Effective Hamiltonian Theory and its Application to Wave Propagation and Interaction in the Presence of Fluctuations.

Details Effective Hamiltonian Theory and its Application to Wave Propagation and Interaction in the Presence of Fluctuations. Effective Hamiltonian Theory and its Application to Wave Propagation and Interaction in the Presence of Fluctuations.

Feb 1991

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1991phdt........67l&link_type=abstract

Thesis (PH.D.)--UNIVERSITY OF MARYLAND COLLEGE PARK, 1991.Source: Dissertation Abstracts International, Volume: 52-09, Section:

Physics

Condensed Matter

Statistical Mechanics

Scientific paper

Many problems in wave propagation and wave interaction in the presence of fluctuations can be formulated in terms of linear stochastic differential equations of Hamiltonian form partialtpsi=H( beta(t))psi, with the fluctuation strength represented by the parameter beta(t). The effect of fluctuations can be investigated by studying the dynamics of the ensemble averaged quantity . It is shown that the dynamics of is described by its effective Hamiltonian H _{rm eff}. This formalism is shown to be more intuitive than the traditional Green's function method. It can be used to handle inhomogeneous and boundary value problems with ease even when the application of the Green's function method faces difficulties or is inapplicable. The new framework is applied to the problems of wave propagation in one dimensional media with fluctuations and of parametric instabilities in the presence of space -time fluctuations in homogeneous and inhomogeneous plasmas. The importance of this analytical theory is that it is independent of the strength of the fluctuations. Some numerical simulations are presented to support the theoretical result. Interestingly, we discover an important connection between the wave traveling in the random medium and the phase transition formulism in statistical mechanics.

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