Real &me correla&on func&ons at finite temperature - - PowerPoint PPT Presentation

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Mar 10, 2023 345 likes •480 views

Real &me correla&on func&ons at finite temperature Based on Formalism + Vacuum Nicolas Wink Pawlowski, Strodthoff, PhysRevD.92.094009 Self-consistent Vacuum N. Strodthoff Strodthoff, arXiv:1611.05036 In collabora/on with J. M.

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Real &me correla&on func&ons at finite temperature

Nicolas Wink

In collabora/on with

N. Strodthoff
J. M. Pawlowski

Based on Formalism + Vacuum Self-consistent Vacuum Finite temperature

Pawlowski, Strodthoff, PhysRevD.92.094009 Strodthoff, arXiv:1611.05036 Pawlowski, Strodthoff, NW, in prep

Nicolas Wink (ITP Heidelberg) FRG, Heidelberg 2017 1

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Why real /me correla/on func/ons?

Bound state spectrum Transport coefficients

PACS-CS collabora/on Chris/ansen, Haas, Pawlowski, Strodthoff PRL, 115 (2015) no.11, 112002

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Use analy/city constrains and KMS condi/on to obtain real /me correla/on func/ons form Matsubara formalism Con/nua/on from Matsubara frequencies Matsubara contour Schwinger-Keldysh contour

From imaginary to real /mes

Nicolas Wink (ITP Heidelberg) FRG, Heidelberg 2017 3

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Calculate for Calculate Matsubara sum

Illustra/ve example

Two bosonic fields with

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Replace sum by contour integral: Bosonic occupa/on number

Illustra/ve example

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Iden/fy ambiguity of the analy/c con/nua/on Unique physical analy/c con/nua/on iden/fied by sedng everywhere Analy/c off the imaginary axis Correct decay behaviour at infinity Mathema/cally rigorous

Baym and Mermin, Journal of Mathema/cal Physics 2, 232 (1961)

Illustra/ve example

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Retarded/Advanced Greens func/on

Retarded Greens func/on Take limit analy/cally Numerical extrapola/on

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No new conceptual problems

Generalisa/on to the FRG

Regulator poles No changes Addi/onal poles

Kamikado, Strodthoff, von Smekal, Wambach, Eur.Phys.J. C74, 2806 (2014) Tripolt, Strodthoff , von Smekal, Wambach, Phys.Rev. D89, 034010 (2014)

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Calculate spectral func/ons of the O(N) model Effec/ve descrip/on of the lightest mesons

Applica/on to the O(N)-Model

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Applica/on to the O(N)-Model

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Applica/on to the O(N)-Model

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Perform analy/c con/nua/on
Conceptual easy algorithm
Finite temperature spectral func/ons

Summary & Outlook

Fully self-consistent trunca/on at finite temperature
Real /me representa/on of ver/ces
Applica/on to different model

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