12 citations · 25 across the 7 of their papers we have counts for
7 papers
Dynamical Evolution in Noncommutative Discrete Phase Space and the Derivation of Classical Kinetic Equations
A. Dimakis, C. Tzanakis
By considering a lattice model of extended phase space, and using techniques of noncommutative differential geometry, we are led to: (a) the conception of vector fields as generato…
Classical Markovian Kinetic Equations: Explicit Form and H-Theorem
Constantinos Tzanakis, Alkis P. Grecos
The probabilistic description of finite classical systems often leads to linear kinetic equations. A set of physically motivated mathematical requirements is accordingly formulated…
Noncommutative geometry and its relation to stochastic calculus and symplectic mechanics
A. Dimakis, C. Tzanakis
In the context of a noncommutative differential calculus on the algebra of real valued functions of an -dimensional manifold , a commutative and associative product of 1-form…
Generalized Moyal structures in phase space, kinetic equations and their classical limit: II. Applications to harmonic oscillator models
C. Tzanakis, A. P. Grecos, P. Hatjimanolaki
The formalism of generalized Wigner transformations developped in a previous paper, is applied to kinetic equations of the Lindblad type for quantum harmonic oscillator models. It…
Generalized Moyal structures in phase space, kinetic equations and their classical limit: I. General Formalism
Constantinos Tzanakis, Alkis P. Grecos
Generalised Wigner and Weyl transformations of quantum operators are defined and their properties, as well as those of the algebraic structure induced on the phase-space are studie…
On the uniqueness of the Moyal structure of phase-space functions
C. Tzanakis, A. Dimakis
It is shown that the only associative algebras with a trivial center defined on functions of $\Rl^N$ by an integral kernel are generalized Moyal algebras, corresponding to some par…