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E. E. Perepelkin

Publications and source records attributed to E. E. Perepelkin.

29 records · Page 2Linked to original sources
arXiv2019

Universal density matrix for the phase space

In this paper, a new representation of the Wigner function for a quantum system in the phase space is proposed. The new representation is of the form $W=\operatorname{Sp}\left[ ρ\mathcal{W} \right]$, where $ρ$ is the density matrix, and $\mathcal{W}$ is the universal density matrix. The density matrix $ρ$ for each quantum system is different, and the universal matrix $\mathcal{W}$ is the same for any quantum system. Thus, the matrix $\mathcal{W}$ has a fundamental character. In the work, the elements of the universal matrix $\mathcal{W}$ were found explicitly and their properties were investigated. The diagonal elements of the matrix $\mathcal{W}$ are the Wigner functions of the harmonic oscillator, which do not introduce dissipation into the quantum system. The off-diagonal elements of the matrix $\mathcal{W}$ contain frequency oscillations responsible for dissipations in the quantum systems.

math-ph↗
arXiv2018

The Vlasov equation correct application based on the higher orders kinematic values for the dissipative systems description

This paper revises traditional phenomenological approaches to the application of Vlasov equation to describe the dissipative systems. The original equation by A.A. Vlasov obtained differs from the classical Vlasov equation used in the scientific literature. The classical Vlasov equation cannot be used to describe the dissipative systems. The original Vlasov equation contains a non-zero right-hand side, derived from the first principles. It is shown that the original Vlasov equation describes the dissipative systems by the non-phenomenological way. The numerical modeling of the dissipative systems using the motion equations solution is performed. The numerical results show the good agreement with the exact solutions of the original Vlasov equation for the dissipative systems. In this way, a wide range of the statistical physics problems, the plasma physics, the astrophysics, the high-energy physics, the controlled fusion using the original Vlasov equation can be revised.

physics.comp-ph↗
arXiv2018

A new class of exact solutions of the Schrodinger equation

The aim of this paper is to find the exact solutions of the Schrodinger equation. As is known, the Schrodinger equation can be reduced to the continuum equation. In this paper, using the non-linear Legendre transform the equation of continuity is linearized. Particular solutions of such a linear equation are found in the paper and an inverse Legendre transform is considered for them with subsequent construction of solutions of the Schrodinger equation. Examples of the classical and quantum systems are considered.

quant-ph↗
arXiv2018

The chain of quantum mechanics equations

The chain of quantum mechanics equations is constructed for wave functions depending on coordinate and time as well as on velocity, acceleration and acceleration of higher orders.

physics.gen-ph↗
arXiv2017

Dissipative systems entropy

In this paper, we introduce the generalized phase space $\left( \vec{r},\vec{v},\dot{\vec{v}},\ddot{\vec{v}},... \right)$, which expands the known phase space $\left( \vec{r},\vec{v} \right)$. The fact is that the introduced space is the infinity dimensional phase space. The paper shows that dissipative systems in generalized phase space may be considered as conservative systems. It is shown that, in infinity dimensional phase space, the entropy is a constant value. It is shown that the transition to finite dimensional phase space leads to dissipations and change of the entropy. The paper contains the rigorous mathematical result.

cond-mat.stat-mech↗
arXiv2016

$Ψ$ - model of micro- and macrosystems

A mathematical model (referred as $Ψ$ - model for convenience) has been developed, which allows describing certain class of micro- and macrosystems. $Ψ$ - model is based on continuum and quantum mechanics. $Ψ$ - model describes micro- and macrosystems, in which vector field of velocities of probability flows, charge, mass has specific spiral structure. The field of velocities has spiral structure on concentric spherical surfaces. The velocity field is not defined and has a characteristic property on the poles of sphere and on the axis and tends to zero at infinity. The behavior of $Ψ$ - model can be described in the general case with unsteady periodic singular solution of the Schrödinger equation. The application of $Ψ$ - model to the description of elementary particles gives naturally the intrinsic magnetic moment (spin) without need in modification of g-factor. The spin is interpreted as rotation in the framework of the relativity theory. The application of $Ψ$ -model to astrophysics gives formally an interpretation of black and white hole, wormhole, structure of the galaxy, anti-galaxy and «enclosed worlds».

physics.gen-ph↗
arXiv2016

Riemann surface and quantization

This paper proposes an approach of the unified consideration of classical and quantum mechanics from the standpoint of the complex analysis effects. It turns out that quantization can be interpreted in terms of the Riemann surface corresponding to the multivalent $\operatorname{Ln}Ψ$ function. A visual interpretation of "trajectories" of the quantum system and of the Feynman's path integral is presented. A magnetic dipole having a magnetic charge that satisfies the Dirac quantization rule was obtained.

quant-ph↗
arXiv2016

The task of the relativistic oscillator in a non-inertial frame of reference

In this paper the analogues of the Lorentz transformations for non-inertial reference frames have been obtained. A common case when the movement speed of one coordinate frame in relation to another one can have time derivatives of higher orders. The obtained transformations conserve invariance of the space-time interval, and in the particular case of inertial frames become the well-known Lorentz transformations. It is shown that the transition from classical mechanics to the theory of relativity is analogous to the consideration of the vibrating system described by the equation of the sine-Gordon type. In this case, if the amplitude of the elliptic functions is $k\to 0$ the fluctuations can be considered small, and that leads to classical mechanics. With $k\to 1$ time depends on the vibration amplitude, which leads to the theory of relativity. In the case of inertial frames the amplitude is $k=β={v}/{c}\;$.

physics.gen-ph↗
arXiv2016

Solution of the nonlinear equation of a divergent type in the corner point domain

The algorithm for generation of exact solutions of the nonlinear equation in partial derivatives of a divergent type which is included in the formulation of magnetostatics, hydro-and aerodynamics, quantum mechanics (stationary Schrödinger equation) has been suggested. The properties of smoothness of solutions in domains with corner points (piecewise smooth boundary) have been considered. The solutions with unlimited derivatives in the corner point domain have been presented on the basis of a new class of special functions.

math-ph↗
arXiv2015

The properties of the first equation of the Vlasov chain of equations

A mathematically rigorous derivation of the first Vlasov equation as a well-known Schrödinger equation for the probabilistic description of a system and families of the classic diffusion equations and heat conduction for the deterministic description of physical systems was inferred. A physical meaning of the phase of the wave function which is a scalar potential of the probabilistic flow velocity is demonstrated. Occurrence of the velocity potential vortex component leads to the Pauli equation for one of the spinar components. A scheme of the construction of the Schrödinger equation solving from the Vlasov equation solving and vice-versa is shown. A process of introduction of the potential to the Schrödinger equation and its interpretation are given. The analysis of the potential properties gives us the Maxwell equation, the equation of the kinematic point movement, and the movement of the medium within electromagnetic fields equation.

math-ph↗