scholarly journals QUANTUM MECHANICS OF A CHARGED PARTICLE IN A BACKGROUND MAGNETIC FIELD INTERACTING WITH LINEARIZED GRAVITATIONAL WAVES

2012 ◽  
Vol 27 (35) ◽  
pp. 1250192 ◽  
Author(s):  
SUNANDAN GANGOPADHYAY ◽  
ANIRBAN SAHA
Keyword(s):  
Charged Particle ◽  
Gravitational Waves ◽  
Quantum Dynamics ◽  
Resonance Condition ◽  
Close Association ◽  
Wave Length ◽  
Geodesic Equation ◽  
Low Velocity ◽  
Deviation Equation ◽  
Background Magnetic Field

We present the quantum dynamics of a charged particle interacting simultaneously with background electromagnetic field and linearized gravitational waves in the long wave-length and low-velocity limit. We start from the geodesic deviation equation, considering its close association with the proper detector frame, rather than the usual geodesic equation which is solved classically in the existing literature. The Hamiltonian is obtained, quantized and solved by using algebraic iterative methods. The solution shows conformity with the classical analysis by exhibiting the same resonance condition.

scholarly journals Relativistic top deviation equation and gravitational waves

2003 ◽  
Vol 312 (3-4) ◽  
pp. 175-186 ◽  
Author(s):  
J.A. Nieto ◽  
J. Saucedo ◽  
V.M. Villanueva
Keyword(s):  
Gravitational Waves ◽  
Deviation Equation

scholarly journals SYMMETRIES OF THE NEAR HORIZON OF A BLACKHOLE BY GROUP THEORETIC METHODS

2007 ◽  
Vol 22 (08n09) ◽  
pp. 1717-1726
Author(s):  
K. MAHARANA
Keyword(s):  
Black Hole ◽  
Charged Particle ◽  
Magnetic Fields ◽  
Lie Algebras ◽  
Quantum Dynamics ◽  
Equations Of Motion ◽  
Scalar Particle ◽  
Lie Point Symmetries

We use group theoretic methods to obtain the extended Lie point symmetries of the quantum dynamics of a scalar particle probing the near horizon structure of a black hole. Symmetries of the classical equations of motion for a charged particle in the field of an inverse square potential and a monopole, in the presence of certain model magnetic fields and potentials are also studied. Our analysis gives the generators and Lie algebras generating the inherent symmetries.

Elastic wave propagation along layers in two-dimensional models

1963 ◽  
Vol 53 (3) ◽  
pp. 593-618
Author(s):  
D. K. Chowdhury ◽  
Peter Dehlinger
Keyword(s):  
Layer Thickness ◽  
High Velocity ◽  
Wave Length ◽  
Two Dimensional ◽  
Layer Model ◽  
Low Velocity ◽  
Long Period ◽  
Low Velocity Layer ◽  
High Velocity Layer ◽  
Velocity Layer

Abstract Propagation of direct waves and dispersive long-period waves along a layered system was investigated experimentally by means of two-dimensional ultrasonic models. Velocities of direct and head waves were measured within layers or in a medium adjacent to layers as functions of layer thickness to wave length or source-from-interface distance to wave length. Amplitudes of direct longitudinal, direct shear, and long-period waves were measured on three profiles, each perpendicular to the layers. Three models were used: the first consisted of a low-velocity layer between two thick sheets; the second of a high-velocity layer between two sheets; the third of six alternating high- and low-velocity layers between two sheets. The source was a wave train, simulating a wave from a seismic explosion. The frequency was varied so as to obtain different ratios of layer thickness to wave length. In the single low-velocity layer model the direct longitudinal wave contained a larger amplitude than the dispersive long-period wave in the layer at offset distance of 6 to 10 times the layer thickness. In the single high-velocity layer model the direct longitudinal wave was attenuated rapidly and the amplitudes of the long-period waves were negligigble. In the multilayered model, direct waves had negligible amplitudes at the corresponding distances; nearly all of the energy was in the dispersive long-period waves. In this model the low-velocity layer carried 1 1/2 to 3 times the amplitude observed in the high-velocity layers, whether the source was located in the high- or low-velocity layers. Dispersion of the long-period waves in the multilayered model was pronounced within the low-velocity layers and weak in the high-velocity layers, when the source was either in a high- or low-velocity layer. Dispersion was anomalous when the source was in a low-velocity layer and normal when in a high-velocity layer.

CHARGED PARTICLE DYNAMICS IN THE FIELD OF A SLOWLY ROTATING COMPACT STAR

2005 ◽  
Vol 14 (03n04) ◽  
pp. 609-620 ◽  
Author(s):  
BABUR M. MIRZA
Keyword(s):  
Electromagnetic Field ◽  
Charged Particle ◽  
Compact Star ◽  
Equations Of Motion ◽  
Geodesic Equation ◽  
Slow Rotation ◽  
Axially Symmetric ◽  
Kerr Spacetime ◽  
Frame Dragging ◽  
Set Up

We study the dynamics of a charged particle in the field of a slowly rotating compact star in the gravitoelectromagnetic approximation to the geodesic equation. The star is assumed to be surrounded by an ideal, highly conducting plasma (taken as a magneto-hydrodynamic fluid) with a stationary, axially symmetric electromagnetic field. The general relativistic Maxwell equations are solved to obtain the effects of the background spacetime on the electromagnetic field in the linearized Kerr spacetime. The equations of motion are then set up and solved numerically to incorporate the gravitational as well as the electromagnetic effects. The analysis shows that in the slow rotation approximation, the frame dragging effects on the electromagnetic field are absent. However the particle is directly effected by the rotating gravitational source such that close to the star the gravitational and electromagnetic field produce contrary effects on the particle trajectories.

scholarly journals Some clarifications about the Bohmian geodesic deviation equation and Raychaudhuri’s equation

2018 ◽  
Vol 33 (03) ◽  
pp. 1850027
Author(s):  
Faramarz Rahmani ◽  
Mehdi Golshani
Keyword(s):  
Quantum Mechanics ◽  
Geodesic Equation ◽  
Theory Of Relativity ◽  
General Theory Of Relativity ◽  
Geodesic Deviation ◽  
Standard Quantum ◽  
Relativity And Gravitation ◽  
Singularity Theorems ◽  
Deviation Equation ◽  
Definition Of

One of the important and famous topics in general theory of relativity and gravitation is the problem of geodesic deviation and its related singularity theorems. An interesting subject is the investigation of these concepts when quantum effects are considered. Since the definition of trajectory is not possible in the framework of standard quantum mechanics (SQM), we investigate the problem of geodesic equation and its related topics in the framework of Bohmian quantum mechanics in which the definition of trajectory is possible. We do this in a fixed background and we do not consider the backreaction effects of matter on the space–time metric.

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