arXiv subjects

Vasily E. Tarasov

Publications and source records attributed to Vasily E. Tarasov.

At least 91 records · Page 5Linked to original sources

arXiv2007

Thermodynamics of Few-Particle Systems

We consider the wide class of few-particle systems that have some analog of the thermodynamic laws. These systems are characterized by the distributions that are determined by the Hamiltonian and satisfy the Liouville equation. Few-particle systems of this class are described by a non-holonomic constraint: the power of non-potential forces is directly proportional to the velocity of the elementary phase volume change. The coefficient of this proportionality is determined by the Hamiltonian. In the general case, the examples of the few-particle systems of this class are the constant temperature systems, canonical-dissipative systems, and Fermi-Bose classical systems.

math-ph↗

arXiv2007

Path Integral for Quantum Operations

In this paper we consider a phase space path integral for general time-dependent quantum operations, not necessarily unitary. We obtain the path integral for a completely positive quantum operation satisfied Lindblad equation (quantum Markovian master equation). We consider the path integral for quantum operation with a simple infinitesimal generator.

quant-ph↗

arXiv2007

Fractional Generalization of Kac Integral

Generalization of the Kac integral and Kac method for paths measure based on the Levy distribution has been used to derive fractional diffusion equation. Application to nonlinear fractional Ginzburg-Landau equation is discussed.

math-ph↗

arXiv2007

Conservation Laws and Hamilton's Equations for Systems with Long-Range Interaction and Memory

Using the fact that extremum of variation of generalized action can lead to the fractional dynamics in the case of systems with long-range interaction and long-term memory function, we consider two different applications of the action principle: generalized Noether's theorem and Hamiltonian type equations. In the first case, we derive conservation laws in the form of continuity equations that consist of fractional time-space derivatives. Among applications of these results, we consider a chain of coupled oscillators with a power-wise memory function and power-wise interaction between oscillators. In the second case, we consider an example of fractional differential action 1-form and find the corresponding Hamiltonian type equations from the closed condition of the form.

math-ph↗

arXiv2007

Fractional Dynamics of Systems with Long-Range Space Interaction and Temporal Memory

Field equations with time and coordinates derivatives of noninteger order are derived from stationary action principle for the cases of power-law memory function and long-range interaction in systems. The method is applied to obtain a fractional generalization of the Ginzburg-Landau and nonlinear Schrodinger equations. As another example, dynamical equations for particles chain with power-law interaction and memory are considered in the continuous limit. The obtained fractional equations can be applied to complex media with/without random parameters or processes.

math-ph↗

arXiv2006

Electromagnetic field of fractal distribution of charged particles

Electric and magnetic fields of fractal distribution of charged particles are considered. The fractional integrals are used to describe fractal distribution. The fractional integrals are considered as approximations of integrals on fractals. Using the fractional generalization of integral Maxwell equation, the simple examples of the fields of homogeneous fractal distribution are considered. The electric dipole and quadrupole moments for fractal distribution are derived.

physics.plasm-ph↗

arXiv2006

Multipole Moments of Fractal Distribution of Charges

In this paper we consider the electric multipole moments of fractal distribution of charges. To describe fractal distribution, we use the fractional integrals. The fractional integrals are considered as approximations of integrals on fractals. In the paper we compute the electric multipole moments for homogeneous fractal distribution of charges.

physics.class-ph↗

arXiv2006

Psi-Series Solution of Fractional Ginzburg-Landau Equation

One-dimensional Ginzburg-Landau equations with derivatives of noninteger order are considered. Using psi-series with fractional powers, the solution of the fractional Ginzburg-Landau (FGL) equation is derived. The leading-order behaviours of solutions about an arbitrary singularity, as well as their resonance structures, have been obtained. It was proved that fractional equations of order $alpha$ with polynomial nonlinearity of order $s$ have the noninteger power-like behavior of order $α/(1-s)$ near the singularity.

nlin.SI↗

arXiv2006

Fractional Variations for Dynamical Systems: Hamilton and Lagrange Approaches

Fractional generalization of an exterior derivative for calculus of variations is defined. The Hamilton and Lagrange approaches are considered. Fractional Hamilton and Euler-Lagrange equations are derived. Fractional equations of motion are obtained by fractional variation of Lagrangian and Hamiltonian that have only integer derivatives.

