Dy Dyna namical Th Ther erma maliz lizatio ion in in the e - - PowerPoint PPT Presentation

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Dy Dyna namical Th Ther erma maliz lizatio ion in in the e - - PowerPoint PPT Presentation

Nov 09, 2022 16 likes •477 views

Dy Dyna namical Th Ther erma maliz lizatio ion in in the e Quark-Me Meson Mo Model with J. Berges, J. Pawlowski, A. Rothkopf (in preparation) Cold Quantum Coffee ITP Heidelberg Lin inda Shen | Instit itute for or Th Theor oretic

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SLIDE 1

Dy Dyna namical Th Ther erma maliz lizatio ion in in the e Quark-Me Meson Mo Model

with J. Berges, J. Pawlowski, A. Rothkopf (in preparation)

Cold Quantum Coffee ITP Heidelberg

Lin inda Shen | Instit itute for

  • r Th

Theor

  • retic

ical l Physic ics | Heid idelb lberg

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SLIDE 2

baryon chemical potential temperature

From heavy ion collisions towards the QCD phase diagram: an equilibration process

04. 04.02. 02.20 20 2 Lin inda Shen | Instit itute for

  • r Th

Theor

  • retic

ical l Physic ics | Heid idelb lberg

Figures from http://wl33.web.rice.edu/images/HI-cartoon.png, http://images.slideplayer.com/25/7893277/slides/slide_3.jpg

  • QCD phase diagram: an equilibrium concept
  • deconfinement + chiral phase transition
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SLIDE 3

From heavy ion collisions towards the QCD phase diagram: an equilibration process

04. 04.02. 02.20 20 3 Lin inda Shen | Instit itute for

  • r Th

Theor

  • retic

ical l Physic ics | Heid idelb lberg

  • QCD phase diagram: an equilibrium concept
  • need out-of-equilibrium dynamics to describe

initial stages of heavy ion collision non-equilibrium

baryon chemical potential temperature

Figures from http://wl33.web.rice.edu/images/HI-cartoon.png, http://images.slideplayer.com/25/7893277/slides/slide_3.jpg

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SLIDE 4

From heavy ion collisions towards the QCD phase diagram: an equilibration process

04. 04.02. 02.20 20 4 Lin inda Shen | Instit itute for

  • r Th

Theor

  • retic

ical l Physic ics | Heid idelb lberg

non-perturbative regime of QCD non-equilibrium

baryon chemical potential temperature

Figures from http://wl33.web.rice.edu/images/HI-cartoon.png, http://images.slideplayer.com/25/7893277/slides/slide_3.jpg

  • QCD phase diagram: an equilibrium concept
  • need out-of-equilibrium dynamics to describe

initial stages of heavy ion collision

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SLIDE 5

We can investigate this equilibration using effective field theories.

04. 04.02. 02.20 20 5 Lin inda Shen | Instit itute for

  • r Th

Theor

  • retic

ical l Physic ics | Heid idelb lberg

φ = 0 φ = 0 µB T

  • 1) Quark-meson model &

non-equilibrium methods 2) Numerical results

initial state thermal state

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SLIDE 6

04. 04.02. 02.20 20 6 Lin inda Shen | Instit itute for

  • r Th

Theor

  • retic

ical l Physic ics | Heid idelb lberg

  • d.o.f.: light quarks and mesons
  • chiral symmetry breaking
  • phase diagram with first order

& crossover transition

The quark-meson model provides a successful formulation of QCD below scales ~1 GeV.

Jungnickel, Wetterich. PRD (1996)

  • Birse. J. Phys. G: Nucl. Part. Phys. (1994)
  • Petropoulos. J. Phys. G: Nucl.Part. Phys (1998)

Berges, Jungnickel, Wetterich.Int. J. Mod. Phys. A (2003) Schaefer, Pirner. arXiv nucl-th/9903003 (1999)

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SLIDE 7

04. 04.02. 02.20 20 7 Lin inda Shen | Instit itute for

  • r Th

Theor

  • retic

ical l Physic ics | Heid idelb lberg

  • d.o.f.: light quarks and mesons
  • chiral symmetry breaking
  • phase diagram with first order

& crossover transition

The quark-meson model provides a successful formulation of QCD below scales ~1 GeV.

