sphaleron transitions and the chiral magnetic...
TRANSCRIPT
Sphaleron transitions and the Chiral Magnetic Effect
Mark Mace University of Jyväskylä
Finnish Particle Physics Day November 23, 2018
Based on: MM, Schlichting, Venugopalan PRD 93 2016, MM, Mueller, Schlichting, Sharma PRD 95 2017
The Chiral Magnetic EffectTopological processes in QCD can produce imbalances of quark chirality through chiral anomaly — but how to see this? Possible in heavy-ion collisions?
Axial charge imbalance in presence of external magnetic field produces an electric (vector) current: the Chiral Magnetic Effect:Kharzeev, McLerran, Warringa NPA 803 2008; Fukushima, Kharzeev, Warringa PRD 78 2008
Red=momentum Blue=spin
2
Son & Zhitnitsky, PRD 70, 074018; Metlitski & Zhitnitsky, PRD 72, 045011Chiral Separation Effect:
Chiral Magnetic Wave: collective gapless excitation from the coupling between density waves of electric and chiral charges
jV ∼ n5B
j5 ∼ nVB
However, life-time of magnetic field in vacuum is short < 1 fm/c
B
STAR PRC 81 (2010)
Magnetic field in HICSpectators in off-central collisions create a strong magnetic field eB ~ mπ2 ~1014 T
Need detailed understanding of pre-equilibrium dynamics to make quantitive statements about CME
3
Li, Sheng, Wang PRC 94 (2016)
jV ∼ n5B
Axial charge imbalanceQCD chiral anomaly generates chiral (axial) charge
Axial current ; receives contributions from sphaleron
transitions,…
Quark mass
Klinkhamer, Manton PRD 30 1984
Sphaleron transition (real time topological transitions) leads to unit change of Chern-Simons number and induce axial charge imbalance
Pote
ntia
l Bar
rier
Vacuum
NCS
Transition overthe sphaleron
Instanton NCSPote
ntial
Bar
rier Sphaleron Transition
10 32
⇠ Eai B
ai (x, t)
V
A V
4
jV ∼ n5B
For HIC, focus on mf ≈ 0Axial charge Change in
winding #
@µjµ5 = 2mh ¯ (x)i�5 (x)i�
g2
8⇡2trFµ⌫(x)F
µ⌫(x)<latexit sha1_base64="bIZd3+i6RXeIM1NbMU4lPXICRqM=">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</latexit><latexit sha1_base64="bIZd3+i6RXeIM1NbMU4lPXICRqM=">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</latexit><latexit sha1_base64="bIZd3+i6RXeIM1NbMU4lPXICRqM=">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</latexit><latexit sha1_base64="bIZd3+i6RXeIM1NbMU4lPXICRqM=">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</latexit>
�N05 = 2mf
Z
xh ¯ (x)i�5 (x)i�2�NCS
<latexit sha1_base64="voI4v/Rxq9n6hsBRdn2EMi3KHiI=">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</latexit><latexit sha1_base64="voI4v/Rxq9n6hsBRdn2EMi3KHiI=">AAACfnicbVFdaxQxFM2MX3Wtuir64ktwUepDtzOLxb4Ixfrgk1R028JmHe5k7+yGJpkhyUiXEPBv+gf0b5idrtS2XggczsnNuTm3bKSwLst+JumNm7du39m427u3ef/Bw/6jx0e2bg3HMa9lbU5KsCiFxrETTuJJYxBUKfG4PD1Y6cff0VhR669u2eBUwVyLSnBwkSr6PzzrHvEGZ4GyDygd0E/F7rcsvBupoqJMaFecUSZBzyVSVoLxbAHOs8aKELbOXgvK5qAUFLv0Qog8M13LX4NSthi26ejCxB98CaHoD7Jh1hW9DvI1GJB1HRb932xW81ahdlyCtZM8a9zUg3GCSww91lpsgJ/CHCcRalBop76bIdCXkZnRqjbxaEc79t8OD8rapSrjTQVuYa9qK/J/2qR11d7UC920DjU/N6paSV1NV7HTmTDInVxGANyIOCvlCzDAXVzOJRcbP7WIy+jFZPKrOVwHR6Nhng3zz28G++/XGW2Q5+QF2SI5eUv2yUdySMaEk1/JZvI0eZaS9FW6ne6cX02Tdc8TcqnSvT8/YcHH</latexit><latexit