Relativistic BCS-BEC Crossover at Quark Level

(1)

Relativistic BCS-BEC Crossover at Quark Level

Lianyi He, Shijun Mao, and Pengfei Zhuang

Physics Department, Tsinghua University, Beijing 100084, China

Abstract. The non-relativisticG0Gformalism of BCS-BEC crossover at ﬁnite temperature is extended to

relativistic fermion systems. The theory recovers the BCS mean ﬁeld approximation at zero temperature and the non-relativistic results in a proper limit. For massive fermions, when the coupling strength increases, there exist two crossovers from the weak coupling BCS superﬂuid to the non-relativistic BEC state and then to the relativistic BEC state. For color superconductivity at moderate baryon density, the matter is in the BCS-BEC crossover region, and the behavior of the pseudogap is quite similar to that found in high temperature superconductors.

Acknowledgements

The work is supported by the NSFC Grant 10735040 and the 973-project 2006CB921404 and 2007CB815000.

References

1. A.J.Leggett,Modern trends in the theory of condensed matter, Springer-Verlag, Berlin (1980)

2. P.Nozieres and S.Schmitt-Rink, J.Low.Temp.Phys.59, 195 (1985)

3. Q.Chen, J.Stajic, S.Tan and K.Levin, Phys.Rept.412, 1 (2005)

4. Y. Nishida and H. Abuki, Phys.Rev. D72, 096004, (2005)

5. J.Deng, A.Schmitt and Q.Wang, Phys.Rev. D78, 034014 (2008)

6. L.He and P.Zhuang, Phys.Rev.D76, 056003 (2007); Phys.Rev. D75, 096004 (2007); Phys.Rev. D75, 096003 (2007)

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July, 2008 Summer School on Dense Matter and HI

July, 2008 Summer School on Dense Matter and HI DubnaDubna 11

Relativistic BCS

-

BEC Crossover at Quark Level

Pengfei Zhuang

Physics Department, Tsinghua University, Beijing 100084

1) Motivation

2) Mean Field Theory at T = 0

3) Fluctuations at T

0

0 4) Application to QCD:

4) Application to QCD:

Color Superconductivity and

Pion

Superfluid

5) Conclusions

1) Motivation

(3)

July, 2008 Summer School on Dense Matter and HI DubnaDubna 33 BCS

BCS--BECBEC

BCS

((BardenBarden, Cooper and Schrieffer, 1957):, Cooper and Schrieffer, 1957): normal superconductivitynormal superconductivity

weak coupling, large pair size, k

weak coupling, large pair size, k--space pairing, space pairing, overlapingoverlapingCooper pairsCooper pairs

BEC

(Bose(Bose--EinsteinEinstein--Condensation, 1924/1925):Condensation, 1924/1925): strong coupling, small pair size, r

strong coupling, small pair size, r--space pairing, ideal gas of bosons, space pairing, ideal gas of bosons, first realization in dilute atomic gas with bosons in 1995.

first realization in dilute atomic gas with bosons in 1995.

BCS

-

BEC crossover

(Eagles, Leggett, 1969, 1980):(Eagles, Leggett, 1969, 1980): BCS wave function at T=0 can be generalized to arbitrary attract

BCS wave function at T=0 can be generalized to arbitrary attraction: aion: asmoothsmooth crossover from BCS to BEC!

crossover from BCS to BEC!

BEC of molecules

BEC of molecules BCS fermionic BCS fermionic superfluidsuperfluid

B k k B k

N N v

2

NB _{k k}ckck

July, 2008 Summer School on Dense Matter and HI DubnaDubna 44 pairings

pairings

in BCS,

in BCS, TT_c_cis determined by thermal excitation of fermions, is determined by thermal excitation of fermions, in BEC,

(4)

in order to study the question of

in order to study the question of ‘‘vacuumvacuum’’, we must turn to a different , we must turn to a different direction: we should investigate some

direction: we should investigate some ‘‘bulkbulk’’phenomena by distributing phenomena by distributing

high energy over a relatively large volume. high energy over a relatively large volume.

