Ginzburg-Landau free energy in superfluid3He

Abstract

The Ginzburg-Landau free energy is a basic quantity in the study of BCS-like superfluids. It has been widely used in superconductivity 1 as well as in the theory of superfluid 3He.2 By minimizing this free energy with respect to the variation of the order parameter, one obtains the Ginzburg=Landau equations, which permit one to study the system when the order parameter is slowly varying. Originally introduced for superconductors near the critical temperature, this free energy has been calculated by Werthamer 3 and Eilenberger 4 for all temperatures by solving the Gor'kov equations. This result has been extended to 3He by Cross, 5 who considered the p-wave case and included Fermi liquid effects. Here we wish to present a general kinetic theory derivation for this free energy in the case of superfluid 3He. Kinetic theory has proved to be a very powerful tool in the theory of spin 6 and of orbital dynamics. 7 Therefore it is of interest to show that the free energy, which is of basic importance for static properties, can be derived directly from the kinetic equation. Moreover, as will be seen, this derivation has the advantage o f being conceptually straightforward, as well as easily lending itself to the inclusion 519