φ = 0 φ = 0 µB T

Jungnickel, Wetterich. PRD (1996)

  • Birse. J. Phys. G: Nucl. Part. Phys. (1994)
  • Petropoulos. J. Phys. G: Nucl.Part. Phys (1998)

Berges, Jungnickel, Wetterich.Int. J. Mod. Phys. A (2003) Schaefer, Pirner. arXiv nucl-th/9903003 (1999)

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SLIDE 8

The quark-meson model provides a successful formulation of QCD below scales ~1 GeV.

04. 04.02. 02.20 20 8 Lin inda Shen | Instit itute for

  • r Th

Theor

  • retic

ical l Physic ics | Heid idelb lberg

S[ ¯ ψ, ψ, σ, π] =

  • x
  • ¯

ψ [iγµ∂µ − mψ] ψ − g Nf ¯ ψ [σ + iγ5τ απα] ψ + 1 2 [∂µσ∂µσ + ∂µπ∂µπ] − 1 2m2 σ2 + παπα − λ 4!N

  • σ2 + παπα2
slide-9
SLIDE 9

The quark-meson model provides a successful formulation of QCD below scales ~1 GeV.

04. 04.02. 02.20 20 9 Lin inda Shen | Instit itute for

  • r Th

Theor

  • retic

ical l Physic ics | Heid idelb lberg

S[ ¯ ψ, ψ, σ, π] =

  • x
  • ¯

ψ [iγµ∂µ − mψ] ψ − g Nf ¯ ψ [σ + iγ5τ απα] ψ + 1 2 [∂µσ∂µσ + ∂µπ∂µπ] − 1 2m2 σ2 + παπα − λ 4!N

  • σ2 + παπα2

u & d quark

slide-10
SLIDE 10

The quark-meson model provides a successful formulation of QCD below scales ~1 GeV.

04. 04.02. 02.20 20 10 10 Lin inda Shen | Instit itute for

  • r Th

Theor

  • retic

ical l Physic ics | Heid idelb lberg

S[ ¯ ψ, ψ, σ, π] =

  • x
  • ¯

ψ [iγµ∂µ − mψ] ψ − g Nf ¯ ψ [σ + iγ5τ απα] ψ + 1 2 [∂µσ∂µσ + ∂µπ∂µπ] − 1 2m2 σ2 + παπα − λ 4!N

  • σ2 + παπα2

u & d quark sigma meson & pions

slide-11
SLIDE 11

The quark-meson model provides a successful formulation of QCD below scales ~1 GeV.

04. 04.02. 02.20 20 11 11 Lin inda Shen | Instit itute for

  • r Th

Theor

  • retic

ical l Physic ics | Heid idelb lberg

S[ ¯ ψ, ψ, σ, π] =

  • x
  • ¯

ψ [iγµ∂µ − mψ] ψ − g Nf ¯ ψ [σ + iγ5τ απα] ψ + 1 2 [∂µσ∂µσ + ∂µπ∂µπ] − 1 2m2 σ2 + παπα − λ 4!N

  • σ2 + παπα2

u & d quark sigma meson & pions Yukawa coupling

slide-12
SLIDE 12

The quark-meson model provides a successful formulation of QCD below scales ~1 GeV.

04. 04.02. 02.20 20 12 12 Lin inda Shen | Instit itute for

  • r Th

Theor

  • retic

ical l Physic ics | Heid idelb lberg

S[ ¯ ψ, ψ, σ, π] =

  • x
  • ¯

ψ [iγµ∂µ − mψ] ψ − g Nf ¯ ψ [σ + iγ5τ απα] ψ + 1 2 [∂µσ∂µσ + ∂µπ∂µπ] − 1 2m2 σ2 + παπα − λ 4!N

  • σ2 + παπα2

u & d quark sigma meson & pions Yukawa coupling

scalar potential

φ V (φ) m2 < 0 m2 > 0

slide-13
SLIDE 13

Non-equilibrium time-evolution

04. 04.02. 02.20 20 13 13 Lin inda Shen | ITP TP & KIP | Heid idelb lberg

S[ϕ] Γ[φ, G] φ G

non-equilibrium non-equilibrium

⇒ initial va value p problem

slide-14
SLIDE 14

Spectral and statistical functions

04. 04.02. 02.20 20 14 14 Lin inda Shen | Instit itute for

  • r Th

Theor

  • retic

ical l Physic ics | Heid idelb lberg

  • spectral fct.
  • statistical fct.
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G = F + i 2 ρ

