Dr Candadi V Sukumar

Abstract:

Atoms confined in a magnetic trap can escape by making spin-flip Majorana transitions due to a breakdown of the adiabatic approximation. Several papers have studied this process for atoms with spin F=1 2 or 1. The present paper calculates the escape rate for atoms with spin F>1. This problem has new features because the perturbation ΔT that allows atoms to escape satisfies a selection rule Δ Fz =0,±1,±2 and multistep processes contribute in leading order. When the adiabatic approximation is satisfied, the leading-order terms can be summed to yield a simple expression for the escape rate. © 2006 The American Physical Society.

Abstract:

An integral relation is established between the Green functions corresponding to two Hamiltonians which are supersymmetric (SUSY) partners and in general may possess both discrete and continuous spectra. It is shown that when the continuous spectrum is present, the trace of the difference of the Green functions for SUSY partners is a finite quantity which may or may not be equal to zero despite the divergence of the traces of each Green function. Our findings are illustrated by using the free particle example considered both on the whole real line and on a half line. © 2005 IOP Publishing Ltd.

Abstract:

The Hamiltonian in Supersymmetric Quantum Mechanics is defined in terms of charges that obey the same algebra as that of the generators of supersymmetry in field theory. The consequences of this symmetry for the spectra of the component parts that constitute the supersymmetric system are explored. The implications of supersymmetry for the solutions of the Schrodinger equation, the Dirac equation, the inverse scattering theory and the multi-soliton solutions of the KdV equation are examined. Applications to scattering problems in Nuclear Physics with specific reference to singular potentials which arise from considerations of supersymmetry will be discussed.