# Presentation: 134967

## Instability of a gapless color superconductor with respect to inhomogeneous fluctuations

- Kenji Fukushima(RIKEN BNL Research Center)
- Ref:  K.Iida and K.Fukushima,  hep-ph/0603179

- May 2006

## Results

**Onset****of the g2SC**

*x*2 is drawn by
*v**g*=0
*x*1 is drawn by
*Q*=* k*TF

- May 2006

## QCD phase diagram

- ~170MeV

- Chiral Critical End-Point

**QGP**

**Color Superconductors**

- May 2006

## Phases in neutral quark matter

- Kenji Fukushima: hep-ph/0510299

**Unknown...**

- May 2006

## Instability    what comes out?

- Inhomogeneous Fluctuations (we consider)
- Gap parameter   **
- Phase   **  ** *e**iAx**  *(*A* = phase factor)
- Amplitude   **  ** +**(*q*)
- Number density   *n** *(*q*)
**Mixed phase**   small-size domains  (large *q*)
**Phase separation**   large-size domains  (small *q*)

**Qualitative difference****(Crossover or 1st?)**

**Related through the condition to minimize the energy**

**LOFF**

**amplitude LOFF**

- May 2006

## Single plane-wave LOFF

**LOFF superconductivity**

- Larkin-Ovchinnikov
- Fulde-Ferrel

**Constant gauge potential = Single plane-wave LOFF**

- Kenji Fukushima: hep-ph/0603216

- May 2006

## Instability    what comes out?

- Inhomogeneous Fluctuations (we consider)
- Gap parameter   **
- Phase   **  ** *e**iAx**  *(*A* = phase factor)
- Amplitude   **  ** +**(*q*)
- Number density   *n** *(*q*)
**Mixed phase**   small-size domains  (small *q *)
**Phase separation**   large-size domains  (large *q *)

**Qualitative difference****(Crossover or 1st?)**

**Related through the condition to minimize the energy**

**LOFF**

**amplitude LOFF**

- May 2006

## Quantities to be evaluated

- Curvatures of the thermodynamic potential

**1st-order phase transition is not considered.**
**We only see the tendency (steepest direction).**

- May 2006

## Clustering

**Thermodynamic**
**Potential**

- Dense domain

- Dilute domain

- May 2006

## Quantities to be evaluated

- Curvatures of the thermodynamic potential

**We don’t consider states separated by the****discontinuous transition.  We only see the****tendency (steepest direction).**

- May 2006

## This is what we see

**Unstable**
**Gapless State**

**tendency**

**guess**

**???**

- We don’t consider,
- for we don’t know...

- May 2006

## Two-flavor quark matter

- Chromomagnetic instability in different two regimes:
- Other instabilities:

**All the instabilities are entangled in the gapless regime.**

**Only qualitative difference... what is it?**

- May 2006

## Intuitive view of classification

**Well-gapped... superconductor**

**Poorly-gapped... normal**

**Amplitude LOFF**

**Mixed phase or Phase separation**

*q*

*q * is very large then...

- May 2006

## Qualitative definition

- Phase separation
- Mixed phase
- LOFF with amplitude
- LOFF without amplitude

- Instability w.r.t. *****n* occurs in the gapless 2SC.

- Instability w.r.t. *****n* occurs in the gapless 2SC.

- Instability w.r.t. ****** occurs in the gapless 2SC.

- Instability w.r.t. ****** occurs in the gapped 2SC.

- May 2006

## Energy balance

- Coulomb energy
- Kinetic energy

**Thomas-Fermi screening length**

**Decreasing func. w.r.t. *****q***

**Quadratic func.**

**Optimal *****q ***** is determined by the energy balance.**

**Weiszacker term**

- May 2006

## More about the kinetic term

- May 2006

## Energy balance

- Coulomb energy
- Kinetic energy

**Thomas-Fermi screening length**

**Decreasing func. w.r.t. *****q***

**Quadratic func.**

**Optimal *****q ***** is determined by the energy balance.**

**Weiszacker term**

- May 2006

## Results

**Onset****of the g2SC**

*x*2 is drawn by
*v**g*=0
*x*1 is drawn by
*Q*=* k*TF

- May 2006

## Conclusions

- Chromomagnetic instability in the gapless 2SC phase induces instability w.r.t. the gap amplitude and the quark number density.
- Domain size is determined by the balance between the Coulomb and kinetic energies.
- Weizsacker energy is crucial for the phase structure.
- What about the three-flavor CFL case?

- May 2006