BCS

BCS--BEC in QCDBEC in QCD

T. D. Lee,

T. D. Lee, Rev. Mod. Phys. 47, 267(1975)Rev. Mod. Phys. 47, 267(1975)

pair dissociation line

BCS BEC

sQGP

QCD phase diagram QCD phase diagram

rich QCD phase structure at high density, natural attractive int

rich QCD phase structure at high density, natural attractive interaction eraction

in QCD, possible BCS

in QCD, possible BCS--BEC crossover ?BEC crossover ?

new phenomena in BCS

new phenomena in BCS--BEC crossover of QCD:BEC crossover of QCD:

relativistic systems, anti

relativistic systems, anti--fermionfermioncontribution, rich inner structure (color, contribution, rich inner structure (color, flavor), medium dependent mass,

flavor), medium dependent mass, …………

July, 2008 Summer School on Dense Matter and HI DubnaDubna 66 theory of BCS

theory of BCS--BEC crossoverBEC crossover

*) Leggett mean field theory (Leggett, 1980) *) Leggett mean field theory (Leggett, 1980) *)NSR scheme (

*)NSR scheme (NozieresNozieresand Schmittand Schmitt--Rink, 1985)Rink, 1985) extension of

extension of ofofBCSBCS--BEC crossover theory at T=0 to TBEC crossover theory at T=0 to T0 (above 0 (above TT_c_c) ) Nishida and

Nishida and AbukiAbuki(2006,2007)(2006,2007) extension of non

extension of non--relativistic NSR theory to relativistic systems, relativistic NSR theory to relativistic systems, BCS

BCS--NBECNBEC--RBEC crossover RBEC crossover

fl

d q

q G G

G

678 ABC

=

*)

*) GG₀₀G scheme (Chen, Levin et al., 1998, 2000, 2005)G scheme (Chen, Levin et al., 1998, 2000, 2005) asymmetric pair susceptibility

asymmetric pair susceptibility G G extension of non

extension of non--relativistic relativistic GG₀₀G scheme to relativistic systems (He, G scheme to relativistic systems (He, Zhuang, 2006, 2007)

Zhuang, 2006, 2007)

*) Bose

*) Bose--fermionfermionmodel (model (FrieddergFriedderg, Lee, 1989, 1990), Lee, 1989, 1990) extension to relativistic systems (Deng, Wang, 2007) extension to relativistic systems (Deng, Wang, 2007)

Kitazawa, Rischke,

Kitazawa, Rischke, ShovkovyShovkovy, 2007, , 2007, NJL+phaseNJL+phasediagram diagram Brauner

(5)

2)

Leggett

Mean Field Theory at T = 0

A.J.Leggett

A.J.Leggett, in Modern trends in the theory of condensed matter, , in Modern trends in the theory of condensed matter, Springer

Springer--VerlagVerlag(1980) (1980)

July, 2008 Summer School on Dense Matter and HI DubnaDubna 88 non

non--relativistic mean field theoryrelativistic mean field theory

fermion

fermionnumber: number: Fermi momentum:

Fermi momentum:

Fermi energy:

F F

k n k p

t

L i h g

m

# # # # # #

( * * (

3 / >

₄ - _?

5 @

g # #_* _* g # #₍ ₍

k k _k

d k E

g "

6 A

7 B

8 C

=

order parameter

k k k k k

E x x e m e k m

n

F kF m

e

thermodynamics in mean field approximation

quasi

quasi--particle energyparticle energy

renormalization to avoid the integration divergence

s

s k

s s

m d k

g a

a g

a a

)

(6)

July, 2008 Summer School on Dense Matter and HI DubnaDubna 99 universality universality - -gap equation gap equation n -number conservation number conservation

n n

1

s k k

k k m d k

a E d k n E "

9 3 > < 4 ? < 5 @ :

3 > < ₄ _? < ₅ _@ ;

=

! ! F F F s k a

d x x

x x

x d x x

x & &

9 3 > < 4 ? < 4 ?

4 ?

<< 5 @ :

3 >

<

4 ?

