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  1. ❚❤❡ ❘♦❧❡ ♦❢ ❋❧✉❝t✉❛t✐♦♥s ✐♥ t❤❡ P❤❛s❡ ❉✐❛❣r❛♠♠ ♦❢ ◗❈ ✷ ❉ ❋✉♥❝t✐♦♥❛❧ ▼❡t❤♦❞s ◆❛s❡❡♠✉❞❞✐♥ ❑❤❛♥✱ ❏❛♥ ▼✳ P❛✇❧♦✇s❦✐✱ ▼✐❝❤❛❡❧ ❙❝❤❡r❡r✱ ❋❛❜✐❛♥ ❘❡♥♥❡❝❦❡ ❯♥✐✈❡rs✐t② ♦❢ ❍❡✐❞❡❧❜❡r❣ ◗❈❉ ♠❡❡ts ❈♦❧❞ ❆t♦♠s ✲ ❊♣✐s♦❞❡ ■■■ ✷✻t❤ ❆✉❣✉st ✷✵✶✷

  2. ♥♦ s✐❣♥ ♣r♦❜❧❡♠ ❝♦♠♣❛r❡ ✇✐t❤ ❧❛tt✐❝❡ r❡s✉❧ts ❝♦❧♦✉r ♥❡✉tr❛❧ ❜♦✉♥❞ st❛t❡s ♦❢ t✇♦ q✉❛r❦s ♣❤❛s❡s ♦❢ s✉♣❡r✢✉✐❞✐t② ❡❛s✐❧② ❛❝❡ss✐❜❧❡ ✐♠♣❛❝t ♦❢ ❜❛r②♦♥s ♦♥ t❤❡ ♣❤❛s❡ ❞✐❛❣r❛♠ ◗❈ ✷ ❉ ▼♦t✐✈❛t✐♦♥ 3 2.5 Deconfined Quark Gluon Plasma Chiral Symmetric 2 π T / m 1.5 Confined Confined 1 Chiral Broken Chiral Symmetric Hadronic Matter Quarkyonic Superfluid 0.5 0 0 0.5 1 1.5 2 2.5 3 µ B / m π [Schaefer Delta Meeting ’10] [Brauner, Fukushima & Hidaka ’09] ✷ ✴ ✷✾

  3. ❝♦❧♦✉r ♥❡✉tr❛❧ ❜♦✉♥❞ st❛t❡s ♦❢ t✇♦ q✉❛r❦s ♣❤❛s❡s ♦❢ s✉♣❡r✢✉✐❞✐t② ❡❛s✐❧② ❛❝❡ss✐❜❧❡ ✐♠♣❛❝t ♦❢ ❜❛r②♦♥s ♦♥ t❤❡ ♣❤❛s❡ ❞✐❛❣r❛♠ ▼♦t✐✈❛t✐♦♥ 3 2.5 Deconfined Quark Gluon Plasma Chiral Symmetric 2 π T / m 1.5 Confined Confined 1 Chiral Broken Chiral Symmetric Hadronic Matter Quarkyonic Superfluid 0.5 0 0 0.5 1 1.5 2 2.5 3 µ B / m π [Schaefer Delta Meeting ’10] [Brauner, Fukushima & Hidaka ’09] ◗❈ ✷ ❉ ♥♦ s✐❣♥ ♣r♦❜❧❡♠ → ❝♦♠♣❛r❡ ✇✐t❤ ❧❛tt✐❝❡ r❡s✉❧ts ✷ ✴ ✷✾

  4. ❝♦❧♦✉r ♥❡✉tr❛❧ ❜♦✉♥❞ st❛t❡s ♦❢ t✇♦ q✉❛r❦s ♣❤❛s❡s ♦❢ s✉♣❡r✢✉✐❞✐t② ❡❛s✐❧② ❛❝❡ss✐❜❧❡ ✐♠♣❛❝t ♦❢ ❜❛r②♦♥s ♦♥ t❤❡ ♣❤❛s❡ ❞✐❛❣r❛♠ ▼♦t✐✈❛t✐♦♥ 3 2.5 Deconfined Quark Gluon Plasma Chiral Symmetric 2 π T / m 1.5 Confined Confined 1 Chiral Broken Chiral Symmetric Hadronic Matter Quarkyonic Superfluid 0.5 0 0 0.5 1 1.5 2 2.5 3 µ B / m π [Schaefer Delta Meeting ’10] [Brauner, Fukushima & Hidaka ’09] ◗❈ ✷ ❉ ♥♦ s✐❣♥ ♣r♦❜❧❡♠ → ❝♦♠♣❛r❡ ✇✐t❤ ❧❛tt✐❝❡ r❡s✉❧ts ✷ ✴ ✷✾

