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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- Winter '11
- OlexeiMotrunich
- Physics, Work, Surface tension, Fundamental physics concepts, capillary waves, Kardar, dxdy σ
-
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