Two talks for the price of one: Cooling by angulon annihilation and Asymmetrical fermion superfluids...
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Transcript of Two talks for the price of one: Cooling by angulon annihilation and Asymmetrical fermion superfluids...
Two talks for the price of Two talks for the price of one:one:
Cooling by angulon Cooling by angulon annihilation annihilation
andand Asymmetrical fermion Asymmetrical fermion
superfluidssuperfluids
P. Bedaque (Berkeley Lab)
G. Rupak, M. Savage, H. Caldas
Cooling of neutron stars by "angulon" annihilationCooling of neutron stars by "angulon" annihilationLight element
envelope
Heavy element envelope
GemingaVela
• Neutron stars start their lives hot and cool down by neutrino and photon emission
• After a minute, degenerate
• Cooling curves depend on emissivity, specific heat, thermal conduction, etc …
Determined by low-lying excitations
Unique laboratory to learn about dense matter
Page et al.
Neutron pairing in the Neutron pairing in the 33PP22 channel for channel for
densities higher than densities higher than nuclear saturationnuclear saturation
most attractive channel
2T
i j ijn n �
traceless symmetric matrix
2T
ij i jn n �
ij real (favored close to Tc)
determined by an orthonormal frame + 2 eigenvalues
2
30
2
3
1 0 0
0 0
0 0
i
i
e
e
eigenvalues are roots of 1
1
0 2
1 2
0 0
0 0
0 0
(2) (3) (1)S LSU SO U (3) (1)JSO U
Symmetry (breaking) patternSymmetry (breaking) pattern
tensor/spin-orbit
discrete discretetensor/spin-orbit
0nn 0nn
approximate exact
4 exactly massless Goldstone bosons4 exactly massless Goldstone bosons
Ripples in the sea of frames =
angulonsangulons
• Contrary to other excitations, not exponentially suppressed by Boltzman factors, dominate low energy/temperature properties
• Couples to neutrino through neutral currents
0 † iA iC Z n n
• Dimensional analysis:
2 9 3,F VG T c T
Effective theory
For E << 0 :i T
S LU e U R R Δ
phasespin
rotationorbital
rotation
2† 2 † 2 †
0 02
00
0
† †0
8 i i i ik j kj
iiV
fv w
H
L Tr Tr
i Z Tr J
Matching to a simple "microscopic" theory
22
2 2 2
20
31
5v
4
F
F
VV
Mk
v
f
f
w
CH
Rate for angulon+angulon
• No rotation symmetry: big complicated mess
• = v k
enhancement on the number of angulons ~ (T/v)3
suppression due to E ~ v
suppression due to kinematical constraint (no decay with v=0)
suppression on the coupling ~ v39
2 17 9 393
3 316 3 3 0
V 9
0.1510 /
v v
0.154 10 /
v v
F
TG T erg cm s
Tc T erg cm K
Does it matter for cooling ?Does it matter for cooling ?
Above Tc no: (modified) Urca N+N N+N+l+
Below Tc maybe: e+e e+e+
But pair formation around TBut pair formation around Tc c on a shellon a shell
~ 1020 T97
A more detailed study is A more detailed study is probably necessaryprobably necessary
Pairing in asymmetrical superfluidsPairing in asymmetrical superfluids
Two fermion species: A and B
up and down quarks, two
different atoms or hyperfine states in a trap,
…
A Bn ndifferent Fermi surfaces,
pairing ?
Relevance for neutron (quark) stars, atomic traps renewed the interest on the problem: some new,
interesting suggestions for the ground state
Variational arguments can rigorously show what is NOT a
ground state
To make it concrete:
3 3 3
† † † †3 3 3
( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )(2 ) (2 ) (2 )
A Bi i k A A k B B A B B A
d k d k d pH N k k k k g p p k k
2
2ik i
i
k
M
mean-field, low density, /<<1
2 3 3
† †3 3
( ) ( ) ( ) ( )(2 ) (2 )
Bi i k k k k
d k d kH N E E k k E k k
g
3
3( ) ( )
(2 ) B A
d kg k k
2
2 2
A B A Bi k k k kkE
Bogoliubov transformation:
2 3 3
† †3 3
( ) ( ) ( ) ( )(2 ) (2 )
Bi i k k k k
d k d kH N E E k k E k k
g
slightly different problem: A and B fixed: minimize H-N
Fill states with negative Ek
† † † †
0 0 0
| ( ) | 0 ( ( ) ( )) ( ) | 0k k k
k k B A BE E E
S k u v k k k
BCS filled with B
A=B
1st order transition
B-A=2
In the real problem nA and nB are fixed: local maximum
(Sarma state) suggested as the ground state (Liu &Wilczek,
gapless superconductor)
† † †
0 0
| ( ( ) ( )) ( ) | 0k k
k k B A BE E
S u v k k k
Mixed state:
(1 )
(1 )A A
B B
n xn x n
n xn x n
,( , ) min ( , ) (1 ) ( )MIXED A B N A B BCS
x nE n n x E n n x E n
minimize
Which is smaller: EMIXED or ESARMA ?
normal fraction
Sarma=BCS=Mixed
Sarmamixed
Sarma=normal
EMIXED < ESARMA
•In atomic traps, bubbles can be imaged. Long sought evidence for superfluidity in fermionic atomic traps ?
• Different dispersion relations (relativity) don’t change anything
•Three flavors is (may be) different !