Related papers: A Short Comparison of Classical Complex Dynamics a…
We describe an iterative approach to computing long-time semiclassical dynamics in the presence of chaos, which eliminates the need for summing over an exponentially large number of classical paths, and has good convergence properties even…
We discuss classical and quantum computations in terms of corresponding Hamiltonian dynamics. This allows us to introduce quantum computations which involve parallel processing of both: the data and programme instructions. Using mixed…
The classical Hamilton equations of motion yield a structure sufficiently general to handle an almost arbitrary set of ordinary differential equations. Employing elementary algebraic methods, it is possible within the Hamiltonian structure…
The classical and quantum dynamics of the noncanonically coupled oscillators is considered. It is shown that though the classical dynamics is well--defined for both harmonic and anharmonic oscillators, the quantum one is well--defined in…
In their simplest formulations, classical dynamics is the study of Hamiltonian flows and quantum mechanics that of propagators. Both are linked, and emerge from the datum of a single classical concept, the Hamiltonian function. We study and…
We reply to a comment on `Semiclassical dynamics of a spin-1/2 in an arbitrary magnetic field'.
Topological semantics for modal logics has recently gained new momentum in many different branches of logic. In this paper, we will consider the topological semantics of both classical and paraconsistent modal logics. This work is a new…
A hybrid formalism is proposed for interacting classical and quantum sytems. This formalism is mathematically consistent and reduces to standard classical and quantum mechanics in the case of no interaction. However, in the presence of…
We establish a general result on the existence of partially defined semiconjugacies between rational functions acting on the Riemann sphere. The semiconjugacies are defined on the complements to at most one-dimensional sets. They are…
A canonical formulation of coupled classical-quantum dynamics is presented. The theory is named symmetric hybrid dynamics. It is proved that under some general conditions its predictions are consistent with the full quantum ones. Moreover…
In this work simple and effective quantization procedure of classical dynamical systems is proposed and illustrated by a number of examples. The procedure is based entirely on differential equations which describe time evolution of systems.
Semi-classical approaches approximate fully quantum descriptions with partially classical ones. Here we use a toy model to highlight the failings of the standard mean-field semi-classical approach, and show how including environmental…
Many theories of physical interest, which admit a Hamiltonian description, exhibit symmetries under a particular class of non - strictly canonical transformation, known as dynamical similarities. The presence of such symmetries allows a…
We consider the dynamics associated with an arbitrary semigroup of transcendental entire functions. Fatou-Julia theory is used to investigate the dynamics of these semigroups. Several results of the dynamics associated with iteration of a…
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Classical vehicle dynamics contains several widely adopted misconceptions that, while intuitively appealing, may lead to inconsistencies when examined under a rigorous mechanical framework. This paper revisits a number of such…
Questioning the experimental basis of continuous descriptions of fundamental interactions we discuss classical gravity as an effective continuous first-order approximation of a discrete interaction. The sub-dominant contributions produce a…
The basic concepts of classical mechanics are given in the operator form. The dynamical equation for a hybrid system, consisting of quantum and classical subsystems, is introduced and analyzed in the case of an ideal nonselective…
The classical and quantum dynamics of noncanonically coupled os- cillators is investigated in its relation to Lie superalgebras. It is shown that the quantum dynamics admits a hidden (super)hamiltonian formulation and, hence, preserves the…
Using semiclassical methods, it is possible to construct very accurate approximations in the short wavelength limit of quantum dynamics that rely exclusively on classical dynamical input. For systems whose classical realization is strongly…