< ₄ _? < ₄ _? < ₅ _@ ;

=

universality universality ! 1 effective coupling effective coupling

July, 2008 Summer School on Dense Matter and HI DubnaDubna 1010

BCS limit

BEC limit

non

non--relativistic BCSrelativistic BCS--BEC crossoverBEC crossover

" ! e e

) &

(7)

July, 2008 Summer School on Dense Matter and HI DubnaDubna 1111 relativistic BCS

relativistic BCS--BEC crossoverBEC crossover

m m

k k k

E k m

m

x x m

m

% % %

%

b

m

m m

e

m m

m

&

'

* BCS

BCS--BEC crossover around BEC crossover around

plays the role of non

plays the role of non--relativistic chemical potentialrelativistic chemical potential

pair binding energy

at

at fermionfermionand antiand anti--fermionfermiondegenerate, degenerate,

relativistic effect

m m

BCS BCS limit limit NBEC

NBEC--BCS BCS crossover crossover NBEC

NBEC RBEC

RBEC--NBEC NBEC crossover crossover RBEC

RBEC limit limit

July, 2008 Summer School on Dense Matter and HI DubnaDubna 1212 relativistic mean field theory

relativistic mean field theory

+

T T

g

L i m i C iC

C i

# # # # # #

-

+

T

g iC

# #

k k k k

d k

E E

g " "

₆ _A

8 C

=

order parameter

antifermion

mean field thermodynamic potential

the most important thermodynamic contribution from the uncondens the most important thermodynamic contribution from the uncondensed ed pairs is from the Goldstone modes, , at T=0, the fluc

pairs is from the Goldstone modes, , at T=0, the fluctuation tuation contribution disappears, and MF is a good approximation at T=0. contribution disappears, and MF is a good approximation at T=0.

T

extremely high T and high density:

extremely high T and high density: pQCDpQCD

finite T (zero density): lattice QCD

moderate T and density: models like 4

moderate T and density: models like 4--fermion interaction (NJL)fermion interaction (NJL)

charge conjunction matrix

fermion

He, Zhuang, 2007

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July, 2008 Summer School on Dense Matter and HI DubnaDubna 1313 broken universality

broken universality

gap equation and number equation:

k k

d k

g E E

d k n

E E

" "

9 3 > < 4 ? 5 @ <

: ₆₃ _{> 3} _>_A < ₇₄ _{? 4} _?_B < ₈₅ _{@ 5} _@_C ;

=

z

x x x x

z

x x

F F s

d x x

E E

d x x

E E

k k a m

$ $

" "

$

9 63 > 3 >A < 74 ? 4 ?B

5 @ 5 @

< 8 C

: ₆ _A

3 > 3 > <

74 ? 4 ?B < ₅ _{@ 5} _@

8 C

;

=

renormalization to avoid the integration divergence

s

k k

a d k

U

U g m m m

3 >

₄ _?

5 @

=

the ultraviolet divergence can not be completely removed, and a the ultraviolet divergence can not be completely removed, and a momentum cutoff still exists in the theory.

momentum cutoff still exists in the theory.

broken universality: broken universality:

explicit density dependence ! explicit density dependence !

m m

kFm

$

non-relativistic limit: 1) non-relativistic kinetics 2) negligible anti-fermions

c c m

m h z h z

*

NBEC

RBEC

non

(9)

July, 2008 Summer School on Dense Matter and HI DubnaDubna 1515 density induced crossover

density induced crossover

atom gas

QCD

k a

_F _s

In non-relativistic case, only one dimensionless variable, , changing the density of the system can not induce a BCS-BEC crossover.

However, in relativistic case, the extra density dependence may induce a BCS-BEC crossover.

F

k

m

z

3) Fluctuations at T

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the the Landau mean field theory Landau mean field theory is a good approximation only at T=0 is a good approximation only at T=0 where there is no thermal excitation,

where there is no thermal excitation, one has to go beyond the mean one has to go beyond the mean

field at finite temperature. field at finite temperature.

pair dissociation line BCS BEC sQGP

an urgent question in relativistic heavy ion collisionsan urgent question in relativistic heavy ion collisions introduction

introduction

t

to understand the o understand the sQGPsQGPphase phase

with possible bound states of

quarks and gluons, one has to

go beyond the mean field !

going beyond mean field selfgoing beyond mean field self--consistently is very difficultconsistently is very difficult NSR Theory (G

NSR Theory (G₀₀GG₀₀Scheme) above Scheme) above TT_c_c: Nishida and : Nishida and AbukiAbuki(2005),(2005), Bose

Bose--Fermi Model: Deng and Wang (2006),Fermi Model: Deng and Wang (2006),

G

G₀₀G Scheme below G Scheme below TT_c_c: He and Zhuang (2007), : He and Zhuang (2007), …………

G k k 0 k m

k k n n g

i Tr G k G k n i Tr G k

n T bosons d k

iT k i

n T fermi

! !