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statistical function spectral function

decomposition

slide-15
SLIDE 15

Spectral and statistical functions

04. 04.02. 02.20 20 15 15 Lin inda Shen | Instit itute for

  • r Th

Theor

  • retic

ical l Physic ics | Heid idelb lberg

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mesons

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p p

  • p p
  • p

p p

  • p

p p

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quarks

slide-16
SLIDE 16

Dynamical thermalization to different phases

04. 04.02. 02.20 20 16 16 Lin inda Shen | Instit itute for

  • r Th

Theor

  • retic

ical l Physic ics | Heid idelb lberg

T

crossover region χs broken phase χ symmetric phase

n0 = 0, σ0 > 0

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n0 > 0, σ0 = 0

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Non-equilibrium initial conditions εinit

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fi fiel eld IC fl fluct ctuation IC

slide-17
SLIDE 17

Gaussian initial state with free propagators

04. 04.02. 02.20 20 17 17 Lin inda Shen | Instit itute for

  • r Th

Theor

  • retic

ical l Physic ics | Heid idelb lberg

fi fiel eld IC fl fluct ctuation IC

σ(t = 0) = σ0 F φ(0, 0, |p|) = 1 2ωφ

p

F ψ(0, 0, |p|) = −γipi + mψ ωψ

p

1 2 − nψ

p

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slide-18
SLIDE 18

Wigner transformed propagators

04. 04.02. 02.20 20 18 18 Lin inda Shen | ITP TP & KIP | Heid idelb lberg

t t τ

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t, t → τ = t + t 2 , ∆t = t − t

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central time relative time

  • iρ(τ, ω, |p|) =
  • d∆t eiω∆tρ (τ, ∆t, |p|)
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t t τ ∆t

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  • iρ(τ, ω, |p|) =
  • d∆t eiω∆tρ (τ, ∆t, |p|)
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slide-19
SLIDE 19

Wigner transformed propagators

04. 04.02. 02.20 20 19 19 Lin inda Shen | ITP TP | Heid idelb lberg

free theory particles weak interactions quasi-particles

slide-20
SLIDE 20

Thermal equilibrium

Fluctuation-dissipation theorem

04. 04.02. 02.20 20 20 20 Lin inda Shen | Instit itute for

  • r Th

Theor

  • retic

ical l Physic ics | Heid idelb lberg

slide-21
SLIDE 21

Approach of quantum thermal equilibrium

04. 04.02. 02.20 20 21 21 Lin inda Shen | Instit itute for

  • r Th

Theor

  • retic

ical l Physic ics | Heid idelb lberg

n(ω, ||) n/(ω) = 1 eβω 1 β = 1/T

  • in thermal equilibrium:

fluctuation-dissipation theorem statistical function spectral function

p p

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  • eff. particle number:

p p p

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slide-22
SLIDE 22

Effective pion particle number

04. 04.02. 02.20 20 22 22 Lin inda Shen | Instit itute for

  • r Th

Theor

  • retic

ical l Physic ics | Heid idelb lberg

approaches Bose-Einstein distribution

  • <latexit sha1_base64="n8l0LtkpG5y8laH560qhc9Dm9c8=">ACdnicdVFdSwJBFL2ufZh9ab0VhChSDym7ovgUiEH1aJEfoCKz410b3C92ZgNZ9g/1K+of9Gq/pMdmt31R6w4znDn3OFyRndNxoWqLlNKemt7Zzezl90/ODw6zuVPetzxPYpd6piON9AJR5PZ2BVMmDhwPSWbmJfn9Gev8VPc4c+1ksXBxbZGYzg1EiJOXkimDJP0OBbiRewQCDPCAIUAGNxBCEH6Q54FqGzoWqRCDcJrqRW1bgKm0BLQAmS6kzyqbPR1KG+hbagJuF8qKmuGAfE4yaGZHPkeX0DmZYWA4tuAu0lWJwvLD0slC0iXvi6FpH/afGDYXaF9m1GnSlW4r4VaSihTSzk4yCOW4xRUPGHd8CbugTD6dh8HTfDgOtqV7L9YdHN31MTJGl1misTaB7ZI5CkjJNbT27TdCrVbV6tf5YL7XaSa4ZOIciXMl/aUILHqADXflPb/AJS/hKfSsXSlm5/LUqaTnFZKUX8AU/6zWw=</latexit>
slide-23
SLIDE 23