  5. ✐♠♣❛❝t ♦❢ ❜❛r②♦♥s ♦♥ t❤❡ ♣❤❛s❡ ❞✐❛❣r❛♠ ▼♦t✐✈❛t✐♦♥ 3 2.5 Deconfined Quark Gluon Plasma Chiral Symmetric 2 π T / m 1.5 Confined Confined 1 Chiral Broken Chiral Symmetric Hadronic Matter Quarkyonic Superfluid 0.5 0 0 0.5 1 1.5 2 2.5 3 µ B / m π [Schaefer Delta Meeting ’10] [Brauner, Fukushima & Hidaka ’09] ◗❈ ✷ ❉ ♥♦ s✐❣♥ ♣r♦❜❧❡♠ → ❝♦♠♣❛r❡ ✇✐t❤ ❧❛tt✐❝❡ r❡s✉❧ts ❝♦❧♦✉r ♥❡✉tr❛❧ ❜♦✉♥❞ st❛t❡s ♦❢ t✇♦ q✉❛r❦s → ♣❤❛s❡s ♦❢ s✉♣❡r✢✉✐❞✐t② ❡❛s✐❧② ❛❝❡ss✐❜❧❡ ✷ ✴ ✷✾

  6. ✐♠♣❛❝t ♦❢ ❜❛r②♦♥s ♦♥ t❤❡ ♣❤❛s❡ ❞✐❛❣r❛♠ ▼♦t✐✈❛t✐♦♥ 3 2.5 Deconfined Quark Gluon Plasma Chiral Symmetric 2 π T / m 1.5 Confined Confined 1 Chiral Broken Chiral Symmetric Hadronic Matter Quarkyonic Superfluid 0.5 0 0 0.5 1 1.5 2 2.5 3 µ B / m π [Schaefer Delta Meeting ’10] [Brauner, Fukushima & Hidaka ’09] ◗❈ ✷ ❉ ♥♦ s✐❣♥ ♣r♦❜❧❡♠ → ❝♦♠♣❛r❡ ✇✐t❤ ❧❛tt✐❝❡ r❡s✉❧ts ❝♦❧♦✉r ♥❡✉tr❛❧ ❜♦✉♥❞ st❛t❡s ♦❢ t✇♦ q✉❛r❦s → ♣❤❛s❡s ♦❢ s✉♣❡r✢✉✐❞✐t② ❡❛s✐❧② ❛❝❡ss✐❜❧❡ ✷ ✴ ✷✾

  7. ▼♦t✐✈❛t✐♦♥ 3 2.5 Deconfined Quark Gluon Plasma Chiral Symmetric 2 π T / m 1.5 Confined Confined 1 Chiral Broken Chiral Symmetric Hadronic Matter Quarkyonic Superfluid 0.5 0 0 0.5 1 1.5 2 2.5 3 µ B / m π [Schaefer Delta Meeting ’10] [Brauner, Fukushima & Hidaka ’09] ◗❈ ✷ ❉ ♥♦ s✐❣♥ ♣r♦❜❧❡♠ → ❝♦♠♣❛r❡ ✇✐t❤ ❧❛tt✐❝❡ r❡s✉❧ts ❝♦❧♦✉r ♥❡✉tr❛❧ ❜♦✉♥❞ st❛t❡s ♦❢ t✇♦ q✉❛r❦s → ♣❤❛s❡s ♦❢ s✉♣❡r✢✉✐❞✐t② ❡❛s✐❧② ❛❝❡ss✐❜❧❡ ✐♠♣❛❝t ♦❢ ❜❛r②♦♥s ♦♥ t❤❡ ♣❤❛s❡ ❞✐❛❣r❛♠ ✷ ✴ ✷✾

