Two-Fluid Model for Anisotropic Superfluids

Introduction Action Principle Classic Approach Sound Propagation Anisotropy
Coupled Wave Equations
∂ 2 δ¯s
∂t 2 − ¯s2 0
ρ s0
ρ n0
∂ 2 δρ
∂t 2
[ (∂T )
( ∂T
∆δρ +
∂¯s
∂ρ
¯s
[ (∂p )
− ∆δρ +
∂ρ
¯s
( ∂p
∂¯s
)
)
]
∆δ¯s
ρ
]
∆δ¯s
ρ
= 0
= 0
plane waves δρ, δ¯s ∝ e i(q·r−ωt) with speed of sound u = ω/q
[ (∂p )
u 4 − u 2 + ρ s 0
s 2 ( ) ]
0 ∂T
∂ρ
¯s
ρ n0 ∂¯s
ρ
[ (∂T ) ( ) ( ) ( ) ]
+¯s 0
2 ρ s0
∂p ∂p ∂T
−
= 0
ρ n0 ∂¯s
ρ
∂ρ
¯s
∂¯s
ρ
∂ρ
¯s
Two-Fluid Model for Anisotropic Superfluids
Carolin Wille