• N Kumar

      Articles written in Proceedings – Section A

    • Insulator-metal transition

      N Kumar K P Sinha

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      A theory of the insulator-metal transition in transition-metal compounds is developed in terms of the collapse of the effective energy gap which is a function of the thermally excited electron-hole pairs. This dependence is shown to arise from the hole-lattice interaction. The reaction of the lattice is found to be equivalent to generating an internal positive pressure (strain). Estimates show that the observed typical behaviour of the conductivity jump and the change of volume at the transition temperature can be explained by the present theory.

    • Quantum kinematics of Fermi-Dirac vacuum-plus-one-electron problem

      N Kumar

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      Following Weisskopf, the kinematics of quantum mechanics is shown to lead to a modified charge distribution for a test electron embedded in the Fermi-Dirac vacuum with interesting consequences.

    • Quantum theoretic explanation of the Schwarz-Hora effect

      N Kumar K P Sinha

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      Following the path-integral approach we show that the Schwarz-Hora effect is a one-electron quantum-mechanical phenomenon in that the de Broglie wave associated with a single electron is modulated by the oscillating electric field. The treatment brings out the crucial role played by the crystal in providing a discontinuity in the longitudinal component of the electric field. The expression derived for the resulting current density shows the appropriate oscillatory behaviour in time and distance. The possibility of there being a temporal counterpart of Aharonov-Bohm effect is briefly discussed in this context.

    • On mass quantisation of elementary particles

      N Kumar M Muthanna K P Sinha

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      A semi-phenomenological theory of mass quantisation is presented, wherein different elementary particles are regarded as excited positiveenergy states of a fundamental extensible object. The latter is essentially an elastic continuum which in its quiescent (classical equilibrium) state is believed to be massless and stressless. The classical Hamiltonian describing its oscillations about the equilibrium configuration is constructed by treating the mass-equivalent of the elastic potential energy as the inertial mass occurring in the denominator of the kinetic energy term. Quantisation of the resulting variable-mass oscillator is then effected by following the procedure given by Pauli and Podolsky.

      The energy-mass eigenvalues (mn) for the above Schrödinger-like equation are given by$$\frac{{m_n }}{{m_0 }} = \left[ {1 + \left( {\frac{9}{2}} \right)^{1/3} \left( {\frac{{\mathchar'26\mkern-10mu\lambda _0 }}{2}} \right)^{2/3} p_n ^{2/3} } \right]$$ where ƛ0 is the Compton wavelength of the lowest (ground state) eigen massm0, rc is the measure of the linear dimension of the object, andpn is the nth root of the Bessel function of order 1/3. In view of their infinite lifetime we treat the electron and the proton as the ground states for the two families of particles with baryon numbers zero and unity respectively. Accordingly, for the two families,m0 andrc are chosen to correspond to the electron and the proton. The calculated mass values show striking agreement with the observed values for the two series.

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