Effective quark particle number

04. 04.02. 02.20 20 23 23 Lin inda Shen | Instit itute for

  • r Th

Theor

  • retic

ical l Physic ics | Heid idelb lberg

approaches Fermi-Dirac distribution

  • <latexit sha1_base64="kgS3fHgK42SRt1bf/DbMNXosGTM=">ACdHicdVHLTsJAFL0tPhBfoDt1gRISE5W0BMLKhGCiLtHIwFCpsMtTugrnakJafo/oY/4Fb9EdcOtZuC3slMzpxz7uTmjOFZjAtN+1LUzNr6xmZ2K7e9s7u3ny8cdLkb+BQ71LVcv28QjhZzsCOYsLDv+Uhsw8KeMbtZ6L0X9DlznScx93Bk6nDTEaJkJSbPwUHxtCFIlzLPQBJvhAgEIDG4hgjDzJs8iXCyp+kKDKkTjfEmraHEV4GegBIk1R4XlKPhxKWBjY6gFuF8oGueGIXEF4xaGOWGAUeP0BmZYmi6juAe0jRLbM7nthEVyzYRz3xZW5D/afGDUS5FBw6j7gSv4r6UNJDQITbyURiHLceYoCnDjm8hN42xj5MofLxrRaHe0C7l+sNjWAEmpoWlWq8vTWD4ZIZCkjJNfTm7VdCtVvRapfZQKzVbSa5ZOIYzOJf/0oAm3EMbOvKfXuEdPuBT+VZP1Ja/rWqStJzCKlSKz/b4bK5</latexit>
slide-24
SLIDE 24

Thermalization temperature

04. 04.02. 02.20 20 24 24 Lin inda Shen | Instit itute for

  • r Th

Theor

  • retic

ical l Physic ics | Heid idelb lberg

p

  • p p
  • p
<latexit sha1_base64="C43ICRMLIMkEZcsK09O+mONZ1Y=">ADNHicdVLNbtNAEB47/JTw0xRucLGIkIpUIrsQ9YRUlQMcC2raSnWIdjfjxsra3nXtNXiAy/AFZ6DA+/AIyBxQ1x5BsaL0mbsWY183fjMfj5YVMtQnDn57fuXb9xs21W93bd+7eW+9t3D/UqioFjoSqjzmTKNMcxyZ1Eg8LkpkGZd4xOevGv7oA5Y6VfmBuShwnLHTPE1SwQxBqvcJctjs/IAtCOAjxJABAwMz4JCAhQJqQp8S95I8JqwkXhATEWMB4T2dlhgBCiR5SZkmHYcJuYSKNHXnG2VX9a7pzbXrXBAbuK5NZqjqnE7tlAGcQeoqg4Zf2W3VlLH7uoNVM0x6/XAQOgsuB1Eb9KG1/cmG9zCeKlFlmBshmdYnUViYsWlSYXEuhtXGgsm5uwUbaJyowsUiyjLtL7IeB08yZiZ6WuAVdxrmHdXYCrPBVqis9c3QJ1QmHOMtRj6y4LjTHFhC6Ly6xO+KTEaW3fvd6rbQTbtFzhYbLCltRI9keDpcm4CWboyGQthkt7+5ycLg9iJ4Phm9f9Hf32r2uwSN4DJv0z3ZgF97APoxAeDPvs/fF+p/93/5v/0/6W+19Y8gAXz/4D5/zaxw=</latexit>

p

p p

<latexit sha1_base64="d+CAm1iyMFUbmHgViO5Ku0NbYs=">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</latexit>

is determined from fit thermal distribution

slide-25
SLIDE 25

Thermalization temperature

04. 04.02. 02.20 20 25 25 Lin inda Shen | Instit itute for

  • r Th

Theor

  • retic

ical l Physic ics | Heid idelb lberg

is the same for all momenta and all components Ti : momentum averaged temperature for i = σ, π, V T : average over components i

slide-26
SLIDE 26

Thermalization

  • Late-time state is thermal
  • fluctuation-dissipation theorem
  • Late-time state has temperature T
  • thermal particle distribution