sha1_base64="voI4v/Rxq9n6hsBRdn2EMi3KHiI=">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</latexit><latexit sha1_base64="voI4v/Rxq9n6hsBRdn2EMi3KHiI=">AAACfnicbVFdaxQxFM2MX3Wtuir64ktwUepDtzOLxb4Ixfrgk1R028JmHe5k7+yGJpkhyUiXEPBv+gf0b5idrtS2XggczsnNuTm3bKSwLst+JumNm7du39m427u3ef/Bw/6jx0e2bg3HMa9lbU5KsCiFxrETTuJJYxBUKfG4PD1Y6cff0VhR669u2eBUwVyLSnBwkSr6PzzrHvEGZ4GyDygd0E/F7rcsvBupoqJMaFecUSZBzyVSVoLxbAHOs8aKELbOXgvK5qAUFLv0Qog8M13LX4NSthi26ejCxB98CaHoD7Jh1hW9DvI1GJB1HRb932xW81ahdlyCtZM8a9zUg3GCSww91lpsgJ/CHCcRalBop76bIdCXkZnRqjbxaEc79t8OD8rapSrjTQVuYa9qK/J/2qR11d7UC920DjU/N6paSV1NV7HTmTDInVxGANyIOCvlCzDAXVzOJRcbP7WIy+jFZPKrOVwHR6Nhng3zz28G++/XGW2Q5+QF2SI5eUv2yUdySMaEk1/JZvI0eZaS9FW6ne6cX02Tdc8TcqnSvT8/YcHH</latexit>
Theorists Overview of CMEGoal: Want to quantitatively study anomalous transport in HIC
(Son & Surowka 2009; Hirono, Hirano, Kharzeev 2014, Jiang et al 2016,…)
5
For CME, earliest times likely most important due to B
Recent progress has lead to a relatively complete qualitative picture of weak coupling thermalization
Berges, Boguslavski, Schlichting Venugopalan Phys.Rev. D89 (2014) no.11, 114007, Epelbaum, Gelis PRL 111 (2013) 232301, Kurkela, Zhu PRL 115 (2015) 18, 182301,…
Simulating early times after heavy-ion collision
Earliest time dynamics described by classical Yang-Mills
Emergence of a characteristic scale, , such that
Non-perturbatively large gluon phase space density
Highly amenable to real-time lattice simulations
Track right hand side of anomaly by measuring Chern-Simons number
Use cooling to remove short range fluctuation and isolate topological transitions
Neglect longitudinal expansion and use SU(2) for simplicity
McLerran, Venugopalan PRD49 2233 (1994)
6
Ambjorn, Krasnitz NPB 506 (1997), Moore PRD 59 (1998)
Venugopalan, Kransitz NPA 237 (1999), Berges, Scheffler, Sexty, PRD 77 034504 (2008)
Qs αS(Qs) ≪ 1
f(p ∼ Qs) ∼ 1αS
Sphalerons in the glasmaDetect integer changes in Chern-Simons number for single configuration
Chern-Simons diffusion of many configurations shows transitions between different topological sectors occurs
-8-6-4-2 0 2 4 6 8
10 12 14
10 15 20 25 30 35 40 45 50 55Time: Qst
Gradient Flow NCSCooled NCS (Qs
2τc=1/4) Cooled NCS (Qs
2τc=250)
MM, Schlichting, Venugopalan PRD 93 2016
Can isolate transitions from background Significant number can occur at early times
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
Qst=10Qsδt=10
Pro
ba
bil
ity
: P(Δ
NC
S)
ΔNCS
Qs2τc=250
Qs2τc=108
Qs2τc=36
Qs2τc=12
7
ΔNCS
Non-equilibrium sphaleron transition rate
Strongly time dependent, largest are early times — dynamics controlled by magnetic screening
Contributions from field strength fluctuations
Non-markovian, not random walk like thermal equilibrium
10-8
10-7
10-6
10-5
10 100
(Qst) -4/3
Γsp
hne
q / Q
s4
Time: Qs t
Qs2τc=1
Qs2τc=12
Qs2τc=36
Qs2τc=108
Qs2τc=216
Qs2τc=324
Increased cooling
MM, Schlichting, Venugopalan PRD 93 2016
8
Time
Qs4
Qst=1 QstQuant=αS-7/4
αS Qs
7/3 4
αS T45
Γ sph
Non-equilibrium,classical regime
Equilibration,Quantum
regimeThermal
equilibrium
Dominant amount of axial charge (should be)
generated at pre-equilibrium stage
Arnold, Son, Yaffee; Moore et al.
