Lattice QCD with chemical potential

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What’s the problem? Z = e −F/T = ∫ DUe −S ∏ f det M(U, m f, µ f ) = ∫ DUe −S(T,µ) Dirac operator: M = m + i∂ µ γ µ • If there is a Q such that M † = Q † MQ, then clearly det M is real. • Q = γ 5 for µ = 0. Nothing for µ ≠ 0. • Monte Carlo simulations of Z fail. • Under CP symmetry {U} → {U ′ } such that det M(U) = [det M(U ′ )] ∗ . • Z remains real and non-negative— thermodynamics is safe. Chemical <strong>potential</strong>/S. Gupta: IMSc, 2003 to plan, Phases, Reweight, Expansion, QNS, strangeness, EOS, masses, end 3
Reweighting: what it is Do simulations at µ f = 0, re-express expectation values in terms of these— β Budapest method 〈O〉 µ = 〈O exp(−∆S)〉〈exp(−∆S)〉 where S = S − ∑ f Tr log M f , Glasgow method µ Reweighting done for coarse lattices (N t = 4) and N f = 4, 2 and 2+1. Chemical <strong>potential</strong>/S. Gupta: IMSc, 2003 to plan, Phases, Reweight, Expansion, QNS, strangeness, EOS, masses, end 4
Page 1: Lattice QCD with chemical potential
Page 6 and 7: Reweighting and other direct approa
Page 8 and 9: Reweighting: lattice artifacts Chem
Page 10 and 11: Derivatives Derivatives of log Z ca
Page 12 and 13: Some notation With two degenerate f
Page 14 and 15: Perturbation theory 1.0 1 0.9 NL HT
Page 16 and 17: Event to event fluctuations Each he
Page 18 and 19: The pressure P (T, µ) = −F/V = P
Page 20 and 21: Radius of convergence: distance to
Page 22: Summary of Results More than one me

Lattice QCD with chemical potential

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