6 A

₇ _B

8 C

)

2

k n ons

9 : ;

2 2=

mf k G k

+

T T g

L# i - m# # #i C # iC #

fermion

fermionpropagator with diagonal and offpropagator with diagonal and off--diagonal elements in diagonal elements in NambuNambu--GorkovGorkovspacespace

bare propagator and

bare propagator and condensate induced selfcondensate induced self--energyenergy

G k F k S k

F k G k

3 > 4 ?

5 @ + mf

G k G k k

F k G k i G k

gap and number equations at finite T gap and number equations at finite T

k k k k k k k k k k

f E f E d k

g E E

d k

n f E f E

E E " "

9 6 A < 7 B

8 C

<

: ₆ _A

3 > 3 >

< ₇₄ _? ₄ _? _B < ₈₅ _@ ₅ _@ _C ;

=

gap and number equations in terms of the

gap and number equations in terms of the fermionfermionpropagatorpropagator

Matsubara frequency summation Matsubara frequency summation

mean field

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mf

t q i q T

G G

mean field theory in scheme

introducing a condensed

introducing a condensed--pair propagatorpair propagator

mf mf q

k t q G q k

2

k i

q Tr G k G q k

2 t

gap equation in condensed phase is determined by uncondensed pai

gap equation in condensed phase is determined by uncondensed pairsrs

G

mf

t

ig t q

g q

problem:

there is no feedback of the uncondensed pairs on the

there is no feedback of the uncondensed pairs on the fermionfermionselfself--energy energy

defining an uncondensed pair propagator defining an uncondensed pair propagator

the name scheme,

G is the mean field

fermion

fermionpropagatorpropagator

GG

T

mf pg

mf

pg

t q t q t q

t q i q

T ig

t q

g q

k i

q Tr G k G q k

2

full pair propagator full pair propagator

q

mf pg

k t q G q k

k k

2

G k G k k

going beyond mean field in scheme

going beyond mean field in schemeG G

with full susceptibility and full propagator

full

full fermionfermionselfself--energyenergy

pg

t

pg

t

fermions and pairs are coupled to each other

new gap equation

new gap equation a new order parameter which is a new order parameter which is T different from the mean field one

different from the mean field one

all the formulas look the same as the mean field ones,

but we do not know the expression of the full

but we do not know the expression of the full fermionfermionpropagator G.propagator G.

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July, 2008 Summer School on Dense Matter and HI DubnaDubna 2121 approximation in condensed phase

approximation in condensed phase

1) peaks at t_pg tpg q

pg pg pg pg

q q

pg pg q

k t q G q k t q G k G k

t q . . . 3 > ₄ _? 5 @

2

q

mf pg pg

k k k G k

pg t pg q q q

ig i i

t q

g q q Z q Z q q

Z Z

q q q

" _" - - - - q $4689 pg b q b q pg

q

f v f v

d q Z

v

! !

!

9 ₎

<< : < <;

=

6

Z Z ! " q Z v

T

_pg

T

the

the pseudogappseudogapis related to the uncondensed is related to the uncondensed

pairs and does not change the symmetry !

full self-energy

2) expansion around

pg

t

gap equation mean field gap equation

gap equation mean field gap equationwithwith ) pg

July, 2008 Summer School on Dense Matter and HI DubnaDubna 2222 thermodynamics thermodynamics

; k k q q B mf fl E E

mf k k k k

fl q

q m

d k

E E e e

g

d q

g q e e

d q

e Z non relativistic boson gas

d q e ! ! " " 6 A 7 B 8 C

=

2 =

=

;

cq _Z _{relativistic boson gas}

9 << : < <;

mf fl

B k k pg B B

n d k

n f " f " Z n n

68 AC

=

number of bosons number of bosons

mf B c n Z P n n

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July, 2008 Summer School on Dense Matter and HI DubnaDubna 2323 BCS

BCS--NBECNBEC--RBEC crossoverRBEC crossover

<

= $

= 449

= $49

= 4$

= 49

c

c c

c pg

T

T T

T

T T T

.

