scholarly journals Partial Differential Hamiltonian Systems

2013 ◽  
Vol 65 (5) ◽  
pp. 1164-1200 ◽  
Author(s):  
Luca Vitagliano
Keyword(s):  
Field Theory ◽  
Phase Space ◽  
Hamiltonian Systems ◽  
Geometric Structure ◽  
Symplectic Manifolds ◽  
Geometric Object ◽  
Noether Theorem ◽  
Partial Differential ◽  
Hamilton Equations ◽  
Dynamical Information

AbstractWe define partial differential (PD in the following), i.e., field theoretic analogues ofHamiltonian systems on abstract symplectic manifolds and study their main properties, namely, PD Hamilton equations, PD Noether theorem, PD Poisson bracket, etc. Unlike the standard multisymplectic approach to Hamiltonian field theory, in our formalism, the geometric structure (kinematics) and the dynamical information on the “phase space” appear as just different components of one single geometric object.

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 Phase Space Homogenization of Noisy Hamiltonian Systems

2018 ◽  
Vol 19 (4) ◽  
pp. 1081-1114 ◽  
Author(s):  
Jeremiah Birrell ◽  
Jan Wehr
Keyword(s):  
Phase Space ◽  
Hamiltonian Systems

scholarly journals Non-Smooth Geodesic Flows and Classical Mechanics

1969 ◽  
Vol 12 (2) ◽  
pp. 209-212 ◽  
Author(s):  
J. E. Marsden
Keyword(s):  
Phase Space ◽  
Kinetic Energy ◽  
Hamiltonian Systems ◽  
Configuration Space ◽  
Smooth Function ◽  
Cotangent Bundle ◽  
Classical Mechanics ◽  
Riemannian Metric ◽  
Geodesic Flows ◽  
Image Position

As is well known, there is an intimate connection between geodesic flows and Hamiltonian systems. In fact, if g is a Riemannian, or pseudo-Riemannian metric on a manifold M (we think of M as q-space or the configuration space), we may define a smooth function Tg on the cotangent bundle T*M (q-p-space, or the phase space). This function is the kinetic energy of q, and locally is given by

Ergodic properties and Weyl M-functions for random linear Hamiltonian systems

2000 ◽  
Vol 130 (5) ◽  
pp. 1045-1079 ◽  
Author(s):  
R. Johnson ◽  
S. Novo ◽  
R. Obaya
Keyword(s):  
Hamiltonian Systems ◽  
Qualitative Description ◽  
Invariant Region ◽  
Absolutely Continuous ◽  
Hamiltonian Equations ◽  
Radial Limits ◽  
Ergodic Properties ◽  
Ergodic Measures ◽  
Linear Hamiltonian Systems ◽  
Dynamical Information

This paper provides a topological and ergodic analysis of random linear Hamiltonian systems. We consider a class of Hamiltonian equations presenting absolutely continuous dynamics and prove the existence of the radial limits of the Weyl M-functions in the L1-topology. The proof is based on previous ergodic relations obtained for the Floquet coefficient. The second part of the paper is devoted to the qualitative description of disconjugate linear Hamiltonian equations. We show that the principal solutions at ±∞ define singular ergodic measures, and determine an invariant region in the Lagrange bundle which concentrates the essential dynamical information. We apply this theory to the study of the n-dimensional Schrödinger equation at the first point of the spectrum.

Hamiltonian Dynamics and Phase Space

2019 ◽  
pp. 83-108
Author(s):  
David D. Nolte
Keyword(s):  
Phase Space ◽  
Hamiltonian Systems ◽  
Hamiltonian Dynamics ◽  
Orbital Dynamics ◽  
Legendre Transform ◽  
Lagrange Equations ◽  
Conservation Of Energy ◽  
Hamiltonian Equations ◽  
Generalized Coordinates ◽  
Conservation Of Momentum

Hamiltonian dynamics are derived from the Lagrange equations through the Legendre Transform that expresses the equations of dynamics in terms of the Hamiltonian, which is a function of the generalized coordinates and of their conjugate momenta. Consequences of the Lagrangian and Hamiltonian equations of dynamics are conservation of energy and conservation of momentum, with applications to collisions and orbital dynamics. Action-angle coordinates can be defined for integrable Hamiltonian systems and reduce all dynamical motions to phase space trajectories on a hyperdimensional torus.

scholarly journals Kinetic field theory: exact free evolution of Gaussian phase-space correlations

2018 ◽  
Vol 2018 (4) ◽  
pp. 043214 ◽  
Author(s):  
Felix Fabis ◽  
Elena Kozlikin ◽  
Robert Lilow ◽  
Matthias Bartelmann
Keyword(s):  
Field Theory ◽  
Phase Space ◽  
Free Evolution ◽  
Kinetic Field
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