相关论文: Classical Markovian Kinetic Equations: Explicit Fo…
A composite quantum system comprising a finite number k of subsystems which are described with position and momentum variables in Z_{n_{i}}, i=1,...,k, is considered. Its Hilbert space is given by a k-fold tensor product of Hilbert spaces…
In its most general formulation a quantum kinematical system is described by a Heisenberg group; the "configuration space" in this case corresponds to a maximal isotropic subgroup. We study irreducible models for Heisenberg groups based on…
Three geometric formulations of the Hamiltonian structure of the macroscopic Maxwell equations are given: one in terms of the double de Rham complex, one in terms of L2 duality, and one utilizing an abstract notion of duality. The final of…
Using a simple geometrical construction based upon the linear action of the Heisenberg--Weyl group we deduce a new nonlinear Schr\"{o}dinger equation that provides an exact dynamic and energetic model of any classical system whatsoever, be…
It is proved that the continuum hypothesis implies the existence of a group M containing a nonalgebraic unconditionally closed set, i.e., a set which is closed in any Hausdorff group topology on M but is not an intersection of finite unions…
From the perspective of Markovian piecewise deterministic processes (PDPs), we investigate the derivation of a kinetic uncertainty relation (KUR), which was originally proposed in Markovian open quantum systems. First, stationary…
This paper introduces several new classes of mathematical structures that have close connections with physics and with the theory of dynamical systems. The most general of these structures, called indivisible stochastic processes,…
We develop a unified kinetic theory for ordered fluids, which systematically extends the phase space with the appropriate generalized angular momenta. Our theory yields a uniquely determined mesoscopic model for any continuum with…
K. It\^{o} characterised in \cite{ito} zero-mean stationary Gauss Markov-processes evolving on a class of infinite-dimensional spaces. In this work we extend the work of It\^{o} in the case of Hilbert spaces: Gauss-Markov families that are…
We establish the continuity of the Markovian semigroup associated with strong solutions of the stochastic 3D Primitive Equations, and prove the existence of an invariant measure. The proof is based on new moment bounds for strong solutions.…
We study deterministic and quantum dynamics from a constructive "finite" point of view, since the introduction of a continuum, or other actual infinities in physics poses serious conceptual and technical difficulties, without any need for…
The Hilbert space of the unitary irreducible representations of a Lie group that is a quantum dynamical group are identified with the quantum state space. Hermitian representation of the algebra are observables. The eigenvalue equations for…
A pedagogical formulation of Loschmidt's paradox and H-theorem is presented with basic notation on occupancy on discrete states without invoking velocity collision operators. A conjecture, so called H-theorem do-conjecture, is formulated.…
A semiclassical approximation is derived by using a family of wavepackets to map arbitrary wavefunctions into phase space. If the Hamiltonian can be approximated as linear over each individual wavepacket, as often done when presenting…
The formalism of classical and quantum mechanics on phase space leads to symplectic and Heisenberg group representations, respectively. The Wigner functions give a representation of the quantum system using classical variables. The…
Relative fluctuations of observables in discrete stochastic systems are bounded at all times by the mean dynamical activity in the system, quantified by the mean number of jumps. This constitutes a kinetic uncertainty relation that is…
We show that the classical mechanics of an algebraic model are implied by its quantizations. An algebraic model is defined, and the corresponding classical and quantum realizations are given in terms of a spectrum generating algebra.…
Astrophysical plasmas in the surrounding of compact objects and subject to intense gravitational and electromagnetic fields are believed to give rise to relativistic regimes. Theoretical and observational evidence suggest that magnetized…
Starting from the Schr\"odinger-equation of a composite system, we derive unified dynamics of a classical harmonic system coupled to an arbitrary quantized system. The classical subsystem is described by random phase-space coordinates…
A mathematically consistent procedure for coupling quasiclassical and quantum variables through coupled Hamilton-Heisenberg equations of motion is derived from a variational principle. During evolution, the quasiclassical variables become…