scholarly journals HAMILTONIAN DESCRIPTION OF HIGHER ORDER LAGRANGIANS

1996 ◽  
Vol 11 (25) ◽  
pp. 4551-4559 ◽  
Author(s):  
M. S. RASHID ◽  
S. S. KHALIL
Keyword(s):  
Phase Space ◽  
Symplectic Structure ◽  
Hamiltonian Formulation ◽  
Higher Order ◽  
Hamiltonian Description

Using Dirac’s analysis of second class constraints, a Hamiltonian formulation of higher order Lagrangians is reached. The new Hamiltonian description recovers the conventional description of such systems due to Ostrogradsky, but unlike the latter, it provides a simpler structure for the phase space and consequently the underlying symplectic structure.

scholarly journals A geometric Hamiltonian description of composite quantum systems and quantum entanglement

2015 ◽  
Vol 12 (07) ◽  
pp. 1550069 ◽  
Author(s):  
Davide Pastorello
Keyword(s):  
Hilbert Space ◽  
Phase Space ◽  
Quantum Entanglement ◽  
Hamiltonian Formulation ◽  
Classical Mechanics ◽  
Hamiltonian Formalism ◽  
Quantum Systems ◽  
Point Of View ◽  
Entanglement Measure ◽  
Hamiltonian Description

Finite-dimensional Quantum Mechanics can be geometrically formulated as a proper classical-like Hamiltonian theory in a projective Hilbert space. The description of composite quantum systems within the geometric Hamiltonian framework is discussed in this paper. As summarized in the first part of this work, in the Hamiltonian formulation the phase space of a quantum system is the Kähler manifold given by the complex projective space P(H) of the Hilbert space H of the considered quantum theory. However the phase space of a bipartite system must be P(H1 ⊗ H2) and not simply P(H1) × P(H2) as suggested by the analogy with Classical Mechanics. A part of this paper is devoted to manage this problem. In the second part of the work, a definition of quantum entanglement and a proposal of entanglement measure are given in terms of a geometrical point of view (a rather studied topic in recent literature). Finally two known separability criteria are implemented in the Hamiltonian formalism.

Shape Dynamics and the Linking Theory

2018 ◽  
Author(s):  
Flavio Mercati
Keyword(s):  
Phase Space ◽  
Degrees Of Freedom ◽  
Line Element ◽  
Hamiltonian Formulation ◽  
Operational Definition ◽  
Extended Phase Space ◽  
Extended Phase ◽  
Problem Of Time ◽  
Definition Of ◽  
Matter Fields

This chapter explains in detail the current Hamiltonian formulation of SD, and the concept of Linking Theory of which (GR) and SD are two complementary gauge-fixings. The physical degrees of freedom of SD are identified, the simple way in which it solves the problem of time and the problem of observables in quantum gravity are explained, and the solution to the problem of constructing a spacetime slab from a solution of SD (and the related definition of physical rods and clocks) is described. Furthermore, the canonical way of coupling matter to SD is introduced, together with the operational definition of four-dimensional line element as an effective background for matter fields. The chapter concludes with two ‘structural’ results obtained in the attempt of finding a construction principle for SD: the concept of ‘symmetry doubling’, related to the BRST formulation of the theory, and the idea of ‘conformogeometrodynamics regained’, that is, to derive the theory as the unique one in the extended phase space of GR that realizes the symmetry doubling idea.

scholarly journals About the non-standard viewpoint on the dynamics of closed vortex filament

2018 ◽  
Vol 32 (33) ◽  
pp. 1850410 ◽  
Author(s):  
S. V. Talalov
Keyword(s):  
Phase Space ◽  
Effective Mass ◽  
Explicit Formula ◽  
Vortex Filament ◽  
Hamiltonian Description ◽  
Suggested Approach ◽  
Galilei Group ◽  
Filament Dynamics

In this paper, we construct the Hamiltonian description of the closed vortex filament dynamics in terms of non-standard variables, phase space and constraints. The suggested approach makes obvious interpretation of the considered system as a structured particle that possesses certain external and internal degrees of the freedom. The constructed theory is invariant under the transformation of Galilei group. The appearance of this group allows for a new viewpoint on the energy of a closed vortex filament with zero thickness. The explicit formula for the effective mass of the structured particle “closed vortex filament” is suggested.

scholarly journals COVARIANT DESCRIPTION OF PARAMETRIZED NONRELATIVISTIC HAMILTONIAN SYSTEMS

2004 ◽  
Vol 19 (15) ◽  
pp. 2473-2493 ◽  
Author(s):  
MAURICIO MONDRAGÓN ◽  
MERCED MONTESINOS
Keyword(s):  
Phase Space ◽  
Gauge Transformation ◽  
Hamiltonian Systems ◽  
Symplectic Structure ◽  
Canonical Formalism ◽  
Extended Phase Space ◽  
Extended Phase ◽  
Algebra Of Observables ◽  
Covariant Description ◽  
Constraint Surface

