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Search Results: 1 - 10 of 145259 matches for " F. Haas "
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Variational approach for the quantum Zakharov system
F. Haas
Physics , 2007, DOI: 10.1063/1.2722271
Abstract: The quantum Zakharov system is described in terms of a Lagrangian formalism. A time-dependent Gaussian trial function approach for the envelope electric field and the low-frequency part of the density fluctuation leads to a coupled, nonlinear system of ordinary differential equations. In the semiclassic case, linear stability analysis of this dynamical system shows a destabilizing r\^ole played by quantum effects. Arbitrary value of the quantum effects are also considered, yielding the ultimate destruction of the localized, Gaussian trial solution. Numerical simulations are shown both for the semiclassic and the full quantum cases.
Harris sheet solution for magnetized quantum plasmas
F. Haas
Physics , 2006,
Abstract: We construct an infinite family of one-dimensional equilibrium solutions for purely magnetized quantum plasmas described by the quantum hydrodynamic model. The equilibria depends on the solution of a third-order ordinary differential equation, which is written in terms of two free functions. One of these free functions is associated to the magnetic field configuration, while the other is specified by an equation of state. The case of a Harris sheet type magnetic field, together with an isothermal distribution, is treated in detail. In contrast to the classical Harris sheet solution, the quantum case exhibits an oscillatory pattern for the density.
Noether symmetries for charged particle motion under a magnetic monopole and general electric fields
F. Haas
Physics , 2002,
Abstract: The search for Noether point symmetries for non-relativistic charged particle motion is reduced to the solution for a set of two coupled, linear partial differential equations for the electromagnetic field. These equations are completely solved when the magnetic field is produced by a fixed magnetic monopole. The result is applied to central electric field cases, in particular to the time-dependent monopole-oscillator problem. As an additional example of the theory, we found all Noether point symmetries and invariants for a constant magnetic field and a time-dependent harmonic electric field with a forcing term.
Generalized Hamiltonian structures for Ermakov systems
F. Haas
Physics , 2002, DOI: 10.1088/0305-4470/35/12/314
Abstract: We construct Poisson structures for Ermakov systems, using the Ermakov invariant as the Hamiltonian. Two classes of Poisson structures are obtained, one of them degenerate, in which case we derive the Casimir functions. In some situations, the existence of Casimir functions can give rise to superintegrable Ermakov systems. Finally, we characterize the cases where linearization of the equations of motion is possible.
Anisotropic Bose-Einstein condensates and completely integrable dynamical systems
F. Haas
Physics , 2002, DOI: 10.1103/PhysRevA.65.033603
Abstract: A Gaussian ansatz for the wave function of two-dimensional harmonically trapped anisotropic Bose-Einstein condensates is shown to lead, via a variational procedure, to a coupled system of two second-order, nonlinear ordinary differential equations. This dynamical system is shown to be in the general class of Ermakov systems. Complete integrability of the resulting Ermakov system is proven. Using the exact solution, collapse of the condensate is analyzed in detail. Time-dependence of the trapping potential is allowed.
Frobenius theorem and invariants for Hamiltonian systems
F. Haas
Physics , 2002, DOI: 10.1088/0305-4470/34/5/306
Abstract: We apply Frobenius integrability theorem in the search of invariants for one-dimensional Hamiltonian systems with a time-dependent potential. We obtain several classes of potential functions for which Frobenius theorem assures the existence of a two-dimensional foliation to which the motion is constrained. In particular, we derive a new infinite class of potentials for which the motion is assurately restricted to a two-dimensional foliation. In some cases, Frobenius theorem allows the explicit construction of an associated invariant. It is proven the inverse result that, if an invariant is known, then it always can be furnished by Frobenius theorem.
Stochastic Quantization of the Time-Dependent Harmonic Oscillator
F. Haas
Physics , 2004,
Abstract: We extend the stochastic quantization method recently developed by Haba and Kleinert to non-autonomous mechanical systems, in the case of the time-dependent harmonic oscillator. In comparison with the autonomous case, the quantization procedure involves the solution of a nonlinear, auxiliary equation.
Variational Method for the Three-Dimensional Many-Electron Dynamics of Semiconductor Quantum Wells
F. Haas
Physics , 2012, DOI: 10.1063/1.3679590
Abstract: The three-dimensional nonlinear dynamics of an electron gas in a semiconductor quantum well is analyzed in terms of a self-consistent fluid formulation and a variational approach. Assuming a time-dependent localized profile for the fluid density and appropriated spatial dependences of the scalar potential and fluid velocity, a set of ordinary differential equations is derived. In the radially symmetric case, the prominent features of the associated breathing mode are characterized.
Jacobi Structures in $\mathbb{R}^3$
F. Haas
Mathematics , 2005, DOI: 10.1063/1.2040347
Abstract: The most general Jacobi brackets in $\mathbb{R}^3$ are constructed after solving the equations imposed by the Jacobi identity. Two classes of Jacobi brackets were identified, according to the rank of the Jacobi structures. The associated Hamiltonian vector fields are also constructed.
Connection between the two branches of the quantum two-stream instability across the k space
A. Bret,F. Haas
Physics , 2010, DOI: 10.1063/1.3400228
Abstract: The stability of two quantum counter-streaming electron beams is investigated within the quantum plasma fluid equations for arbitrarily oriented wave vectors. The analysis reveals that the two quantum two-stream unstable branches are indeed connected by a continuum of unstable modes with oblique wave vectors. Using the longitudinal approximation, the stability domain for any k is analytically explained, together with the growth rate.
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