On classical and quantum relativistic dynamics

A canonical formalism for the relativistic classical mechanics of many particles is proposed. The evolution equations for a charged particle in an electromagnetic field are obtained and the relativistic two-body problem with an invariant interaction is treated. Along the same line a quantum formalism for the spinless relativistic particle is obtained by means of imprimitivity systems according to Mackey theory. A quantum formalism for the spin-1/2 particle is constructed and a new definition of spin1/2 in relativity is proposed. An evolution equation for the spin-1/2 particle in an external electromagnetic field is given. The Bargmann Michel, and Telegdi equation follows from this formalism as a quasiclassical approximation. Finally, a new relativistic model for hydrogenlike atoms is proposed. The spectrum predicted is in agreement with Dirac's when radiative corrections have been added.     

An approach to comparing Kolmogorov-Sinai and permutation entropy

In this paper we discuss the relationship between permutation entropy and Kolmogorov-Sinai entropy in the one-dimensional case. For this, we consider partitions of the state space of a dynamical system using ordinal patterns of order (d + n? 1) on the one hand, and using n-letter words of ordinal patterns of order d on the other hand. The answer to the question of how different these partitions are provides an approach to comparing the entropies.     

Kolmogorov-Sinai entropy of the dilute wet granular gas

We present an analytical expression for the Kolmogorov-Sinai entropy of a wet granular gas. The influence of the liquid is modeled by a hysteretic interaction force. For the dilute limit (two-particle collisions only), we find a simple expression accounting for the contribution of both the scattering states and the bound states in arbitrary dimensions. It is shown that the system is significantly more chaotic than a gas of (dry) hard spheres, as reflected by a pronounced increase of the Kolmogorov-Sinai entropy.     

On superposition and entropy in quantum dynamics

Some considerations on the existence of nonlinear reversible dynamical evolutions for isolated quantum systems are developed within the Hilbert model with the aid of the superposition principle and the law of entropy.     

Possibility of constructing a gauge-invariant quantum formulation for nongauge classical theory

A general method is proposed for the construction of a gauge-invariant canonical quantum formulation for the gauge-invariant classical theory that depends on the set of parameters. The conditions for closure of the algebra of operators, which generate quantum gauge transformations, entails constraints on the parameters of the theory. The approach described is demonstrated by the example of a closed bosonic string, interacting with a background tachyonic field. The condition of a mass shell for the tachyon is reproduced within the framework of the proposed canonical formulation. Tomsk State Pedagogical Institute. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 18–24, June, 1997.     

Caldirola-kanai oscillator in the classical formulation of quantum mechanics

The quadrature distribution for a quantum damped oscillator is introduced in the frame of formulation of quantum mechanics based on a tomography scheme. The probability distribution for coherent and Fock states of the damped oscillator is expressed explicitly in terms of Gaussian and Hermite polynomials, respectively.     

On the relation between the divergence of trajectories and the Kolmogorov-Sinai entropy

Automorphisms of the torus are considered and the Kolmogorov-Sinai entropy explicitly computed via rate of growth of volumes. The usual rate of growth of exponentiating trajectories is shown to give only a lower bound to K-S entropy.     

Metafluid dynamics and Hamilton-Jacobi formalism

Metafluid dynamics was investigated within Hamilton-Jacobi formalism and the existence of the hidden gauge symmetry was analyzed. The obtained results are in agreement with those of Faddeev-Jackiw approach.     

New universal scaling laws of diffusion and Kolmogorov-Sinai entropy in simple liquids

A new universal scaling law relating the self-diffusivities of the components of a binary fluid mixture to their excess entropies is derived using mode coupling theory. These scaling laws yield numerical results, for a hard sphere as well as Lennard-Jones fluid mixtures, in excellent agreement with simulation results even at a low density region, where the empirical scaling laws of Dzugutov [Nature (London) 381, 137 (1996)]] and Hoyt, Asta, and Sadigh [Phys. Rev. Lett. 85, 594 (2001)]] fail completely. A new scaling law relating the Kolmogorov-Sinai entropy to the excess entropy is also obtained.     

Roles of classical dynamics and quantum dynamics on activated processes occurring in liquids

This paper reviews the reactive flux correlation function approach to studying the classical dynamics of activated processes in liquids. The possibilities and consequences of nonadiabatic electronic transitions in affecting this dynamics is also considered. We emphasize the feasibility of quantitative trajectory studies and the fact that these studies have yet to be fully exploited in the development of approximate theories of activated processes.     

Hamilton-Jacobi functional theory for the integration of classical field equations

By employing the terminology of functional differential calculus, Hamilton-Jacobi theory is extended to apply to classical field equations. It is shown that an asymptotic solution to the Hamilton-Jacobi functional differential equation provides an asymptotic general solution to the associated nonlinear classical field equations.Work supported by a National Science Foundation grant.     

Environment and initial state engineered dynamics of quantum and classical correlations

Based on an open exactly solvable system coupled to an environment with nontrivial spectral density, we connect the features of quantum and classical correlations with some features of the environment, initial states of the system, and the presence of initial system–environment correlations. Some interesting features not revealed before are observed by changing the structure of environment, the initial states of system, and the presence of initial system–environment correlations. The main results are as follows. (1) Quantum correlations exhibit temporary freezing and permanent freezing even at high temperature of the environment, for which the necessary and sufficient conditions are given by three propositions. (2) Quantum correlations display a transition from temporary freezing to permanent freezing by changing the structure of environment. (3) Quantum correlations can be enhanced all the time, for which the condition is put forward. (4) The one-to-one dependency relationship between all kinds of dynamic behaviors of quantum correlations and the initial states of the system as well as environment structure is established. (5) In the presence of initial system–environment correlations, quantum correlations under local environment exhibit temporary multi-freezing phenomenon. While under global environment they oscillate, revive, and damp, an explanation for which is given.     

Hamilton-Jacobi formulation of the Harada gauged Floreanini-Jackiw action

We study the front-form Harada gauged Floreanini-Jackiw action and its BRST-anti-BRST symmetry within Hamilton-Jacobi formalism. Presented at the 11th Colloquium “Quantum Groups and Integrable Systems”, Prague, 20–22 June 2002. This paper is partially supported by the Scientific and Technical Research Council of Turkey.