We consider a model for a single molecule with a large frozen spin sandwiched in between two BCS superconductors at equilibrium, and show that this system has a $pi$ junction behavior at low temperature. The $pi$ shift can be reversed by varying the other parameters of the system, e.g., temperature or the position of the quantum dot level, implying a controllable $pi$ junction with novel application as a Josephson current switch. In contrast to previous works the importance of the contribution from the continuum of states above the superconducting gap is brought out. The free energy for certain configuration of parameters shows a bistable nature, which is a necessary pre-condition for achievement of a qubit.

The tremendous red-shifting of the perturbations during the inflationary epoch suggests that physics at the Planck scale may leave its imprints on the primordial spectrum and the cosmic microwave background. In the first part of the talk, I discuss the Planck scale corrections to the inflationary perturbation spectrum that arise in two different, locally Lorentz invariant, high-energy models. In the second part, I show that, given a modified spectrum, it can be reproduced with a suitably chosen squeezed state in the standard theory. I, therefore, argue that the primordial spectrum, by itself, may not be able to help us discriminate between the different Planck scale models of matter fields.

Magnetic fields ordered on kiloparsec scales and larger are found in disk galaxies and even clusters of galaxies. How such fields arise and how they aquire such large scale coherence is still a matter of active research. Battery and dynamo mechanisms for such magnetogenesis will be discussed. The current problems with both dynamo mechanisms and seed field generation mechanisms will be highlighted.