相关论文: Features of Moyal Trajectories
We present a method for studying the secular gravitational dynamics of hierarchical multiple systems consisting of nested binaries, which is valid for an arbitrary number of bodies and arbitrary hierarchical structure. We derive the…
An elementary system leading to the notions of fractional integrals and derivatives is considered. Various physical situations whose description is associated with fractional differential equations of motion are discussed.
Quantization of constraint systems within the Weyl-Wigner-Groenewold-Moyal framework is discussed. Constraint dynamics of classical and quantum systems is reformulated using the skew-gradient projection formalism. The quantum deformation of…
In this paper we develop a fractional Hamiltonian formulation for dynamic systems defined in terms of fractional Caputo derivatives. Expressions for fractional canonical momenta and fractional canonical Hamiltonian are given, and a set of…
Motivated by situations with temporal evolution and spatial symmetries both singled out, we develop a new 2+1+1 decomposition of spacetime, based on a nonorthogonal double foliation. Time evolution proceeds along the leaves of the spatial…
We study the most general form of a three dimensional classical integrable system with axial symmetry and invariant under the axis reflection. We assume that the three constants of motion are the Hamiltonian, $H$, with the standard form of…
We investigate the difference between classical and quantum dynamics of coupled magnetic dipoles. We prove that in general the dynamics of the classical interaction Hamiltonian differs from the corresponding quantum model, regardless of the…
One classical theory, as determined by an equation of motion or set of classical trajectories, can correspond to many unitarily {\em in}equivalent quantum theories upon canonical quantization. This arises from a remarkable ambiguity, not…
In this paper we introduce the notion of fractional martingale as the fractional derivative of order $\alpha$ of a continuous local martingale, where $\alpha\in(-{1/2},{1/2})$, and we show that it has a nonzero finite variation of order…
Consistent dynamics which couples classical and quantum degrees of freedom exists, provided it is stochastic. This dynamics is linear in the hybrid state, completely positive and trace preserving. One application of this is to study the…
Hamilton's principle of stationary action lies at the foundation of theoretical physics and is applied in many other disciplines from pure mathematics to economics. Despite its utility, Hamilton's principle has a subtle pitfall that often…
The recently developed method (Paper 1) enabling one to investigate the evolution of dynamical systems with an accuracy not dependent on time is developed further. The classes of dynamical systems which can be studied by that method are…
In this study, a new expansion of planetary disturbing function is developed for describing the resonant dynamics of minor bodies with arbitrary inclinations and semimajor axis ratios. In practice, the disturbing function is expanded around…
The Hamilton theories for higher orders classical Lagrange functions result on a well known Ostrogradski's instabilities. In this work, we propose a different definition for the second order canonical momentum and obtain a new set of second…
The evolution equations of quantum observables are derived from the classical Hamiltonian equations of motion with the only additional assumption that the phase space is non-commutative. The demonstration of the quantum evolution laws is…
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.
We consider a nonlocal generalization of the Fisher-KPP equation in one spatial dimension. As a parameter is varied the system undergoes a Turing bifurcation. We study the dynamics near this Turing bifurcation. Our results are two-fold.…
The classical and quantum evolution of a generic probability distribution is analyzed. To that end, a formalism based on the decomposition of the distribution in terms of its statistical moments is used, which makes explicit the differences…
The behavior of solution trajectories usually changes if we replace the classical derivative in a system by a fractional one. In this article, we throw a light on the relation between two trajectories $X(t)$ and $Y(t)$ of such a system,…
We extend a contraction mapping argument for ordinary state-dependent delay differential equations to evolutionary partial differential equations in the sense of R. Picard, that is, to equations of the form $\bigl(\partial_{t}…