  8. ▼♦t✐✈❛t✐♦♥ ❞❡❣r❡❡s ♦❢ ❢r❡❡❞♦♠ ✸ ✴ ✷✾

  9. ▼♦t✐✈❛t✐♦♥ ❞❡❣r❡❡s ♦❢ ❢r❡❡❞♦♠ ✹ ✴ ✷✾

  10. ▼♦t✐✈❛t✐♦♥ ❞❡❣r❡❡s ♦❢ ❢r❡❡❞♦♠ ✺ ✴ ✷✾

  11. ❛♥t✐✉♥✐t❛r✐t② ♦❢ ❉✐r❛❝ ♦♣❡r❛t♦r✿ ❉ t ✷ ❈ ✺ ❉ ✺ ❈t ✷ ❡①t❡♥❞❡❞ ✢❛✈♦✉r s②♠♠❡tr②✿ ❙❯ ◆ ❢ ❙❯ ◆ ❢ ❯ ✶ ❇ ❙❯ ✷ ◆ ❢ ▲ ❘ ▲ ✐ ❉ ❘ ✐ ❉ ✐ ❉ ◗❈ ✷ ❉ ▲ ❘ ✉ ▲ ❞ ▲ ▲ ✷ t ✷ ❘ ❘ ✉ ❘ ❘ ❞ ❘ ❛❧❧♦✇s ✉s t♦ r♦t❛t❡ ❘ ✱ s✐♠✐❧❛r❧② ▲ t ❚ ♣s❡✉❞♦r❡❛❧✐t② ♦❢ ❙❯ ✷ ❝ ❣❛✉❣❡ ❣r♦✉♣ ❣❡♥❡r❛t♦rs✿ t ❛ t ✷ t ❛ t ✷ ❛ ❋❡❛t✉r❡s ♦❢ ◗❈ ✷ ❉ ✻ ✴ ✷✾

  12. ❛♥t✐✉♥✐t❛r✐t② ♦❢ ❉✐r❛❝ ♦♣❡r❛t♦r✿ ❉ t ✷ ❈ ✺ ❉ ✺ ❈t ✷ ❡①t❡♥❞❡❞ ✢❛✈♦✉r s②♠♠❡tr②✿ ❙❯ ◆ ❢ ❙❯ ◆ ❢ ❯ ✶ ❇ ❙❯ ✷ ◆ ❢ ▲ ❘ ▲ ✐ ❉ ❘ ✐ ❉ ✐ ❉ ◗❈ ✷ ❉ ▲ ❘ ✉ ▲ ❞ ▲ ▲ ✷ t ✷ ❘ ❘ ✉ ❘ ❘ ❞ ❘ ❛❧❧♦✇s ✉s t♦ r♦t❛t❡ ❘ ✱ s✐♠✐❧❛r❧② ▲ ❋❡❛t✉r❡s ♦❢ ◗❈ ✷ ❉ ♣s❡✉❞♦r❡❛❧✐t② ♦❢ ❙❯ ( ✷ ) ❝ ❣❛✉❣❡ ❣r♦✉♣ ❣❡♥❡r❛t♦rs✿ t ∗ ❛ = t ❚ ❛ = − t ✷ t ❛ t ✷ ✻ ✴ ✷✾

  13. ▲ ✐ ❉ ❘ ✐ ❉ ✐ ❉ ◗❈ ✷ ❉ ▲ ❘ ✉ ▲ ❞ ▲ ▲ ✷ t ✷ ❘ ❘ ✉ ❘ ❘ ❞ ❘ ❛❧❧♦✇s ✉s t♦ r♦t❛t❡ ❘ ✱ s✐♠✐❧❛r❧② ▲ ❡①t❡♥❞❡❞ ✢❛✈♦✉r s②♠♠❡tr②✿ ❙❯ ◆ ❢ ❙❯ ◆ ❢ ❯ ✶ ❇ ❙❯ ✷ ◆ ❢ ▲ ❘ ❋❡❛t✉r❡s ♦❢ ◗❈ ✷ ❉ ♣s❡✉❞♦r❡❛❧✐t② ♦❢ ❙❯ ( ✷ ) ❝ ❣❛✉❣❡ ❣r♦✉♣ ❣❡♥❡r❛t♦rs✿ t ∗ ❛ = t ❚ ❛ = − t ✷ t ❛ t ✷ ❛♥t✐✉♥✐t❛r✐t② ♦❢ ❉✐r❛❝ ♦♣❡r❛t♦r✿ ❉ ∗ = − t ✷ ❈ γ ✺ ❉ γ ✺ ❈t ✷ ✻ ✴ ✷✾

