Related papers: Hamel's Formalism and Variational Integrators on a…
We show here that the Hamiltonian for an electronic system may be written exactly in terms of fluctuation operators that transition constituent fragments between internally correlated states, accounting rigorously for inter-fragment…
This study investigates the use of fractional order differential models to simulate the dynamic response of non-homogeneous discrete systems and to achieve efficient and accurate model order reduction. The traditional integer order approach…
The worldline formalism shares with string theory the property that it allows one to write down master integrals that effectively combine the contributions of many Feynman diagrams. While at the one-loop level these diagrams differ only by…
This work presents the basic elements of the formalism involved in the treatment of Hamiltonian dynamical systems with symmetry and the geometrical description of collective motion.
We consider a fractional generalization of Hamiltonian and gradient systems. We use differential forms and exterior derivatives of fractional orders. We derive fractional generalization of Helmholtz conditions for phase space. Examples of…
The system of a closed vortex filament is an integrable Hamiltonian one, namely, a Hamiltonian system with an infinite sequense of constants of motion in involution. An algebraic framework is given for the aim of describing differential…
Quantum chaos---the study of quantized nonintegrable Hamiltonian systems---is an extremely well-developed and sophisticated field. By contrast, very little work has been done in looking at quantum versions of systems which classically…
In this paper, we compare the performance of different numerical schemes in approximating Pontryagin's Maximum Principle's necessary conditions for the optimal control of nonholonomic systems. Retraction maps are used as a seed to construct…
Some well-known examples of constrained quantum systems commonly quantized via Feynman path integrals are re-examined using the notion of conditional integrators introduced in [1]. The examples yield some new perspectives on old results. As…
This paper extends previous work on finitedifference schemes over staggered grids for infinite-dimensional port-Hamiltonian systems. In the one-dimensional setting, it generalizes the discretization approach originally developed for the…
In this paper, we present a formalism for representing infinite systems in quantum mechanics by employing a strategy that embraces divergences rather than avoiding them. We do this by representing physical quantities such as inner products,…
In the context of non-relativistic quantum field theory, a method is proposed for multiplying field operators at the same spatial point and obtaining regular (i.e. rigorously defined) interaction terms for the Hamiltonian. The basic idea is…
In order to perform numerical studies of long-term stability in nonlinear Hamiltonian systems, one needs a numerical integration algorithm which is symplectic. Further, this algorithm should be fast and accurate. In this paper, we propose…
Harmonic maps are nonlinear extensions of harmonic functions. They are critical points of natural energy functionals between Riemannian manifolds. Such type of problems appear in Physics, Geometry of Finance and the study of regularity and…
We improve the arithmetic duality formalism of the rational etale site. This improvement allows us to avoid some exotic approximation arguments on local fields with ind-rational base, thus simplifying the proofs of the previously…
Symplectic integrators for Hamiltonian systems have been quite successful for studying few-body dynamical systems. These integrators are frequently derived using a formalism built on symplectic maps. There have been recent efforts to extend…
A description of Lagrangian and Hamiltonian formalisms naturally arisen from the invariance structure of given nonlinear dynamical systems on the infinite--dimensional functional manifold is presented. The basic ideas used to formulate the…
In order to derive a large set of Hamiltonian dynamical systems, but with only first order Lagrangian, we resort to the formulation in terms of Lagrange-Souriau 2-form formalism. A wide class of systems derived in different phenomenological…
Multi-symplectic integrators are typically regarded as a discretization of the Hamiltonian partial differential equations. This is due to the fact that, for generic finite-dimensional Hamiltonian systems, there exists only one independent…
Preliminary results toward the analysis of the Hamiltonian structure of multifield theories describing complex materials are mustered: we involve the invariance under the action of a general Lie group of the balance of substructural…