The various phase spaces involved in the dynamics of parametrized nonrelativistic Hamiltonian systems are displayed by using Crnkovic and Witten's covariant canonical formalism. It is also pointed out that in Dirac's canonical formalism there exists a freedom in the choice of the symplectic structure on the extended phase space and in the choice of the equations that define the constraint surface with the only restriction that these two choices combine in such a way that any pair (of these two choices) generates the same gauge transformation. The consequence of this freedom on the algebra of observables is also discussed.

scholarly journals QUANTIZATION OF THE TOPOLOGICAL σ-MODEL AND THE MASTER EQUATION OF THE BV FORMALISM

1994 ◽  
Vol 09 (06) ◽  
pp. 491-500 ◽  
Author(s):  
S. AOYAMA
Keyword(s):  
Phase Space ◽  
Master Equation ◽  
Symplectic Structure ◽  
Kähler Manifold ◽  
Quantum Master Equation ◽  
Kahler Manifold ◽  
Invariant States

We quantize the topological σ-model. The quantum master equation of the Batalin-Vilkovisky formalism ΔρΨ=0 appears as a condition which eliminates the exact states from the BRST invariant states Ψ defined by QΨ=0. The phase space of the BV formalism is a supermanifold with a specific symplectic structure, called the fermionic Kähler manifold.

Higher order point and continuum mechanics from phase-space action

2002 ◽  
Vol 305 (3-4) ◽  
pp. 93-99 ◽  
Author(s):  
J Shamanna ◽  
B Talukdar ◽  
U Das
Keyword(s):  
Phase Space ◽  
Continuum Mechanics ◽  
Higher Order ◽  
Space Action

Optomechanical Interactions

2020 ◽  
pp. 105-128
Author(s):  
Ivan Favero
Keyword(s):  
Radiation Pressure ◽  
Hamiltonian Formulation ◽  
Mechanical Action ◽  
Gradient Force ◽  
Optical Forces ◽  
Hamiltonian Description ◽  
Optomechanical Systems ◽  
Equal Footing ◽  
Scientific Potential ◽  
Effects Of Radiation

Light exerts mechanical action on matter through various mechanisms, the most famous being radiation pressure, with the associated picture of a photon bouncing on a perfectly reflective movable mirror and transferring twice its momentum. But still today, unambiguously observing the effects of radiation pressure remains a challenge. In the quantum domain, the radiation pressure interaction between a moving mirror and light stored in a cavity accepts a simple Hamiltonian formulation. But this Hamiltonian description is sometimes oversimplified and underestimates or misses other mechanical effects of light accompanying radiation pressure in experiments. In this chapter, we will not only address radiation pressure but also other relevant optical forces such as the optical gradient force, electrostriction, or the photothermal and optoelectronic forces, which are key in micro- and nanoscale devices and must all be controlled on an equal footing to fully harness the technological and scientific potential of miniature optomechanical systems.

scholarly journals Very-High-Eccentricity Librations at Some Higher Order Resonances

1992 ◽  
Vol 152 ◽  
pp. 153-158 ◽  
Author(s):  
J.C. Klafke ◽  
S. Ferraz-Mello ◽  
T. Michtchenko
Keyword(s):  
Phase Space ◽  
Numerical Integration ◽  
Higher Order ◽  
Planar Problem ◽  
High Eccentricity ◽  
Disturbing Potential ◽  
Numerical Exploration ◽  
Numerical Integrations ◽  
Short Period ◽  
Very High

Motions near the 3:1, 4:1 and 5:2 resonances with Jupiter are studied by means of numerical integrations of a semi-analytically averaged Sun-Jupiter-asteroid planar problem. In order to have a model including the very-high-eccentricity regions of the phase space, we adopted a set of local expansions of the disturbing potential, adequate to perform the numerical exploration of regions in the phase space with eccentricities higher than 0.9 (Ferraz-Mello and Klafke, 1991). Individual solutions and qualitative results thus obtained are completely reproduced by numerical integration of the complete equations by filtering off the short-period components of these solutions.

scholarly journals Phase space description of the dynamics due to the coupled effect of the planetary oblateness and the solar radiation pressure perturbations

2019 ◽  
Vol 131 (9) ◽  
Author(s):  
Elisa Maria Alessi ◽  
Camilla Colombo ◽  
Alessandro Rossi
Keyword(s):  
Phase Space ◽  
Solar Radiation ◽  
Radiation Pressure ◽  
Equilibrium Points ◽  
Hamiltonian Formulation ◽  
Solar Radiation Pressure ◽  
Major Axis ◽  
Integral Of Motion ◽  
Semi Major Axis ◽  
Pressure Perturbations

Abstract The aim of this work is to provide an analytical model to characterize the equilibrium points and the phase space associated with the singly averaged dynamics caused by the planetary oblateness coupled with the solar radiation pressure perturbations. A two-dimensional differential system is derived by considering the classical theory, supported by the existence of an integral of motion comprising semi-major axis, eccentricity and inclination. Under the single resonance hypothesis, the analytical expressions for the equilibrium points in the eccentricity-resonant angle space are provided, together with the corresponding linear stability. The Hamiltonian formulation is also given. The model is applied considering, as example, the Earth as major oblate body, and a simple tool to visualize the structure of the phase space is presented. Finally, some considerations on the possible use and development of the proposed model are drawn.

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