math-ph↗

arXiv2006

Wave Equation for Fractal Solid String

We use the fractional integrals to describe fractal solid. We suggest to consider the fractal solid as special (fractional) continuous medium. We replace the fractal solid with fractal mass dimension by some continuous model that is described by fractional integrals. The fractional integrals are considered as approximation of the integrals on fractals. We derive fractional generalization of the action functional and the Euler-Lagrange equation for the fractal solid string.The solution of wave equation for fractal solid string is considered.

physics.class-ph↗

arXiv2006

Gravitational Field of Fractal Distribution of Particles

In this paper we consider the gravitational field of fractal distribution of particles. To describe fractal distribution, we use the fractional integrals. The fractional integrals are considered as approximations of integrals on fractals. Using the fractional generalization of the Gauss's law, we consider the simple examples of the fields of homogeneous fractal distribution. The examples of gravitational moments for fractal distribution are considered.

astro-ph↗

arXiv2006

Fractional Generalization of Gradient Systems

We consider a fractional generalization of gradient systems. We use differential forms and exterior derivatives of fractional orders. Examples of fractional gradient systems are considered. We describe the stationary states of these systems.

nlin.CD↗

arXiv2006

Transport Equations from Liouville Equations for Fractional Systems

We consider dynamical systems that are described by fractional power of coordinates and momenta. The fractional powers can be considered as a convenient way to describe systems in the fractional dimension space. For the usual space the fractional systems are non-Hamiltonian. Generalized transport equation is derived from Liouville and Bogoliubov equations for fractional systems. Fractional generalization of average values and reduced distribution functions are defined. Hydrodynamic equations for fractional systems are derived from the generalized transport equation.

cond-mat.stat-mech↗

arXiv2006

Coupled oscillators with power-law interaction and their fractional dynamics analogues

The one-dimensional chain of coupled oscillators with long-range power-law interaction is considered. The equation of motion in the infrared limit are mapped onto the continuum equation with the Riesz fractional derivative of order $α$, when $0<α<2$. The evolution of soliton-like and breather-like structures are obtained numerically and compared for both types of simulations: using the chain of oscillators and using the continuous medium equation with the fractional derivative.

math-ph↗

arXiv2006

Nonholonomic Constraints with Fractional Derivatives

We consider the fractional generalization of nonholonomic constraints defined by equations with fractional derivatives and provide some examples. The corresponding equations of motion are derived using variational principle.

math-ph↗

arXiv2006

Fractional Liouville and BBGKI Equations

We consider the fractional generalizations of Liouville equation. The normalization condition, phase volume, and average values are generalized for fractional case.The interpretation of fractional analog of phase space as a space with fractal dimension and as a space with fractional measure are discussed. The fractional analogs of the Hamiltonian systems are considered as a special class of non-Hamiltonian systems. The fractional generalization of the reduced distribution functions are suggested. The fractional analogs of the BBGKI equations are derived from the fractional Liouville equation.

nlin.CD↗

arXiv2006

Phase-Space Metric for Non-Hamiltonian Systems

We consider an invariant skew-symmetric phase-space metric for non-Hamiltonian systems. We say that the metric is an invariant if the metric tensor field is an integral of motion. We derive the time-dependent skew-symmetric phase-space metric that satisfies the Jacobi identity. The example of non-Hamiltonian systems with linear friction term is considered.

math.DS↗

arXiv2006

Stationary Solutions of Liouville Equations for Non-Hamiltonian Systems

We consider the class of non-Hamiltonian and dissipative statistical systems with distributions that are determined by the Hamiltonian. The distributions are derived analytically as stationary solutions of the Liouville equation for non-Hamiltonian systems. The class of non-Hamiltonian systems can be described by a non-holonomic (non-integrable) constraint: the velocity of the elementary phase volume change is directly proportional to the power of non-potential forces. The coefficient of this proportionality is determined by Hamiltonian. The constant temperature systems, canonical-dissipative systems, and Fermi-Bose classical systems are the special cases of this class of non-Hamiltonian systems.

cond-mat.stat-mech↗