# Thermodynamics of Quasi- Particles

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27 Οκτ 2013 (πριν από 3 χρόνια και 8 μέρες)

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Thermodynamics of Quasi
-
Particles

Fernanda Steffens

Mackenzie

São Paulo

Collaboration with F. G. Gardim

New State, dominated by degrees of freedom

of quarks and gluons

Lattice QCD: Phase transition at T
c
. Stephan
-
Boltzmann limit at very large T

Perturbative QCD: up to order g
s
6

ln(1/g
s
)

Kajantie et al. PRD67:105008, 2003

Series is weakly convergent

Valid only for T ~ 10
5
T
c

Resum:
Hard Thermal Loops effective action

Andersen,Strickland, Annals Phys. 317: 281, 2005

2
-
loop
F

derivable approximation

Blaizot, Iancu, Rebhan, Phys. Rev. D63:065003, 2001

Region close to T
c
: quasi
-
particles?

Quasi
-
Particles: modified dispersion relations

Quark and gluon masses dependent on the

temperature T and/or the chemical potential
m

What is the thermodynamics of quasi
-
particles?

Originally: Gorenstein and Yang

PRD 52 (1995) 5206

Follow up: Peshier, Cassing, Kampfer, Blaizot, Rebhan, Weise, Bluhm, etc

Peshier et al. PRD 54 (1996) 2399

Goal: To calculate thermodynamics functions that reproduce the data

from lattice QCD and the results from perturbative QCD at large

T and/or
m

Peshier et al., PRC 61 (2000) 045203

Thaler, Schneider, Weise, PRC 69 (2004) 035210

Bluhm et al., PRC 76 (2007) 034901

Thermodynamics in a grand canonical ensemble

If the mass is independent of

T and
m
, then
F

f
:

the grand potential

Partition Function

F

=
-

T
ln
Z
(m

;

V; T
)

However, in general:

Not zero if H depends

on T and on
m

The extra terms lead to an inconsistency in the

thermodynamics relations

Generalization

Extra term forces

a consistent formulation

With

What is the meaning of B?

Quantum interpretation

Density Operator

The internal energy:

Zero point energy

For T=0, we subtract the zero point energy

For finite T (and
m
), the dispersion relation depends on T

So does the zero point energy

It can not be subtracted

is the energy of the system in the absence of quasi
-
particles

The lowest energy of the system

The thermodynamics functions of the system are then

From all possible solutions, which ones are physically relevant?

g

= 0

Entropy unchanged

Originally developed for
m
=0

Solution of the type Gorenstein

Yang

Extension to finite
m
: Peshier, Cashing, etc

GY1 Solution

Set
a
=
l
,
h = g = 0

Entropy unchanged

Internal energy unchanged

Simpler

Smaller number of constants

Other solutions of the kind Gorenstein

Yang?
Yes

GY2 Solution

This solution allows us to write explicit expressions for the thermodynamics

functions

Reduced entropy: s’(T,
m
)

s’(T,0)

HTL mass was used

Number density

Pressure

Comparison to lattice QCD

Unpublished

HTL = Hard Thermal Loop

loops dominated by k~T

What about perturbative QCD at T >> T
c

? (HTL mass)

GY1 Solution

GY2 Solution

QCD

Both solutions fail!!

FG,FMS, NP A825: 222, 2009

Is there a solution that reproduces both, lattice QCD and

perturbative QCD?

YES

Solution with
a
=
㴠0
=
Doing the integrals
...

And similar for the entropy density, energy density and number density...

Lattice data:

FG,FMS, NP A825: 222, 2009

HTL mass in NLO was used, and

Factor of 1/2!

Disagreement:

Hard Thermal Loop (HTL) masses were used

Redefinition of the mass:

And agreement is found with
both

pQCD and Lattice QCD...

Main points:

General formulation of thermodynamics consistency for a system whose

masses depend on both T and
m

Multiple ways to obtain consistency

First explicit calculation of the thermodynamics functions

Good agreement with lattice QCD with a smaller number of free

parameters

Possible agreement with perturbative QCD and lattice QCD for finite T

and
m
for a particular solution

The usual quasi
-
particle approach (Gorenstein
-
Yang) does not reproduce

perturbative QCD and lattice QCD at finite chemical potential

Single framework to study a large portion of the T
m

plane

Feliz aniversário, Tony!