<₌ _$9

pg

TT

BCS: no pairs

NBEC: heavy pairs, no

NBEC: heavy pairs, noantianti--pairspairs

RBEC: light pairs, almost th

RBEC: light pairs, almost the same e same number of pairs and anti

number of pairs and anti--pairspairs

m

m k _F &m

F

m k

B B r n n

F B r r

number fractions at

number fractions at TTcc, ,

in RBEC,

in RBEC, TT_ccis large enough and is large enough and

there is a strong competition

between condensation and

dissociation.

July, 2008 Summer School on Dense Matter and HI DubnaDubna 2424 discussion on

discussion on

G G

+

pg

G

k

i

S

k

i

G

k

3 >

4 ₄

?

_?

5 @

can the symmetry be restored in the

can the symmetry be restored in the pseudogappseudogapphase? phase?

fermion

fermionpropagator including fluctuations (to the order of )propagator including fluctuations (to the order of ) ::

the

the pseudogappseudogapappears in the diagonal elements of the propagator appears in the diagonal elements of the propagator

and does not break the symmetry of the system.

Kandanoff

Kandanoffand Martin: and Martin:

the scheme can not give a correct symmetry restorat

the scheme can not give a correct symmetry restoration ion

picture and the specific heat is wrong.

GG

V

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July, 2008 Summer School on Dense Matter and HI DubnaDubna 2525 BCS

BCS--BEC in BoseBEC in Bose--fermionfermionmodelmodel

Deng, Wang, 2007

mean field thermodynamics mean field thermodynamics

fluctuation changes the phase fluctuation changes the phase transition to be first

transition to be first--order.order.

4) Application to QCD:

Color Superconductivity and

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motivation

* QCD phase transitions like

* QCD phase transitions like chiralchiralsymmetry restoration, color symmetry restoration, color

superconductivity, and

superconductivity, and pionpionsuperfluidsuperfluidhappen in nonhappen in non--perturbativeperturbative temperature and density region, the coupling is strong.

temperature and density region, the coupling is strong.

* relativistic BCS

* relativistic BCS--BEC crossover is controlled by , the BECBEC crossover is controlled by , the BEC--BCS BCS

crossover would happen when the light quark mass changes in the

QCD medium.

* effective models at

* effective models at hadronhadronlevel can only describe BEC state, they level can only describe BEC state, they can not describe BEC

can not describe BEC--BCS crossover. One of the models that enables BCS crossover. One of the models that enables

us to describe both quarks and mesons and

us to describe both quarks and mesons and diquarksdiquarksis the NJL model is the NJL model

at quark level.

disadvantage: no confinement

* there is no problem to do lattice simulation for real QCD at f

* there is no problem to do lattice simulation for real QCD at finite inite

isospin

isospindensitydensity

m

+ + +

C ij ij C

NJL S i D i j i j

L # i - m G ## # #i G # i # # i #

C C C C C C

u d d u d u u d u u d d

# # # # # # # # # # # # u C d d C u d C u u C d u C u d C d # # # # # # # # # # # # 3 > 4 ? 4 ? 4 ? 4 ? 4 ? 4 ? 4 ? 4 ? 4 ? 4 ? 4 ? 4 ? 4 ? 4 ? 4 ? 4 ? 4 ? 4 ? 5 @ ## + C ij i i j

# #

order parameters of spontaneous

order parameters of spontaneous chiralchiraland color symmetry breakingand color symmetry breaking

quark propagator in 12D

quark propagator in 12D NambuNambu--GorkovGorkovspacespace

A B C D E F S S S S S S S 3 > 4 ? 4 ? 4 ? 4 ? 4 ? 4 ? 4 ? 4 ? 5 @ I I I I I G S G

3 >

4 ?