04. 04.02. 02.20 20 26 26 Lin inda Shen | Instit itute for

  • r Th

Theor

  • retic

ical l Physic ics | Heid idelb lberg

slide-27
SLIDE 27

Chiral symmetric phase

High temperature

04. 04.02. 02.20 20 27 27 Lin inda Shen | Instit itute for

  • r Th

Theor

  • retic

ical l Physic ics | Heid idelb lberg

slide-28
SLIDE 28

Pion sp spectr tral al function

04. 04.02. 02.20 20 28 28 Lin inda Shen | Instit itute for

  • r Th

Theor

  • retic

ical l Physic ics | Heid idelb lberg

shows a quasi-particle peak described by a Breit-Wigner function

slide-29
SLIDE 29

Pion stati statisti stical al function

04. 04.02. 02.20 20 29 29 Lin inda Shen | Instit itute for

  • r Th

Theor

  • retic

ical l Physic ics | Heid idelb lberg

shows decreasing occupation

slide-30
SLIDE 30

Quark stati statisti stical al function

04. 04.02. 02.20 20 30 30 Lin inda Shen | Instit itute for

  • r Th

Theor

  • retic

ical l Physic ics | Heid idelb lberg

shows increasing occupation (as opposed to the bosons)

slide-31
SLIDE 31

Dispersion and momentum-dependent width

04. 04.02. 02.20 20 31 31 Lin inda Shen | Instit itute for

  • r Th

Theor

  • retic

ical l Physic ics | Heid idelb lberg

p p p

p

<latexit sha1_base64="ZwQxA4ZhesOEZUir0TYm4aWB4Gg=">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</latexit>

are obtained from a fit to the Breit-Wigner function

fi fiel eld IC

slide-32
SLIDE 32

Quasi-particle mass and width

04. 04.02. 02.20 20 32 32 Lin inda Shen | Instit itute for

  • r Th

Theor

  • retic

ical l Physic ics | Heid idelb lberg

are obtained from p and p in the limit p

<latexit sha1_base64="pXWQcfXbi2q/JfgRtgnmWAEAR6c=">AEP3icnVNb9NAEJ3YfLThK4Ujl4i0EkhtZAdFPSGV9AXpIJIWykJ0a49Tlbx2tbuGlQZX7jCjV/EkZ/AL+CGuCIujLc+kLThwFqrnXlv3szsyMuzWGjed8ajnvl6rXrG5vNGzdv3b7T2rp7rNcBTgM0jhVp5xpjEWCQyNMjKeZQiZ5jCd8cVjxJ29RaZEmr81ZhPJZomIRMAMQWnrN+zAU5iCgIcwBgMctiFNtkpSECYEVL57wmRZBuYA4cICsigJPQRcU9sfAyJPTnlmsEINsmv8r6h2D3wKfr/K4zJlnT6f1WY1JULQgLKFdNW5GnScqrMCckpf2kVaCtPL61RrnTDoEkMo2xITEqRlVbQfRBCQiJiUtvPtvt15Vbrb7FNLKMcodV9XtL9WyXsZCu6icmX9I2VZ41yvM+lJ3T3FZRtud3xHikKqetjtf17GpfNPza6EC9jqZbDX8cpkEuMTFBzLQe+V5mJgVTRgQxls1xrjFjwYLNsIjSxOgMg2WUSa3PJC/bO5KZuV7lKnAdZxOWzSU4T0SQhrhndUvUiMyESdSTwj4QaiPEiB6I9Qod8anCsCxePRuUhb/v7dJ3SQyPc6yDqpBev7/SAVdsgYaUGo1kIqm6LA5fDNsDJWZzUw3ZXx3pReO41/Ufd/sve52DQT3uDbgPD+gH8WEfDuA5HMEQAmfsfHA+Op/cL+5394f78zUadSae7C03F9/AIX2DNo=</latexit>

p

<latexit sha1_base64="MOMxLhcQ0xCECcQ0XEQG1ye/YvA=">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</latexit>