  14. ▲ ✐ ❉ ❘ ✐ ❉ ✐ ❉ ◗❈ ✷ ❉ ▲ ❘ ✉ ▲ ❞ ▲ ▲ ✷ t ✷ ❘ ❘ ✉ ❘ ❘ ❞ ❘ ❛❧❧♦✇s ✉s t♦ r♦t❛t❡ ❘ ✱ s✐♠✐❧❛r❧② ▲ ❋❡❛t✉r❡s ♦❢ ◗❈ ✷ ❉ ♣s❡✉❞♦r❡❛❧✐t② ♦❢ ❙❯ ( ✷ ) ❝ ❣❛✉❣❡ ❣r♦✉♣ ❣❡♥❡r❛t♦rs✿ t ∗ ❛ = t ❚ ❛ = − t ✷ t ❛ t ✷ ❛♥t✐✉♥✐t❛r✐t② ♦❢ ❉✐r❛❝ ♦♣❡r❛t♦r✿ ❉ ∗ = − t ✷ ❈ γ ✺ ❉ γ ✺ ❈t ✷ ❡①t❡♥❞❡❞ ✢❛✈♦✉r s②♠♠❡tr②✿ ❙❯ ( ◆ ❢ ) ▲ × ❙❯ ( ◆ ❢ ) ❘ × ❯ ( ✶ ) ❇ → ❙❯ ( ✷ ◆ ❢ ) ✻ ✴ ✷✾

  15. ▲ ✐ ❉ ❘ ✐ ❉ ✐ ❉ ◗❈ ✷ ❉ ▲ ❘ ✉ ▲ ❞ ▲ ▲ ✷ t ✷ ❘ ❘ ✉ ❘ ❘ ❞ ❘ ❛❧❧♦✇s ✉s t♦ r♦t❛t❡ ❘ ✱ s✐♠✐❧❛r❧② ▲ ❋❡❛t✉r❡s ♦❢ ◗❈ ✷ ❉ ♣s❡✉❞♦r❡❛❧✐t② ♦❢ ❙❯ ( ✷ ) ❝ ❣❛✉❣❡ ❣r♦✉♣ ❣❡♥❡r❛t♦rs✿ t ∗ ❛ = t ❚ ❛ = − t ✷ t ❛ t ✷ ❛♥t✐✉♥✐t❛r✐t② ♦❢ ❉✐r❛❝ ♦♣❡r❛t♦r✿ ❉ ∗ = − t ✷ ❈ γ ✺ ❉ γ ✺ ❈t ✷ ❡①t❡♥❞❡❞ ✢❛✈♦✉r s②♠♠❡tr②✿ ❙❯ ( ◆ ❢ ) ▲ × ❙❯ ( ◆ ❢ ) ❘ × ❯ ( ✶ ) ❇ → ❙❯ ( ✷ ◆ ❢ ) ✻ ✴ ✷✾

  16. ✐ ❉ ✉ ▲ ❞ ▲ ▲ ✷ t ✷ ❘ ❘ ✉ ❘ ❘ ❞ ❘ ❛❧❧♦✇s ✉s t♦ r♦t❛t❡ ❘ ✱ s✐♠✐❧❛r❧② ▲ ❋❡❛t✉r❡s ♦❢ ◗❈ ✷ ❉ ♣s❡✉❞♦r❡❛❧✐t② ♦❢ ❙❯ ( ✷ ) ❝ ❣❛✉❣❡ ❣r♦✉♣ ❣❡♥❡r❛t♦rs✿ t ∗ ❛ = t ❚ ❛ = − t ✷ t ❛ t ✷ ❛♥t✐✉♥✐t❛r✐t② ♦❢ ❉✐r❛❝ ♦♣❡r❛t♦r✿ ❉ ∗ = − t ✷ ❈ γ ✺ ❉ γ ✺ ❈t ✷ ❡①t❡♥❞❡❞ ✢❛✈♦✉r s②♠♠❡tr②✿ ❙❯ ( ◆ ❢ ) ▲ × ❙❯ ( ◆ ❢ ) ❘ × ❯ ( ✶ ) ❇ → ❙❯ ( ✷ ◆ ❢ ) L ◗❈ ✷ ❉ = ψ † ▲ ✐ σ µ ❉ µ ψ ▲ + ψ † ❘ ✐ σ † µ ❉ µ ψ ❘ ✻ ✴ ✷✾

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