5 @

q S

M m G

IA B C D E F

k q k D

E k M

E+ E G

+

color superconductivity

color breaking from SU(3) to SU(2)

diquark

diquark& meson polarizations& meson polarizations

>

D

diquark

diquark& meson propagators at RPA& meson propagators at RPA

leading order of 1/N

(16)

BCS

BCS--BEC and color neutralityBEC and color neutrality

gap equations for

gap equations for chiralchiraland and diquarkdiquarkcondensates at T=0condensates at T=0

"

k B k B

s k B

p

d

E E d k

m m G m E

E E E

d k G

E E

9 6 A

< 7 B

8 C

< :

6 A < ₇ _B < ₈ _C ;

=

B d s

m m G G

to guarantee color neutrality, we introduce

color chemical potential:

" "

r g B b B

there exists a BCS

there exists a BCS--BEC crossoverBEC crossover

color neutrality speeds up the

color neutrality speeds up the chiralchiral restoration and reduces the BEC region

restoration and reduces the BEC region

r m He, Zhuang, 2007

vector meson coupling and magnetic instability

vector

vector--meson couplingmeson coupling

+

V V

L G 6₇# # # # A_B

8 C

gap equation

V GV

# #

vector meson coupling slows down

the

the chiralchiralsymmetry restoration and symmetry restoration and enlarges the BEC region.

enlarges the BEC region.

vector condensate

" k B k B

V V k B

E E d k

G E

E E

6 A

₇ _B

8 C

=

Meissner

Meissnermasses of some gluons masses of some gluons are negative for the BCS Gapless

are negative for the BCS Gapless

CSC,

CSC, but the magnetic instability but the magnetic instability is cured in BEC region.

is cured in BEC region.

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July, 2008 Summer School on Dense Matter and HI DubnaDubna 3131 beyond men field

beyond men field

>? q +>?

'

T

is determined by the coupling and chemical potentialis determined by the coupling and chemical potential

going beyond mean field reduces the critical temperature of cologoing beyond mean field reduces the critical temperature of color r superconductivity

superconductivity

pairing effect is important around the critical temperature and

pairing effect is important around the critical temperature and dominates the dominates the symmetry restored phase

symmetry restored phase

NJL with

NJL with isospinisospinsymmetry breakingsymmetry breaking

@B

u u d d

T

G S

V

q q

- - _, - - _, - - _, - - _, - - -

+

NJL i

L # i - m #G ## # #i

u d u uu d dd

##

chiral

chiraland pionand pioncondensates with finite pair momentumcondensates with finite pair momentum

quark propagator in MF quark propagator in MF

+

u

d

p q m iG

S p q

iG k q m

₄3 0 >_?

4 ₀ ?

5 @

mm G

+ +

iq x iq x

ui d e di u e

0 0

quark chemical potentials quark chemical potentials

u B I

d B I

3 > 3 >

₄ _? ₄ _?

5 @

thermodynamic potential and gap equations: thermodynamic potential and gap equations:

pion

(18)

+

m

m i m i m i m

9 < < :

< < ;

<

@

mn m n

d p

k i S p k S p

₌

meson propagator at RPA

pole of the propagator determines meson masses pole of the propagator determines meson masses

considering all possible channels in the bubble summation

4

m

k M k G k G k G k G k

G k G k G k G k

3 >

4 ?

meson polarization functions

mixing among normal in

mixing among normal in pionpionsuperfluidsuperfluidphase, phase,

the new

the new eigeneigenmodes are linear combinations of modes are linear combinations of

4 ?

5 @

m M

D

mesons in RPA

I B

chiral

chiraland pionand pioncondensates at condensates at in NJL, Linear Sigma Model and

in NJL, Linear Sigma Model and ChiralChiral Perturbation Theory, there is no remarkable Perturbation Theory, there is no remarkable difference around the critical point.

difference around the critical point. analytic result: analytic result: critical

critical isospinisospinchemical potential for chemical potential for pionpion superfluidity

superfluidityis exactly the is exactly the pionpionmass in the mass in the vacuum:

vacuum:

