We derive an exact system of nonlinear equations that describe the dynamics of a degenerateHe3 - He4 solution, and compute the nonlinear correction to the propagation velocity of first sound (proportional to the amplitude) in the collisionless limit. Our nonlinear treatment requires the third functional derivative of the total energy with respect to the distribution function of He3 quasi particles in addition to the second functional derivative (the Landau function). We find the Fermi-liquid parameters in the limit of small He3 concentrations from a microscopic calculation, and obtain an explicit expression for the correction.
|Number of pages
|Journal of Experimental and Theoretical Physics
|Published - 1996