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1 
Analysis of Multidimensional Phase Space Hamiltonian Dynamics: Methods and ApplicationsShchekinova, Elena Y. 17 March 2006 (has links)
Diverse complex phenomena that are found in many fundamental
problems of atomic physics and chemistry can be understood in the
framework of nonlinear theory. Most of simple atomic and chemical
systems are classically described by the Hamiltonian models of
dimension three and higher. The multidimensional nature of these
problems makes widely used diagnostics of dynamics to be
impractical. We demonstrate the application of rigorous and
effective computational methods to treat multidimensional systems
in strongly perturbative regimes.
The results of a qualitative analysis of the phase space stability
structures are presented for two multidimensional nonintegrable
Hamiltonian systems: highly excited planar carbonyl sulfide
molecule and hydrogen atom in elliptically polarized microwave
fields. The molecular system of the planar carbonyl sulfide and
atomic system of hydrogen in elliptically polarized microwave
fields are treated for different regimes of energies including
regimes of classical ionization of hydrogen and dissociation of
carbonyl sulfide molecule.

2 
Classical and quantum quadratic Hamiltonians / by Philip BroadbridgeBroadbridge, Philip January 1982 (has links)
Typescript (photocopy) / 198 leaves ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.)University of Adelaide, Dept. of Mathematical Physics, 1983

3 
Classical and quantum quadratic Hamiltonians /Broadbridge, Philip. January 1982 (has links) (PDF)
Thesis (Ph.D.)  University of Adelaide, Dept of Mathematical Physics, 1983. / Typescript (photocopy).

4 
Analysis of multidimensional phase space Hamiltonian dynamics methods and applications /Shchekinova, Elena Y. January 2006 (has links)
Thesis (Ph. D.)Physics, Georgia Institute of Technology, 2006. / Mustafa Aral, Committee Member ; John Wood, Committee Member ; Kurt Wiesenfeld, Committee Member ; M. Raymond Flannery, Committee Member ; Turgay Uzer, Committee Chair.

5 
Symplectic Integration of Nonseparable Hamiltonian SystemsCurry, David M. (David Mason) 05 1900 (has links)
Numerical methods are usually necessary in solving Hamiltonian systems since there is often no closedform solution. By utilizing a general property of Hamiltonians, namely the symplectic property, all of the qualities of the system may be preserved for indefinitely long integration times because all of the integral (Poincare) invariants are conserved. This allows for more reliable results and frequently leads to significantly shorter execution times as compared to conventional methods. The resonant triad Hamiltonian with one degree of freedom will be focused upon for most of the numerical tests because of its difficult nature and, moreover, analytical results exist whereby useful comparisons can be made.

6 
Stochastic calculus, gauge fixing, and the quantization of constrained systemsLeppard, Steven January 2000 (has links)
No description available.

7 
Stability analysis of homogeneous shear flow : the linear and nonlinear theories and a Hamiltonian formulationHagelberg, Carl R. 17 October 1989 (has links)
The stability of steadystate solutions of the equations governing twodimensional,
homogeneous, incompressible fluid flow are analyzed in the context
of shearflow in a channel. Both the linear and nonlinear theories are
reviewed and compared. In proving nonlinear stability of an equilibrium,
emphasis is placed on using the stability algorithm developed in Holm et al.
(1985). It is shown that for certain types of equilibria the linear theory is
inconclusive, although nonlinear stability can be proven.
Establishing nonlinear stability is dependent on the definition of a norm
on the space of perturbations. McIntyre and Shepherd (1987) specifically
define five norms, two for corresponding to one flow state and three to a
different flow state, and suggest that still others are possible. Here, the
norms given by McIntyre and Shepherd (1987) are shown to induce the same
topology (for the corresponding flow states), establishing their equivalence as
norms, and hence their equivalence as measures of stability. Summaries of the
different types of stability and their mathematical definitions are presented.
Additionally, a summary of conditions on shearflow equilibria under which
the various types of stability have been proven is presented.
The Hamiltonian structure of the twodimensional Euler equations is
outlined following Olver (1986). A coordinatefree approach is adopted emphasizing
the role of the Poisson bracket structure. Direct calculations are
given to show that the Casimir invariants, or distinguished functionals, are
timeindependent and therefore are conserved quantities in the usual sense. / Graduation date: 1990

8 
Spatial evaluation of Lyapunov exponents in Hamiltonian systemsStanley, Paul Elliott 11 December 1995 (has links)
A new method for evaluating the Lyapunov exponent for a Hamiltonian system
involves a spatial evaluation, rather than a numerical time integration. The
introduction of a novel vector field to the phase space allows the Lyapunov exponent
to be expressed in a form that does not involve time. The Lyapunov exponent
is seen to be a property of the geometry and topology of ergodic regions of phase
space. As a result it has a more regular behavior than previously thought. The
Lyapunov exponent is found to be a differentiable function of the perturbation coupling
in regions where it was previously thought to be discontinuous. Properties
of the Lyapunov function once taken for granted are shown to be artifacts of the
traditional computation methods. The technique is discussed with examples from a
system of coupled quartic oscillators. / Graduation date: 1996

9 
Starunitary transformation and stochasticity emergence of white, 1/f noise through resonances /Kim, Sungyun. January 2002 (has links) (PDF)
Thesis (Ph. D.)University of Texas at Austin, 2002. / Vita. Includes bibliographical references. Available also from UMI Company.

10 
Ray and wave dynamics in three dimensional asymmetric optical resonators /Lacey, Scott Michael, January 2003 (has links)
Thesis (Ph. D.)University of Oregon, 2003. / Typescript. Includes vita and abstract. Includes bibliographical references (leaves 184187). Also available for download via the World Wide Web; free to University of Oregon users.

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