950 research outputs found
State-space distribution and dynamical flow for closed and open quantum systems
We present a general formalism for studying the effects of dynamical
heterogeneity in open quantum systems. We develop this formalism in the state
space of density operators, on which ensembles of quantum states can be
conveniently represented by probability distributions. We describe how this
representation reduces ambiguity in the definition of quantum ensembles by
providing the ability to explicitly separate classical and quantum sources of
probabilistic uncertainty. We then derive explicit equations of motion for
state space distributions of both open and closed quantum systems and
demonstrate that resulting dynamics take a fluid mechanical form analogous to a
classical probability fluid on Hamiltonian phase space, thus enabling a
straightforward quantum generalization of Liouville's theorem. We illustrate
the utility of our formalism by analyzing the dynamics of an open two-level
system using the state-space formalism that are shown to be consistent with the
derived analytical results
Adiabatic nonlinear waves with trapped particles: III. Wave dynamics
The evolution of adiabatic waves with autoresonant trapped particles is
described within the Lagrangian model developed in Paper I, under the
assumption that the action distribution of these particles is conserved, and,
in particular, that their number within each wavelength is a fixed independent
parameter of the problem. One-dimensional nonlinear Langmuir waves with deeply
trapped electrons are addressed as a paradigmatic example. For a stationary
wave, tunneling into overcritical plasma is explained from the standpoint of
the action conservation theorem. For a nonstationary wave, qualitatively
different regimes are realized depending on the initial parameter , which is
the ratio of the energy flux carried by trapped particles to that carried by
passing particles. At , a wave is stable and exhibits group velocity
splitting. At , the trapped-particle modulational instability (TPMI)
develops, in contrast with the existing theories of the TPMI yet in agreement
with the general sideband instability theory. Remarkably, these effects are not
captured by the nonlinear Schr\"odinger equation, which is traditionally
considered as a universal model of wave self-action but misses the
trapped-particle oscillation-center inertia.Comment: submitted together with Papers I and I
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