• R K Varma

      Articles written in Pramana – Journal of Physics

    • Charged particle trajectories in a magnetic field on a curved space-time

      A R Prasanna R K Varma

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      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 ofVeff, would scatter away after being turned away by the magnetic field. (ii) Whereas those with energies higher than this would go into the central star seeing no barrier. (iii) Particles initially located within the potential well are naturally trapped, and they execute Larmor motion in bound gyrating orbits. (iv) and those with initial positions corresponding to the extrema ofVeff follow circular orbits which are stable for non-relativistic particles and unstable for relativistic ones. We have also considered the case of negative canonical angular momentum and found that no trapping in bound orbits occur for this case.

      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.

    • Charged particle trajectories in a magnetic field on a curved space-time

      A R Prasanna R K Varma

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    • Deterministic model equations of motion for quantum mechanics and some new modes of quantum behaviour

      R K Varma

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      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.

    • Feedback stabilization of drift cyclotron loss cone instability by modulated electron sources

      Avinash R K Varma

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      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 −50Ωi 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.

    • A geometric generalization of classical mechanics and quantization

      R K Varma

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      A geometrization of classical mechanics is presented which may be considered as a realization of the Hertz picture of mechanics. The trajectories in thef-dimensional configuration spaceVf of a classical mechanical system are obtained as the projections onVf of the geodesics in an (f + 1) dimensional Riemannian spaceVf + 1, with an appropriate metric, if the additional (f + 1)th coordinate, taken to be an angle, is assumed to be “cyclic”.

      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 inVf + 1.

    • A generalized Schrödinger formalism as a Hilbert space representation of a generalized Liouville equation

      R K Varma

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      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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