Search results for "Hamiltonian"

Lagrangians, Hamiltonians and Noether’s Theorem

2015

This chapter is intended to remind the basic notions of the Lagrangian and Hamiltonian formalisms as well as Noether’s theorem. We shall first start with a discrete system with N degrees of freedom, state and prove Noether’s theorem. Afterwards we shall generalize all the previously introduced notions to continuous systems and prove the generic formulation of Noether’s Theorem. Finally we will reproduce a few well known results in Quantum Field Theory.

C3v Top Data System (C3vTDS) software for spectrum simulation of XY3Z symmetric-top molecules using the group chain

2010

Abstract The C3v Top Data System (C3vTDS) program suite has been developed with the aim of studying any rovibrational band or polyad of XY3Z (C3v) symmetric-tops molecules in a singlet electronic state. It is developed in the same way as similar programs for various molecular symmetries (Td, Oh, C4v, C2v and D2h). We work in the O ( 3 ) ⊃ C ∞ v ⊃ C 3 v group chain and this choice has consequences on the method used to specify the input parameters for Hamiltonian and transition moment calculations. One example concerning the ν 2 band of the CH 3 12 D symmetric-top molecule is presented. This package consists in a series of FORTRAN programs called by scripts. The whole package is freely acces…

An Interlude: Writing the Hamiltonian

2012

Massive evaluation and analysis of Poincar�� recurrences on grids of initial data: a tool to map chaotic diffusion

2020

We present a novel numerical method aimed to characterize global behaviour, in particular chaotic diffusion, in dynamical systems. It is based on an analysis of the Poincar\'e recurrence statistics on massive grids of initial data or values of parameters. We concentrate on Hamiltonian systems, featuring the method separately for the cases of bounded and non-bounded phase spaces. The embodiments of the method in each of the cases are specific. We compare the performances of the proposed Poincar\'e recurrence method (PRM) and the custom Lyapunov exponent (LE) methods and show that they expose the global dynamics almost identically. However, a major advantage of the new method over the known g…

An Ecology and Economy Coupling Model. A global stationary state model for a sustainable economy in the Hamiltonian formalism

2020

Abstract The severity of the two deeply correlated crises, the environmental and the economic ones, needs to be faced also in theoretical terms; thus, the authors propose a model yielding a global “stationary state”, following the idea of a “steady-state economics” by Georgescu-Rogen and Herman Daly, by constructing only one dynamical system of ecological and economic coupled variables. This is possible resorting to the generalized Volterra model, that, translated in the Hamiltonian formalism and its Hamilton equations, makes possible to “conjugate” every pair of variables, one economic, the other one ecological, in describing the behavior in time of a unique dynamical system. Applying the …

The closed-form solution for a family of four-dimension nonlinear MHDS

2008

In this article we propose a method for solving a general class of four-dimension nonlinear modified Hamiltonian dynamic systems in closed form. This method may be used to study several intertemporal optimization problems sharing a common structure, which involves unbounded technological constraints as well as multiple controls and state variables. The method is developed by solving the first-order conditions associated with the planner's problem corresponding to the Lucas [1988. On the mechanics of economic development. Journal of Monetary Economics 22, 3-42] two-sector model of endogenous growth, and allows for explicitly showing the transitional dynamics of the model. Despite the externa…

Microscopic calculation of the LSP detection rates for the 71Ga, 73Ge and 127I dark-matter detectors

2004

Abstract We have investigated the nuclear-structure details of the cross sections for the elastic scattering of Lightest Supersymmetric Particles (LSPs) from the promising dark-matter detectors 71 Ga, 73 Ge and 127 I. The associated LSP detection sensitivities have been obtained by a folding procedure for several recently proposed SUSY models with different scalar and axial-vector characteristics. For the nuclear problem, a realistic microscopic Hamiltonian has been used within realistic model spaces. The diagonalization of this Hamiltonian has been done by using the Microscopic Quasiparticle–Phonon Model (MQPM), suitable for description of spectroscopic properties of medium-heavy and heavy…

Spontaneous emission of an atom near an oscillating mirror

2019

We investigate the spontaneous emission of one atom placed near an oscillating reflecting plate. We consider the atom modeled as a two-level system, interacting with the quantum electromagnetic field in the vacuum state, in the presence of the oscillating mirror. We suppose that the plate oscillates adiabatically, so that the time-dependence of the interaction Hamiltonian is entirely enclosed in the time-dependent mode functions, satisfying the boundary conditions at the plate surface, at any given time. Using time-dependent perturbation theory, we evaluate the transition rate to the ground-state of the atom, and show that it depends on the time-dependent atom-plate distance. We also show t…

Exactly solvable model of two three-dimensional harmonic oscillators interacting with the quantum electromagnetic field: The far-zone Casimir-Polder …

2005

We consider two three-dimensional isotropic harmonic oscillators interacting with the quantum electromagnetic field in the Coulomb gauge and within dipole approximation. Using a Bogoliubov-like transformation, we can obtain transformed operators such that the Hamiltonian of the system, when expressed in terms of these operators, assumes a diagonal form. We are also able to obtain an expression for the energy shift of the ground state, which is valid at all orders in the coupling constant. From this energy shift the nonperturbative Casimir-Polder potential energy between the two oscillators can be obtained. When approximated to the fourth order in the electric charge, the well-known expressi…

Single particle motion in a Penning trap: description in the classical canonical formalism

1992

This paper aims at the development of methods for the calculation of the characteristic frequencies of a Penning trap, taking into account deviations of the actual geometry from the ideal one, anharmonicities of the electric potential, misalignments and inhomogeneities of the magnetic field, additional time dependent electromagnetic fields, and so on. The paper starts by describing the motion of a single charged particle in an ideal hyperbolic Penning trap using the formalism of classical hamiltonian mechanics. The usefulness of rotating coordinates is pointed out, and the importance of conservation of canonical angular momentum is stressed. After transformation to action-angle variables th…