Prof. Kumar's Homepage

Research And Publications:

Recent Talks and Posters:



Recent publications and preprints

Go to the Los Alamos Archives listing of my recent papers.

CV and a list of all publications

My research has been in the theory of Condensed Matter Physics.  The references refer to the list of all publicaitons

1. Higher Order Phase Transitions

It appears that the transition to superconductivity in Ba(1-x)KxBiO3 may be of order four in the original classification of phase transitions by Ehrenfest. In collaboration with Donavan Hall (NHMFL) and R. G Goodrich we have noted the anomalous experimental results in the measurement of magnetization. A higher order ( say of order n) phase transition is where the nth derivative of the free energy with respect to temperature and/or a mechanical variabe such as magnetic field is discontinuous. For example for a 2nd order phase transition, the specific heat is found to be discontinuous. Often the discontinuity is replaced by a weak (nearly logarithmic) divergence characterized by scaling exponents and the exponents in turn, satisfy scaling laws. In a higher order transition, the first singular derivative of the free energy can be associated with exponents. 

We have also derived a Ginzburg-Landau like free energy which describes a higher order phase transition. This free energy implies an anomalous temperature dependence for the thermodynamic critical field, as well as for the lower critical field.  In other words, the specific heat is continuous at Tc, it rises with a charactertistic power below Tc.  Moreover there is an anomalous temperature dependence in superfluid density.  These results are in agreement with experiments.

A recent talk (and a paper in preparation) will address the problem of interacting phase boundaries invovling at least one describing a higher order transition.

2. Competing and Conflicting Order:  

In Chemistry or in Materials Science, a phase boundary is almost never simple and neither is a phase diagram.  The phase diagram is a proverbial map showing a  large list of possible ground states as a thermodynamic parameter is varied. The phase boundaries cross other phase boundaries forming multicritical points where several different ground states coexist.  There are coexisting phases that are homogeneously mixed orthere are domains separted by domain walls. 

We have been looking at the properites of a complex phase diagram that can be derived from the symmetry properties fo the underlying free energy.  Our approach is based on geometry.

3. Multiferroics: