Related papers: General formalism for singly-thermostated Hamilton…
Classical Hamiltonian mechanics, characterized by a single conserved Hamiltonian (energy) and symplectic geometry, `hides' other invariants into symmetries of the Hamiltonian or into the kernel of the Poisson tensor. Nambu mechanics aims to…
We propose a generalization of Heisenberg picture quantum mechanics in which a Lagrangian and Hamiltonian dynamics is formulated directly for dynamical systems on a manifold with non--commuting coordinates, which act as operators on an…
We define a thermostatic system to be a convex space of states together with a concave function sending each state to its entropy, which is an extended real number. This definition applies to classical thermodynamics, classical statistical…
Descriptions of molecular systems usually refer to two distinct theoretical frameworks. On the one hand the quantum pure state, i.e. the wavefunction, of an isolated system which is determined to calculate molecular properties and to…
In this work we present a new approach on studying dynamical systems. Combining the two ways of expressing the uncertainty, using probabilistic theory and credibility theory, we have research the generalized fractional hybrid equations. We…
The stability against perturbations of a dynamical system conserving a generalized phase-space volume is studied by exploiting the similarity between statistical physics formalism and that of ergodic theory. A general continuity theorem is…
We introduce a Hamiltonian dynamics for the description of long-range interacting systems in contact with a thermal bath (i.e., in the canonical ensemble). The dynamics confirms statistical mechanics equilibrium predictions for the…
This review paper is devoted to presenting the standard multisymplectic formulation for describing geometrically classical field theories, both the regular and singular cases. First, the main features of the Lagrangian formalism are…
A novel scheme to simulate the evolution of a restricted set of observables of a quantum system is proposed. The set comprises the spectrum-generating algebra of the Hamiltonian. The idea is to consider a certain open-system evolution,…
Construction, in the framework of a Nonequilibrium Statistical Ensemble Formalism, of a Mesoscopic Hydro-Thermodynamics, that is, covering phenomena involving motion displaying variations short in space and fast in time -unrestricted values…
Within the generalized hydrodynamics (GHD) formalism for quantum integrable models, it is possible to compute simple expressions for a number of correlation functions at the Eulerian scale. Specializing to integrable relativistic field…
We show a unified second-order scheme for constructing simple, robust and accurate algorithms for typical thermostats for configurational sampling for the canonical ensemble. When Langevin dynamics is used, the scheme leads to the BAOAB…
The classical Hamiltonian system of time-dependent harmonic oscillator driven by the arbitrary external time-dependent force is considered. Exact analytical solution of the corresponding equations of motion is constructed in the framework…
A generalized formalism of the so-called non-adiabatic quantum molecular dynamics is presented, which applies for atomic many-body systems in external laser fields. The theory treats the nuclear dynamics and electronic transitions…
A method to construct Hamiltonian theories for systems of both ordinary and partial differential equations is presented. The knowledge of a Lagrangian is not at all necessary to achieve the result. The only ingredients required for the…
We investigate the detailed dynamics of multidimensional Hamiltonian systems by studying the evolution of volume elements formed by unit deviation vectors about their orbits. The behavior of these volumes is strongly influenced by the…
If a higher derivative theory arises from a transformation of variables that involves time derivatives, a tailor-made Hamiltonian formulation is shown to exist. The details and advantages of this elegant Hamiltonian formulation, which…
I consider the generic situation where a finite number of identical test systems in varying (possibly unknown) initial states are subjected independently to the same unknown process. I show how one can infer from the output data alone…
In the Hamiltonian formalism, and in the presence of a symmetry Lie group, a variational reduction procedure has already been developed for Hamiltonian systems without constraints. In this paper we present a procedure of the same kind, but…
We develop a Magnus formalism for periodically driven systems which provides an expansion both in the driving term and the inverse driving frequency, applicable to isolated and dissipative systems. We derive explicit formulas for a driving…