Physics 127B – Homework Set 5:(due February 17)Problem 1: Superfluid He4-He3mixturesProblem 2.4 in Kardar, “Statistical Physics of Fields,” p. 33.Suggestion: For various formal manipulations, it can be convenient to write the terms containingc(x) as a complete square and shift variables.Problem 2: Thermal excitation of capillary wavesConsider gas and liquid in equilibrium.The two phases are separated by an interface, which ismicroscopically non-flat.In this problem we study thermal excitation of the interface (capillarywaves). Leth(x, y) denote the height (measured from appropriate reference).Consider first the situation in the presence of gravitation where the energy is given byE=integraldisplaydxdyρliquid−ρgas2gh2(x, y) +integraldisplaydxdy σradicalBigg1 +parenleftbigg∂h∂xparenrightbigg2+parenleftbigg∂h∂yparenrightbigg2−1.(1)The first term is change in the gravitational energy due to the deformationh(x, y), withgthe
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