Prequantum Dynamics from Hamiltonian Equations on the Infinite-Dimensional Phase Space

2014 ◽  
pp. 167-192
Keyword(s):  
Phase Space ◽  
Hamiltonian Equations ◽  
Infinite Dimensional ◽  
Dimensional Phase Space

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.

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.

A one-dimensional self-gravitating stellar gas

1966 ◽  
Vol 25 ◽  
pp. 46-48 ◽  
Author(s):  
M. Lecar
Keyword(s):  
Gravitational Field ◽  
Phase Space ◽  
Motion Picture ◽  
Space Distribution ◽  
Two Dimensional ◽  
One Dimensional ◽  
Phase Space Distribution ◽  
Dimensional Phase Space ◽  
The Mean

“Dynamical mixing”, i.e. relaxation of a stellar phase space distribution through interaction with the mean gravitational field, is numerically investigated for a one-dimensional self-gravitating stellar gas. Qualitative results are presented in the form of a motion picture of the flow of phase points (representing homogeneous slabs of stars) in two-dimensional phase space.

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