R K Varma
Articles written in Pramana – Journal of Physics
Volume 8 Issue 3 March 1977 pp 229-244 Astrophysics
Charged particle trajectories in a magnetic field on a curved space-time
In this paper we have studied the motion of charged particles in a dipole magnetic field on the Schwarzscbild background geometry. A detailed analysis has been made in the equatorial plane through the study of the effective potential curves. In the case of positive canonical angular momentum the effective potential has two maxima and two minima giving rise to a well-defined potential well rear the event horizon. This feature of the effective potential categorises the particle orbits into four classes, depending on their energies. (i) Particles, coming from infinity with energy less than the absolute maximum of
In the case when particles are not confined to the equatorial plane we have found that the particles execute oscillatory motion between two mirror points if the magnetic field is sufficiently high, but would continuously fall towards the event horizon otherwise.
Volume 8 Issue 4 April 1977 pp 395-395 Erratum
Charged particle trajectories in a magnetic field on a curved space-time
Volume 10 Issue 1 January 1978 pp 89-113 Quantum Mechanics
In this paper we propose a deterministic basis for quantum mechanics and give equations of motion (derivable from an action principle) which describe deterministic trajectories in an extended space that the quantum events are assumed to follow. By applying the laws of classical probability, namely the conservation of probability along the deterministic trajectories, we derive a probability description which is found to be a generalization of the Schrödinger description with built-in probability interpretation. The generalized description admits of an infinite number of wave functions following coupled set of Schrödinger-like equations while the total probability is given by the sum of the modulus squared of all these wave functions, one of which is identified as the Schrödinger function. If all the functions other than the Schrödinger wave function be neglected the Schrödinger description is retrieved. It is thus concluded that the classical probability not only embrances probability in quantum mechanics but allows other new modes for its propagation.
We thus predict new modes of quantum behaviour and we discuss two situations and propose experiments where these modes could be looked for. Finally, our theory also provides an identification for the quantum of action, ħ.
Volume 16 Issue 2 February 1981 pp 131-138 Plasma Physics
Feedback stabilization of drift cyclotron loss cone instability by modulated electron sources
It is shown that the drift cyclotron loss cone instability can be suppressed by modulating electron density within the plasma. With the feedback in +90° phase the critical density gradient needed for the onset of the drift cyclotron loss cone instability increases approximately linearly with the gain. Typically with the gain of −50Ω_{i} the critical density gradient can be pushed up by as much as two orders of magnitude and minimum mirror plasma radius can be brought down in the same proportion.
Volume 23 Issue 3 September 1984 pp 369-379 Quantum Mechanics
A geometric generalization of classical mechanics and quantization
A geometrization of classical mechanics is presented which may be considered as a realization of the Hertz picture of mechanics. The trajectories in the
When the additional (angular) coordinate is not cyclic we obtain what may be regarded as a generalization of classical mechanics in a geometrized form. This defines new motions in the neighbourhood of the classical motions. It has been shown that, when the angular coordinate is “quasi-cyclic”, these new motions can be used to describe events in the quantum domain with appropriate periodicity conditions on the geodesics in
Volume 49 Issue 1 July 1997 pp 17-31 Quantum Mechanics
A generalized Schrödinger formalism has been presented which is obtained as a Hilbert space representation of a Liouville equation generalized to include the action as a dynamical variable, in addition to the positions and the momenta. This formalism applied to a classical mechanical system had been shown to yield a similar set of Schrödinger like equations for the classical dynamical system of charged particles in a magnetic field. The novel quantum-like predictions for this classical mechanical system have been experimentally demonstrated and the results are presented.
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