Two-Fluid Model for Anisotropic Superfluids

Introduction Action Principle Classic Approach Sound Propagation Anisotropy
First and Second Sound in an anisotropic superfluid
coupled wave equations
[ (∂p
∂ 2 ) ( ) ]
δ ˜ρ
∂p
∂t 2 − ∆δ ˜ρ + ∆δ¯s = 0
∂ ˜ρ
¯s
∂¯s
˜ρ
[ (∂T
∂ 2 ) ( ) ]
δ¯s
∂T
∂t 2 − ¯s2 0ρ −1
n0 ik
ρ s0kj ∂ i ∂ j δ ˜ρ + ∂ i ∂ j δ¯s = 0
∂ ˜ρ
¯s
∂¯s
˜ρ
ansatz δ¯s, δ ˜ρ ∝ e i(q·r−ωt) , q ⊥ ⊥ ê dipole , q ‖ ‖ ê dipole
⎛
⎞
ρ n0⊥ 0 0
⎜
⎟
diagonal form ρ n = ⎝ 0 ρ n0⊥ 0 ⎠
0 0 ρ n0‖
Two-Fluid Model for Anisotropic Superfluids
Carolin Wille