scholarly journals Quantum field dynamics in a uniform magnetic field: Description using fields in oblique phase space

2002 ◽  
Vol 65 (4) ◽  
Author(s):  
Seok Kim ◽  
Choonkyu Lee ◽  
Kimyeong Lee
Keyword(s):  
Magnetic Field ◽  
Phase Space ◽  
Uniform Magnetic Field ◽  
Quantum Field

Nonlinear interaction between longitudinal waves in a magnetized plasma

1978 ◽  
Vol 19 (3) ◽  
pp. 405-410 ◽  
Author(s):  
A. A. Selim
Keyword(s):  
Magnetic Field ◽  
Field Theory ◽  
Quantum Field Theory ◽  
Nonlinear Interaction ◽  
Uniform Magnetic Field ◽  
Magnetized Plasma ◽  
Quantum Field ◽  
Arbitrary Angle ◽  
Longitudinal Waves ◽  
Coupled Mode

Quantum field theory is used to investigate the resonant nonlinear interaction between three longitudinal waves propagating at any arbitrary angle to a uniform magnetic field in a plasma. The coupled mode equations, coupling coefficient and a formula for the growth rates are derived.

scholarly journals Coherent State Quantization and Moment Problem

10.14311/1185 ◽  
2010 ◽  
Vol 50 (3) ◽  
Author(s):  
J. P. Gazeau ◽  
M. C. Baldiotti ◽  
D. M. Gitman
Keyword(s):  
Magnetic Field ◽  
Charged Particle ◽  
Energy Spectrum ◽  
Phase Space ◽  
Coherent State ◽  
Moment Problem ◽  
Coherent States ◽  
Uniform Magnetic Field ◽  
Classical Motion ◽  
Negative Numbers

Berezin-Klauder-Toeplitz (“anti-Wick”) or “coherent state” quantization of the complex plane, viewed as the phase space of a particle moving on the line, is derived from the resolution of the unity provided by the standard (or gaussian) coherent states. The construction of these states and their attractive properties are essentially based on the energy spectrum of the harmonic oscillator, that is on natural numbers. We follow in this work the same path by considering sequences of non-negative numbers and their associated “non-linear” coherent states. We illustrate our approach with the 2-d motion of a charged particle in a uniform magnetic field. By solving the involved Stieltjes moment problem we construct a family of coherent states for this model. We then proceed with the corresponding coherent state quantization and we show that this procedure takes into account the circle topology of the classical motion.

scholarly journals WIGNER FUNCTIONS FOR THE LANDAU PROBLEM IN NONCOMMUTATIVE SPACES

2002 ◽  
Vol 17 (29) ◽  
pp. 1937-1944 ◽  
Author(s):  
ÖMER F. DAYI ◽  
LARA T. KELLEYANE
Keyword(s):  
Magnetic Field ◽  
Phase Space ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Uniform Magnetic Field ◽  
Effective Hamiltonian ◽  
Wigner Functions ◽  
Noncommutative Spaces

An electron moving on plane in a uniform magnetic field orthogonal to the plane is known as the Landau problem. Wigner functions for the Landau problem when the plane is noncommutative are found employing solutions of the Schrödinger equation as well as solving the ordinary ⋆-genvalue equation in terms of an effective Hamiltonian. Then, we let momenta and coordinates of the phase space be noncommutative and introduce a generalized ⋆-genvalue equation. We solve this equation to find the related Wigner functions and show that under an appropriate choice of noncommutativity relations they are independent of noncommutativity parameter.

Nonlinear effects of two modified ordinary monochromatic waves

1974 ◽  
Vol 12 (2) ◽  
pp. 287-295 ◽  
Author(s):  
A. A. Selim
Keyword(s):  
Magnetic Field ◽  
Field Theory ◽  
Uniform Magnetic Field ◽  
Nonlinear Effects ◽  
Field Amplitude ◽  
Physical Parameters ◽  
Quantum Field ◽  
Frequency Shifts ◽  
Diagrammatic Technique ◽  
Monochromatic Waves

Quantum field theory is used to investigate the nonlinear effects of two modified ordinary monochromatic waves propagating across a uniform magnetic field. Amplitude-dependent wavelength and frequency shifts are derived. Unlike previous work that employs the Krylov–Bogoliubov–Mitropolskii method, the investigation uses the diagrammatic technique of field theory. The calculations show that increase of the above-mentioned physical parameters due to nonlinear interaction and drifting electrons depends upon the ratio of drifting to phase velocity.

Theory of resonances observed in ionograms taken by sounders above the ionosphere

1966 ◽  
Vol 289 (1417) ◽  
pp. 214-234 ◽  
Keyword(s):  
Magnetic Field ◽  
Uniform Magnetic Field ◽  
Plasma Frequency ◽  
Relative Importance ◽  
Quantum Field ◽  
Zero Temperature ◽  
Complicated Structure ◽  
Hybrid Frequency ◽  
Hot Plasma ◽  
Zero Range

This paper describes a theory of the resonant effects observed by sounding equipment on the ionospheric satellite ‘Alouette’. The model consists of an oscillating dipole immersed in a uniform hot plasma with uniform magnetic field. A formal expression for the electric field throughout space is readily constructed. In simple cases (zero temperature and either no magnetic field or infinite light velocity) this reduces to an integral which can be evaluated analytically and the resonance shown explicitly. In general we try to locate the frequencies at which resonance will occur without evaluating the field. This can be done by the ‘pinching-poles’ technique used in quantum field theory. The results show that resonances would occur at the following frequencies: the plasma frequency, ω p ; the gyrofrequency of the electrons, Ω e and its harmonics n Ω e , the ‘hybrid’ frequency, (ω 2 p + Ω 2 e ) 1/2 and the ‘zero range’ frequencies, which satisfy ω 2 ± Ωω - ω 2 p = 0. Some idea of the relative importance of these resonances can also be gained for the theory. The fundamental of the gyrofrequency series, and the zero-range frequencies, would give only weak resonances. The series ω = n Ω e has a complicated structure, and is really the superposition of four series, some of which are slightly shifted from the exact harmonics.

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