NONLOCAL LAGRANGIANS AND HAMILTONIAN FORMALISM

1994 ◽  
Vol 03 (01) ◽  
pp. 211-214
Author(s):  
LLOSA J. ◽  
VIVES J.
Keyword(s):  
Phase Space ◽  
Classical Mechanics ◽  
Hamiltonian Formalism ◽  
Lagrangian Systems ◽  
Infinite Dimensional ◽  
First Order ◽  
Dimensional Phase Space ◽  
Set Up

A presymplectic formalism is set up for nonlocal Lagrangian systems. The method is based on an ‘equivalent’ first order Lagrangian that is processed by standard ways of classical mechanics. The Hamiltonian formalism for the latter is then pulled back onto the infinite dimensional phase space of the nonlocal system.

Geometric Hamiltonian quantum mechanics and applications

2016 ◽  
Vol 13 (Supp. 1) ◽  
pp. 1630017 ◽  
Author(s):  
Davide Pastorello
Keyword(s):  
Quantum Mechanics ◽  
Phase Space ◽  
Projective Space ◽  
Star Product ◽  
Hamiltonian Formulation ◽  
Classical Mechanics ◽  
Point Of View ◽  
Quantum Theories ◽  
Geometric Point ◽  
Set Up

Adopting a geometric point of view on Quantum Mechanics is an intriguing idea since, we know that geometric methods are very powerful in Classical Mechanics then, we can try to use them to study quantum systems. In this paper, we summarize the construction of a general prescription to set up a well-defined and self-consistent geometric Hamiltonian formulation of finite-dimensional quantum theories, where phase space is given by the Hilbert projective space (as Kähler manifold), in the spirit of celebrated works of Kibble, Ashtekar and others. Within geometric Hamiltonian formulation quantum observables are represented by phase space functions, quantum states are described by Liouville densities (phase space probability densities), and Schrödinger dynamics is induced by a Hamiltonian flow on the projective space. We construct the star-product of this phase space formulation and some applications of geometric picture are discussed.

DISSIPATIVE SOLITON PULSATIONS WITH PERIODS BEYOND THE LASER CAVITY ROUND TRIP TIME

2005 ◽  
Vol 14 (02) ◽  
pp. 177-194 ◽  
Author(s):  
N. AKHMEDIEV ◽  
J. M. SOTO-CRESPO ◽  
M. GRAPINET ◽  
Ph. GRELU
Keyword(s):  
Phase Space ◽  
Nonlinear System ◽  
Fiber Laser ◽  
Laser Cavity ◽  
Continuous Model ◽  
Round Trip Time ◽  
Round Trip ◽  
Infinite Dimensional ◽  
Trip Time ◽  
Dimensional Phase Space

We review recent results on periodic pulsations of the soliton parameters in a passively mode-locked fiber laser. Solitons change their shape, amplitude, width and velocity periodically in time. These pulsations are limit cycles of a dissipative nonlinear system in an infinite-dimensional phase space. Pulsation periods can vary from a few to hundreds of round trips. We present a continuous model of a laser as well as a model with parameter management. The results of the modeling are supported with experimental results obtained using a fiber laser.

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