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HW5 - Physics 127B Homework Set 5(due February 17 Problem 1...

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Physics 127B – Homework Set 5: (due February 17) Problem 1: Superfluid He 4 -He 3 mixtures Problem 2.4 in Kardar, “Statistical Physics of Fields,” p. 33. Suggestion: For various formal manipulations, it can be convenient to write the terms containing c ( x ) as a complete square and shift variables. Problem 2: Thermal excitation of capillary waves Consider gas and liquid in equilibrium. The two phases are separated by an interface, which is microscopically non-flat. In this problem we study thermal excitation of the interface (capillary waves). Let h ( x, y ) denote the height (measured from appropriate reference). Consider first the situation in the presence of gravitation where the energy is given by E = integraldisplay dxdy ρ liquid ρ gas 2 gh 2 ( x, y ) + integraldisplay dxdy σ radicalBigg 1 + parenleftbigg ∂h ∂x parenrightbigg 2 + parenleftbigg ∂h ∂y parenrightbigg 2 1 . (1) The first term is change in the gravitational energy due to the deformation h ( x, y ), with g the
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