B

T q

c I m

B nB

I

pion

pionsuperfluiditysuperfluidityphase diagram in phase diagram in plane at T=0

plane at T=0

: average Fermi surface : average Fermi surface

: Fermi surface mismatch : Fermi surface mismatch homogeneous (

homogeneous (SarmaSarma, ) and , ) and inhomogeneous

inhomogeneous pionpionsuperfluidsuperfluid(LOFF, )(LOFF, ) magnetic instability of

magnetic instability of SarmaSarmastate at high state at high

average Fermi surface leads to the LOFF state

q.

q

phase diagram of

(19)

BCS

BCS--BEC crossover of BEC crossover of pionpionsuperfluidsuperfluid

k F$D k

! !

meson spectra function meson spectra function meson mass, Goldstone mode

meson mass, Goldstone mode

phase diagram phase diagram

BEC

BCS

BCS

BCS--BEC crossover in asymmetric nuclear matterBEC crossover in asymmetric nuclear matter

Mao, Huang, Zhuang, 2008

transition from BCS pairing to BEC in lowtransition from BCS pairing to BEC in low--density asymmetric nuclear matter, density asymmetric nuclear matter,

U. Lombardo, P. Nozi

U. Lombardo, P. Nozièères:PRC64, 064314 (2001)res:PRC64, 064314 (2001)

spatial structure of neutron Cooper pair in low density uniformspatial structure of neutron Cooper pair in low density uniformmatter, matter,

Masayuki Matsuo:PRC73, 044309 (2006) Masayuki Matsuo:PRC73, 044309 (2006)

BCSBCS--BEC crossover of neutron pairs in symmetric and asymmetric nucleBEC crossover of neutron pairs in symmetric and asymmetric nuclear ar

matters,

matters, J. J. MargueronMargueron: arXiv:0710.4241: arXiv:0710.4241

asymmetric nuclear matter with both

np

npand and nnnnand and pp pp pairingspairings

considering density dependent Paris potential and

nucleon mass

there exists a strong

Friedel

Friedeloscillation in BCS oscillation in BCS region, and it is washed

region, and it is washed

away in BEC region.

ip r d p

r e p

#

0

₌

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near side correlation as a signature of

DD

sQGPsQGP

we take drag coefficient to

be a parameter charactering

the coupling strength

*

* c quark motion in QGP:c quark motion in QGP:

*

* QGP evolution: QGP evolution: ideal hydrodynamics

ideal hydrodynamics

for strongly interacting quark

for strongly interacting quark--gluon plasma: gluon plasma:

at RHIC, the backat RHIC, the back--toto--back correlation is washed out.back correlation is washed out.

at LHC, c quarks are fast at LHC, c quarks are fast thermalizedthermalized, the strong , the strong flow push the D and

flow push the D and DbarDbarto the near side!to the near side!

Zhu, Xu, Zhuang, PRL100, 152301(2008) Zhu, Xu, Zhuang, PRL100, 152301(2008)

large drag parameter is confirmed by R_AA and v_2 of large drag parameter is confirmed by R_AA and v_2 of non

non--photonic electronsphotonic electrons(PHENEX, 2007; Moore and (PHENEX, 2007; Moore and TeaneyTeaney, , 2005; Horowitz, Gyulassy, 2007).

2005; Horowitz, Gyulassy, 2007).

conclusions

*

* BCSBCS--BEC crossover is a general phenomena from cold atom gas BEC crossover is a general phenomena from cold atom gas to quark matter.

to quark matter.

*

* BCSBCS--BEC crossover is closely related to QCD key problems: BEC crossover is closely related to QCD key problems: vacuum, color symmetry,

vacuum, color symmetry, chiralchiralsymmetry, symmetry, isospinisospinsymmetry symmetry …………

* BCS

* BCS--BEC crossover of color superconductivity and BEC crossover of color superconductivity and pionpion superfluid

superfluidis not induced by simply increasing the coupling is not induced by simply increasing the coupling

constant of the attractive interaction but by changing the

corresponding charge number.

*

* There are potential applications in heavy ion collisions (at There are potential applications in heavy ion collisions (at CSR/Lanzhou, FAIR/GSI and RHIC/BNL) and compact stars.

CSR/Lanzhou, FAIR/GSI and RHIC/BNL) and compact stars.

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