sum rule

slide-33
SLIDE 33

Crossover region

Intermediate temperature

04. 04.02. 02.20 20 33 33 Lin inda Shen | Instit itute for

  • r Th

Theor

  • retic

ical l Physic ics | Heid idelb lberg

slide-34
SLIDE 34

Quark spectral density

04. 04.02. 02.20 20 34 34 Lin inda Shen | Instit itute for

  • r Th

Theor

  • retic

ical l Physic ics | Heid idelb lberg

slide-35
SLIDE 35

Quark statistical function

04. 04.02. 02.20 20 35 35 Lin inda Shen | Instit itute for

  • r Th

Theor

  • retic

ical l Physic ics | Heid idelb lberg

slide-36
SLIDE 36

Macroscopic field

Symmetry breaking

04. 04.02. 02.20 20 36 36 Lin inda Shen | Instit itute for

  • r Th

Theor

  • retic

ical l Physic ics | Heid idelb lberg

slide-37
SLIDE 37

Field expectation value

04. 04.02. 02.20 20 37 37 Lin inda Shen | Instit itute for

  • r Th

Theor

  • retic

ical l Physic ics | Heid idelb lberg

approaches stationary late-time value

thermal field expectation value from time average

<latexit sha1_base64="2B9KzgMt60AY0tYJPUO6EQq8pnU=">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</latexit>
slide-38
SLIDE 38

Thermal field value

04. 04.02. 02.20 20 38 38 Lin inda Shen | Instit itute for

  • r Th

Theor

  • retic

ical l Physic ics | Heid idelb lberg

depends on the energy provided by the initial condition

slide-39
SLIDE 39

Effective quantum potential

04. 04.02. 02.20 20 39 39 Lin inda Shen | Instit itute for

  • r Th

Theor

  • retic

ical l Physic ics | Heid idelb lberg

slide-40
SLIDE 40

Late-time thermal limit

Crossover phase transition

04. 04.02. 02.20 20 40 40 Lin inda Shen | Instit itute for

  • r Th

Theor

  • retic

ical l Physic ics | Heid idelb lberg

slide-41
SLIDE 41

Quark spectral function

04. 04.02. 02.20 20 41 41 Lin inda Shen | Instit itute for

  • r Th

Theor

  • retic

ical l Physic ics | Heid idelb lberg

slide-42
SLIDE 42

Dispersion relation

04. 04.02. 02.20 20 42 42 Lin inda Shen | Instit itute for

  • r Th

Theor

  • retic

ical l Physic ics | Heid idelb lberg

slide-43
SLIDE 43

Mass softening

04. 04.02. 02.20 20 43 43 Lin inda Shen | Instit itute for

  • r Th

Theor

  • retic

ical l Physic ics | Heid idelb lberg

characterizes the crossover phase transition

slide-44
SLIDE 44

Main decay mode Q

04. 04.02. 02.20 20 44 44 Lin inda Shen | Instit itute for

  • r Th

Theor

  • retic

ical l Physic ics | Heid idelb lberg

is determined by the maximum of the momentum-dependent width

slide-45
SLIDE 45

Order parameters

04. 04.02. 02.20 20 45 45 Lin inda Shen | Instit itute for

  • r Th

Theor

  • retic

ical l Physic ics | Heid idelb lberg

show the crossover phase transition

slide-46
SLIDE 46

Th Thank you!

Conclusion

04. 04.02. 02.20 20 46 46 Lin inda Shen | Instit itute for

  • r Th

Theor

  • retic

ical l Physic ics | Heid idelb lberg

T

crossover region χs broken phase χ symmetric phase

n0 = 0, σ0 > 0

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n0 > 0, σ0 = 0

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Non-equilibrium initial conditions εinit

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S[ ¯ ψ, ψ, σ, π] =

  • x
  • ¯

ψ [iγµ∂µ − mψ] ψ − g Nf ¯ ψ [σ + iγ5τ απα] ψ + 1 2 [∂µσ∂µσ + ∂µπ∂µπ] − 1 2m2 σ2 + παπα − λ 4!N

  • σ2 + παπα2

quar quark-meson

  • n

mod

  • del

quantum thermal l equilib ilibriu ium tim ime evolu

  • lution

ion of

  • f

spectral l function ions

  • r
  • rder parameters
  • f
  • f phase transit

ition ion