Thermodynamics of Quasi-Particles
Fernanda Steffens
Mackenzie – São Paulo
Collaboration with F. G. Gardim
Hadronic Matter New State, dominated by degrees of freedom of quarks and gluons
Lattice QCD: Phase transition at Tc. Stephan-Boltzmann limit at very large T
Perturbative QCD: up to order gs6 ln(1/gs) – Kajantie et al. PRD67:105008, 2003
Series is weakly convergentValid only for T ~ 105Tc
Resum: Hard Thermal Loops effective action Andersen,Strickland, Annals Phys. 317: 281, 2005 2-loop derivable approximation Blaizot, Iancu, Rebhan, Phys. Rev. D63:065003, 2001
Region close to Tc: quasi-particles?
Quasi-Particles: modified dispersion relations
Quark and gluon masses dependent on the temperature T and/or the chemical potential
What is the thermodynamics of quasi-particles?
Originally: Gorenstein and Yang – PRD 52 (1995) 5206Follow 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
What about finite chemical potential? 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 , then the grand potential
Partition Function = - T lnZ V; T)
However, in general:
Not zero if H depends on T and on
The extra terms lead to an inconsistency in thethermodynamics relations
Generalization
Extra term forcesa 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 ), 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?
= 0 Entropy unchangedOriginally developed for =0
Solution of the type Gorenstein – Yang
Extension to finite : Peshier, Cashing, etc
GY1 Solution
Set = , Entropy unchangedInternal energy unchanged
SimplerSmaller number of constants
Other solutions of the kind Gorenstein – Yang? Yes
GY2 Solution
This solution allows us to write explicit expressions for the thermodynamicsfunctions
Reduced entropy: s’(T,) – 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 >> Tc ? (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 andperturbative QCD?
YES
Solution with = 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
• 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 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 plane
Feliz aniversário, Tony!
E obrigada pela sua amizade e por todo o resto!!!!
Top Related