arXiv subjects

V. V. Kozlov

Publications and source records attributed to V. V. Kozlov.

12 recordsLinked to original sources

arXiv2006

Mass Spectrum, Actons and Cosmological Landscape

It is suggested that the properties of the mass spectrum of elementary particles could be related with cosmology. Solutions of the Klein-Gordon equation on the Friedmann type manifold with the finite action are constructed. These solutions (actons) have a discrete mass spectrum. We suggest that such solutions could select a universe from cosmological landscape. In particular the solutions with the finite action on de Sitter space are investigated.

hep-th↗

arXiv2006

Finite Action Klein-Gordon Solutions on Lorentzian Manifolds

The eigenvalue problem for the square integrable solutions is studied usually for elliptic equations. In this note we consider such a problem for the hyperbolic Klein-Gordon equation on Lorentzian manifolds. The investigation could help to answer the question why elementary particles have a discrete mass spectrum. An infinite family of square integrable solutions for the Klein-Gordon equation on the Friedman type manifolds is constructed. These solutions have a discrete mass spectrum and a finite action. In particular the solutions on de Sitter space are investigated.

gr-qc↗

arXiv2005

Billiards, Invariant Measures, and Equilibrium Thermodynamics

The questions of justification of the Gibbs canonical distribution for systems with elastic impacts are discussed. A special attention is paid to the description of probability measures with densities depending on the system energy.

physics.class-ph↗

arXiv2005

On Justification of Gibbs Distribution

The paper develop a new approach to the justification of Gibbs canonical distribution for Hamiltonian systems with finite number of degrees of freedom. It uses the condition of nonintegrability of the ensemble of weak interacting Hamiltonian systems.

nlin.SI↗

arXiv2005

Canonical Gibbs distribution and thermodynamics of mechanical systems with a finite number of degrees of freedom

Traditional derivation of Gibbs canonical distribution and the justification of thermodynamics are based on the assumption concerning an isoenergetic ergodicity of a system of $n$ weakly interacting identical subsystems and passage to the limit $n\to\infty$. In the presented work we develop another approach to these problems assuming that $n$ is fixed and $n\ge2$. The ergodic hypothesis (which frequently is not valid due to known results of the KAM-theory) is substituted by a weaker assumption that the perturbed system does not have additional first integrals independent of the energy integral. The proof of nonintegrability of perturbed Hamiltonian systems is based on the Poincare method. Moreover, we use the natural Gibbs assumption concerning a thermodynamic equilibrium of bsystems at vanishing interaction. The general results are applied to the system of the weakly connected pendula. The averaging with respect to the Gibbs measure allows to pass from usual dynamics of mechanical systems to the classical thermodynamic model.

nlin.SI↗

arXiv2005

On the Integration Theory of Equations of Nonholonomic Mechanics

The paper deals with the problem of integration of equations of motion in nonholonomic systems. By means of well-known theory of the differential equations with an invariant measure the new integrable systems are discovered. Among them there are the generalization of Chaplygin's problem of rolling nonsymmetric ball in the plane and the Suslov problem of rotation of rigid body with a fixed point. The structure of dynamics of systems on the invariant manifold in the integrable problems is shown. Some new ideas in the theory of integration of the equations in nonholonomic mechanics are suggested. The first of them consists in using known integrals as the constraints. The second is the use of resolvable groups of symmetries in nonholonomic systems. The existence conditions of invariant measure with analytical density for the differential equations of nonholonomic mechanics is given.

nlin.SI↗

arXiv2005

Kinetics of Collisionless Continuous Medium

In this article we develop Poincaré ideas about a heat balance of ideal gas considered as a collisionless continuous medium. We obtain the theorems on diffusion in nondegenerate completely integrable systems. As a corollary we show that for any initial distribution the gas will be eventually irreversibly and uniformly distributed over all volume, although every particle during this process approaches arbitrarily close to the initial position indefinitely many times. However, such individual returnability is not uniform, which results in diffusion in a reversible and conservative system. Balancing of pressure and internal energy of ideal gas is proved, the formulas for limit values of these quantities are given and the classical law for ideal gas in a heat balance is deduced. It is shown that the increase of entropy of gas under the adiabatic extension follows from the law of motion of a collisionless continuous medium.

nlin.CD↗

arXiv2005

Galton Board

In this paper, we present results of simulations of a model of the Galton board for various degrees of elasticity of the ball-to-nail collision.

nlin.CD↗

arXiv2005

Notes on diffusion in collisionless medium

A collisionless continuous medium in Euclidean space is discussed, i.e. a continuum of free particles moving inertially, without interacting with each other. It is shown that the distribution density of such medium is weakly converging to zero as time increases indefinitely. In the case of Maxwell's velocity distribution of particles, this density satisfies the well-known diffusion equation, the diffusion coefficient increasing linearly with time.

nlin.CD↗

arXiv2005

Billiards, invariant measures, and equilibrium thermodynamics. II

The kinetics of collisionless continuous medium is studied in a bounded region on a curved manifold. We have assumed that in statistical equilibrium, the probability distribution density depends only on the total energy. It is shown that in this case, all the fundamental relations for a multi-dimensional ideal gas in thermal equilibrium hold true.

nlin.CD↗

arXiv2001

Ultrahigh reflection from a medium with ultraslow group velocity

We show that an incident wavepacket at the boundary to a medium with extremely slow group velocity, experiences enhanced reflection and a substantial spatial and temporal distortion of the transmitted wave packet. In the limit of vanishing group velocity, light cannot be transferred into the medium due to its perfect reflectivity.

quant-ph↗

arXiv2001

Dark Area Theorem

We report the discovery of a "dark area theorem," a new quantum optical relation for propagation of unmatched pulses in thick three-level $Λ$-type media. We define dark area and derive the dark area theorem for a coherently prepared and inhomogeneously broadened lambda medium. We also obtain the first equation for the spatial evolution of the dark state amplitude prior to pulse-matching.

physics.optics↗