The effect of a super-normal phase transition on the collective mass parameter
We derive an expression for the temperature-dependent collective masses for the general collective motion. It is an application of the time dependent BCS approximation, which is usually used for the ground state, to finite temperature. The resulting masses show a very prominent structure, that is, it changes discontinuously across the critical temperature.
A method of solving the eikonal equation, in either flat or curved space–times, with arbitrary Cauchy data, is extended to the case of data given on a characteristic surface. We find a beautiful relationship between the Cauchy and characteristic data for the same solution, namely they are related by a Legendre transformation. From the resulting solutions, we study and describe the wave-front singularities that are associated with their level surfaces (the characteristic surfaces or “big wave fronts”).