Thermodynamics of Quasi-Particles
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Thermodynamics of Quasi-Particles
Fernanda Steffens
Mackenzie – São Paulo
Collaboration with F. G. Gardim
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Hadronic Matter New State, dominated by degrees of freedom of quarks and gluons
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Lattice QCD: Phase transition at Tc. Stephan-Boltzmann limit at very large T
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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?
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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
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Peshier et al. PRD 54 (1996) 2399
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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
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Thermodynamics in a grand canonical ensemble
If the mass is independent of T and , then the grand potential
Partition Function = - T lnZ V; T)
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However, in general:
Not zero if H depends on T and on
The extra terms lead to an inconsistency in thethermodynamics relations
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Generalization
Extra term forcesa consistent formulation
With
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What is the meaning of B?
Quantum interpretation
Density Operator
The internal energy:
Zero point energy
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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
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The thermodynamics functions of the system are then
From all possible solutions, which ones are physically relevant?
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= 0 Entropy unchangedOriginally developed for =0
Solution of the type Gorenstein – Yang
Extension to finite : Peshier, Cashing, etc
GY1 Solution
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Set = , Entropy unchangedInternal energy unchanged
SimplerSmaller number of constants
Other solutions of the kind Gorenstein – Yang? Yes
GY2 Solution
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This solution allows us to write explicit expressions for the thermodynamicsfunctions
Reduced entropy: s’(T,) – s’(T,0)
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HTL mass was used
Number density Pressure
Comparison to lattice QCD
Unpublished
HTL = Hard Thermal Loop – loops dominated by k~T
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What about perturbative QCD at T >> Tc ? (HTL mass)
GY1 Solution
GY2 Solution
QCD
Both solutions fail!!
FG,FMS, NP A825: 222, 2009
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Is there a solution that reproduces both, lattice QCD andperturbative QCD?
YES
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Solution with = 0
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Doing the integrals...
And similar for the entropy density, energy density and number density...
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Lattice data:
FG,FMS, NP A825: 222, 2009
HTL mass in NLO was used, and
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Factor of 1/2! Disagreement:
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Hard Thermal Loop (HTL) masses were used
Redefinition of the mass:
And agreement is found with both pQCD and Lattice QCD...
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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
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Feliz aniversário, Tony!
E obrigada pela sua amizade e por todo o resto!!!!