fractal trajectories in phase space of dynamical system related with wave equation considered by means of Feynman integral. Methodology of introduction of feynmanons is quite general and is closely connected with nonlocality of fractional Laplasians.

Published
2016

2. Feynman integrals as connecting component between radio еngineering, fractal paradigm and quantum mechanics

Author

A.A. Potapov and A.E. Rassadin

Subjects
path integral, fractal trajectory, harmonic oscillator, quasiparticle, radio system, photon, schrödinger equation, quasioptics, green’s function, peano curve, Physics, QC1-999, Electronics, TK7800-8360
Abstract

Analysing Feynman integral for one-dimensional harmonic oscillator we have found that it is possible to introduce quasiparticle of radio systems. This quasiparticle we have called radion. One can understand radion as object moving along fractal trajectories in phase space of oscillator. The same arguments have led us to the conclusion about natural fractality of all radio systems working with spectrum of signal. Under radiation of electromagnetic wave into medium with arbitrary dielectric permeability radion continues its fractal movement. Interrelations of radion and photon also have been discussed.

Published
2015

6. THE MODIFIED WHITHAM MODULATION THEORY FOR THE NONLINEAR KLEIN-GORDON-FOCK EQUATION WITH THE SIMPLEST RATIONAL FUNCTION AS ITS POTENTIAL

Author

E.S. Alekseeva and A.E. Rassadin

Subjects
Physics, Nonlinear system, symbols.namesake, Work (thermodynamics), Amplitude, symbols, Interval (mathematics), Rational function, Klein–Gordon equation, Stable distribution, Mathematical physics, Fock space
Abstract

It is well-known that one can construct approximate solution of the nonlinear KleinGordon-Fock equation (NKGF) by means of the Whitham modulation theory (Whitham, 1977). In this work in the framework of the modified Whitham modulation theory presented at (Alekseeva, Rassadin, 2018) and (Kostromina et al., 2017) for NKGF with potential U(x) = (x–1/x)2 its asymptotic solution v(x, t) has been found. Due to isochronism of onedimensional movement of classical particle with unit mass in this potential amplitude a(x, t) of asymptotical solution obeys the linear transfer equation ∂a/∂t + V∂a/∂x = 0 with velocity V belonging to the interval –1 of asymptotic solution of NKGF has been calculated under assumption that its initial phase shift is random value with stable distribution of probabilities. The obtained asymptotic solution due to its simplicity and informativity can be used by lecturers to illustrate abilities of the Whitham modulation theory.

Published
2019
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