Related papers: Non-autonomous Hamiltonian systems related to high…
This paper investigates the geometric structure of higher-derivative formulations of classical mechanics. It is shown that every even-order formulation of classical mechanics higher than the second order is intrinsically variational, in the…
In recent works we have used quantum tools in the analysis of the time evolution of several macroscopic systems. The main ingredient in our approach is the self-adjoint Hamiltonian $H$ of the system $\Sc$. This Hamiltonian quite often, and…
A wide class of Hamiltonian systems with N degrees of freedom and endowed with, at least, (N-2) functionally independent integrals of motion in involution is constructed by making use of the two-photon Lie-Poisson coalgebra. The set of…
We present a theory of resonances for a class of non-autonomous Hamiltonians to treat the structural instability of spatially localized and time-periodic solutions associated with an unperturbed autonomous Hamiltonian. The mechanism of…
Near-integrability is usually associated with smooth small perturbations of smooth integrable systems. Studying integrable mechanical Hamiltonian flows with impacts that respect the symmetries of the integrable structure provides an…
In high-energy physics, coordinate noncommutativity represents the core idea that space itself can be quantized, as expressed through the frameworks of string theory and noncommutative field theory. Influence of such a noncommutativity on…
We propose path integral description for quantum mechanical systems on compact graphs consisting of N segments of the same length. Provided the bulk Hamiltonian is segment-independent, scale-invariant boundary conditions given by…
We consider the motion of a point particle with spin in a stationary spacetime. We define, following Witzany (2019) and later Ramond (2022), a twelve dimensional Hamiltonian dynamical system whose orbits coincide with the solutions of the…
A systematic Hamiltonian formulation of the Einstein-Cartan system, based on the Hilbert-Palatini action with the Barbero-Immirzi and cosmological constants, is performed using the traditional ADM decomposition and without fixing the time…
The question of controllability is investigated for a quantum control system in which the Hamiltonian operator components carry explicit time dependence which is not under the control of an external agent. We consider the general situation…
We consider a Gaudin magnet (central spin model) with a time-dependent exchange couplings. We explicitly show that the Schr\"odinger equation is analytically solvable in terms of generalized hypergeometric functions for particular choices…
The Lie product and the order relation are viewed as defining structures for Hamiltonian dynamical systems. Their admissible combinations are singled out by the requirement that the group of the Lie automorphisms be contained in the group…
Finite-dimensional non-canonical Hamiltonian systems arise naturally from Hamilton's principle in phase space. We present a method for deriving variational integrators that can be applied to perturbed non-canonical Hamiltonian systems on…
We study non-self-adjoint Hamiltonian systems on Sturmian time scales, defining Weyl-Sims sets, which replace the classical Weyl circles, and a matrix-valued $M-$function on suitable cone-shaped domains in the complex plane. Furthermore, we…
We consider linear and quadratic integrals of motion for general variable quadratic Hamiltonians. Fundamental relations between the eigenvalue problem for linear dynamical invariants and solutions of the corresponding Cauchy initial value…
In the last two decades, significant effort has been put in understanding and designing so-called structure-preserving numerical methods for the simulation of mechanical systems. Geometric integrators attempt to preserve the geometry…
In this study, firstly, the k-th order extension of complex product manifold is consid- ered. Then the higher order vertical, complete lifts of geometric structures on product manifold to its extended spaces are given. Also higher order…
The equilibrium states of the discrete Peyrard-Bishop Hamiltonian with one end fixed are computed exactly from the two-dimensional nonlinear Morse map. These exact nonlinear structures are interpreted as domain walls (DW), interpolating…
We discuss the time evolution of physical finite dimensional systems which are modelled by non-hermitian Hamiltonians. We address both general non-hermitian Hamiltonians and pseudo-hermitian ones. We apply the theory of Krein Spaces to…
In general relativity, the motion of an extended body moving in a given spacetime can be described by a particle on a (generally non-geodesic) worldline. In first approximation, this worldline is a geodesic of the underlying spacetime, and…