in Relativistic System and Its

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15 Νοε 2013 (πριν από 4 χρόνια και 1 μήνα)

109 εμφανίσεις

2013/11/15

1


BCS
-
BEC Crossover


in Relativistic System and Its


Possible Realization in QCD


Lianyi He and Pengfei Zhuang

Physics Department, Tsinghua U.


References:

Phys.Rev.D75:096003,2007


Phys.Rev.D75:096004,2007

Phys.Rev.D76:056003,2007


E
-
print Arxiv: 0709.2246


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2013/11/15

2


Impact of Superconductivity

Phenomena

Order parameter


Pair Breaking effect

Metallic
superconductivity

Zeeman Splitting

Superfluidity in
Ultracold Fermi
atoms

Population imbalance

Chiral symmetry

breaking in QCD

Baryon chemical potential

Color
superconductivity

in dense quark
matter

Isospin chemical potential


Strange quark mass

flavor superfluidity

in isospin matter

Baryon chemical potential





2
1



L R
q q
T
q q

5
ui d

0
Z
E H


2
1
2
1
N
N
N
N
P



B
m
I
m
s
m
B
m
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3

Theoretical History of Crossover:



Leggett (1980)

noted that BCS T=0 wavefunction could be


generalized to arbitrary attraction: a
smooth

BCS
-
BEC crossover !



2
/
1
2
2
/
1
1
k
B
k
B
k
N
N
v




BCS



0
exp
2
/
1
0






k
k
k
k
c
c
N
B

BEC

Introduction to BCS
-
BEC Crossover

weak coupling

strong coupling

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2013/11/15

4

Eagles (1969): Pairing without superconductivity

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In HTSC, the root of PG is not

quite clear. The pre
-
formed boson

mechanism is only one explanation.

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5

Experimental evidence for pseudogap


in ultracold fermions

Science 307, 1296 (2005)

0,0
0,4
0,0
0,4
-20
0
20
40
0,0
0,4
0,0
0,4
(d)
(c)


(a)





fractional loss in |2>
RF frequency offset (kHz)
(b)



Science 305, 1128 (2004)

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T
*
2013/11/15

6

T



BEC
?

SQGP?

Relativistic BCS
-
BEC Crossover

Motivation:

1) QCD phase diagram at moderate temperature and


density, strong coupling nature!

2) BCS
-
BEC crossover in CSC? Pseudogap of CSC

3) NJL model: BCS theory of chiral symmetry breaking.


Chiral pesudogap above Tc?

pseudogap?

CSC


SB

c
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Quark Spectrum and pseudogap, M. Kitazawa, et.al. 2005

Structure change of Cooper pairs,

H.Abuki, et.al.2002

Progress in this field of research

H.Abuki and Y.Nishida: NSR approach,


new crossover: BCS
-
BEC
-
RBEC

L.He and P.Zhuang: BCS
-
Leggett theory at zero T


and pesudogap theory at finite T


BCS
-
BEC vs. Chiral Restoration

J.Deng and Q.Wang: Boson
-
fermion model


in mean field and beyond mean field

M.Kitazawa, D.Rischke and I.Shovkovy:


Possible Diquark BEC in NJL

T.Brauner: Collective Excitation


1/N expansion including quantum fluctuation


(with H.Abuki)

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8

Zero Temperature: BCS
-
Leggett mean Field Theory

Model Lagrangian

Mean Field Equations

k
< L
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9

Fermionic Excitation Spectrum

(
)
2
2 2 2
0
k
E k m
m
-
= + - + D
(
)
2
2 2 2
0
k
E k m
m
+
= + + + D
fermion

anti
-
fermion

1.
Non
-
relativistic limit




2.
Criterion for BCS and BEC: Minimum of the dispersion



BCS: at , existence of Fermi surface


BEC: at , molecule condensation


3.
The role of fermion mass (new aspect in QCD)


BCS
-
BEC Chiral symmetry breaking& restoration


2
2
2
0
2
k NR
k
E
m
m
-
æ ö
÷
ç
÷
= - + D
ç
÷
ç
÷
ç
è ø
k m
=
m m
m
-
=
NR
m
m m
= -
(
)
2
2
0
k k
E m E
m
+ -
= + + D
?
0
k
¹
0
k
=
Û
m
m
>
Û
m
m
<
Û
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The Non
-
Relativistic Limit

f
k
m
z
=
For small value of the parameter , the NR version of


BCS
-
Leggett result is recovered

z
1
f s
k a
h
=
2
2
f
f
k
m
e
=
The condition or is needed

m m
m
-
=
1
h z
-
=
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11

Relativistic Effect I: BCS
-
NBEC
-
RBEC Crossover

2 2
f f
E k m
= +
Physical picture:


2
1
2
b
s
E m
ma
=
:
Þ
1
s c
a
m
l
=
:
1
h z
-
:
RBEC: , anti
-
particles available!

0
m
®
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2013/11/15

12

Relativistic Effect II: Density Induced Crossover

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13

Collective Mode Evolution

Effective action


Dispersion of the collective mode

Goldstone mode

1
3
f
k
c
m
=
BCS

NBEC

(
)
2 2
8
2 2
B BB
B B B
n a
k k
q
m m m
p
w
æ ö
÷
ç
÷
= +
ç
÷
ç
÷
ç
è ø
(
)
q cq
w
=
Bogoliubov theory

RBEC

(
)
q q
w
;
Ultra
-
relativistic BEC

A
-
B mode

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14



K.Levin and Qijin Chen, et.al,

Phys.Rept. 412, 1(2005)

Nonzero Temperature:

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Pseudogap theory

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15



Tc Calculation

NBEC regime

RBEC regime

m
m
<
Bound states above Tc

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16



BCS
-
BEC Crossover in QCD?

Two color QCD

QCD at finite isospin density

Phys.Rev.D75:096004,2007

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In the BEC region, quark energy gap is different from

the order parameter! Can be confirmed in Lattice!

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Chiral restoration vs. BCS
-
BEC crossover

2
B
m
m
m
= =
BEC

BCS

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18



1
c
g
g

 
2
2
4
c
c
g
N



Quark mass is still large above

chiral phase transition!

Nc dependence

qq
Condensation and Chiral Phase Transition

Pseudogap in QCD?

NJL Model

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Quark pesudogap remarkable!

Diquark condensation and color superconductivity

NJL model, 2SC phase

400,5
MeV m MeV
m
= =
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0
0.57
c
T
<
D
A high Tc superconductor!

(
)
0
0.5
pg c
T
D
D
:
2
/
3
T
C
pg

0
T
®
Non
-
Fermi liquid behavior

at low T!

(High T, see M.Kitazawa, 2005)

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21

Summary

1. BCS
-
BEC crossover theory has been generalized


to relativistic system, both at zero and at finite


temperature.

2. Proper NR limit is recovered and new relativistic


effects are found.

3. Possible BCS
-
BEC crossover in diquark and


isospin matter is discussed.

4. The size of quark pseudogap in chiral and CSC


phase transition is calculated.

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Outlook

1.
Determine the pseudogap phase in QCD phase diagram

2.
Signals of diquark fluctuation and pesudogap in HIC

3.
Effect of the pseudogap on compact star cooling

4.
More precise theory, including quantum fluctuation

2013/11/15

22



Thank You!

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