Axial Charge from Sphaleron Transition
�NCS =g2
8⇡
Zd4xEa ·Ba
�J05 = �2�NCS + 2mf
Zd4xh i�5 i
eB = 0, m ⌧ r�1sph
-0.1 0
0.1
0 0.2 0.4 0.6 0.8 1 1.2 1.4t/tsph
0
0.5
1
1.5
2
Ja0+2ΔNCS
Ja0
-2 ΔNCSJa
0: Wilson NLO Ja
0: Overlap M=1.5
MM, Mueller, Schlichting, Sharma PRD 95 2017
Good agreement found between discretization
Consider isolated sphaleron of size rsph, timescale tsph
Unit change in Chern-Simons number induces axial charge imbalance
9
To study full CME dynamics, need to extend non-equilibrium gauge field studies to include fermions
Cannot use classical approximation for fermions
Solve operator Dirac equation: (i /D �m) = j<latexit sha1_base64="Zk9Qseawpse9PpB4adGCGiye6hE=">AAACIHicbZDLSsNAFIYn9VbrLerSTWgR6sKSiKAboagLlxXsBZpQJpNJO3ZmEmYmQgnZ+xw+gFt9BHfiUl/A13CaZmGrBwY+/v+cOTO/H1MilW1/GqWl5ZXVtfJ6ZWNza3vH3N3ryCgRCLdRRCPR86HElHDcVkRR3IsFhsynuOuPr6Z+9wELSSJ+pyYx9hgcchISBJWWBma1TlxJoRzhIL3OjtmRO4IqdWNJsosc77OBWbMbdl7WX3AKqIGiWgPz2w0ilDDMFdJXy75jx8pLoVAEUZxV3ETiGKIxHOK+Rg4Zll6a/yWzDrUSWGEk9OHKytXfEylkUk6YrzsZVCO56E3F/7x+osJzLyU8ThTmaLYoTKilImsajBUQgZGiEw0QCaLfaqERFBApHd/cliKvrKKTcRZz+Audk4ZjN5zb01rzssioDA5AFdSBA85AE9yAFmgDBB7BM3gBr8aT8Wa8Gx+z1pJRzOyDuTK+fgA/06QZ</latexit><latexit sha1_base64="Zk9Qseawpse9PpB4adGCGiye6hE=">AAACIHicbZDLSsNAFIYn9VbrLerSTWgR6sKSiKAboagLlxXsBZpQJpNJO3ZmEmYmQgnZ+xw+gFt9BHfiUl/A13CaZmGrBwY+/v+cOTO/H1MilW1/GqWl5ZXVtfJ6ZWNza3vH3N3ryCgRCLdRRCPR86HElHDcVkRR3IsFhsynuOuPr6Z+9wELSSJ+pyYx9hgcchISBJWWBma1TlxJoRzhIL3OjtmRO4IqdWNJsosc77OBWbMbdl7WX3AKqIGiWgPz2w0ilDDMFdJXy75jx8pLoVAEUZxV3ETiGKIxHOK+Rg4Zll6a/yWzDrUSWGEk9OHKytXfEylkUk6YrzsZVCO56E3F/7x+osJzLyU8ThTmaLYoTKilImsajBUQgZGiEw0QCaLfaqERFBApHd/cliKvrKKTcRZz+Audk4ZjN5zb01rzssioDA5AFdSBA85AE9yAFmgDBB7BM3gBr8aT8Wa8Gx+z1pJRzOyDuTK+fgA/06QZ</latexit><latexit sha1_base64="Zk9Qseawpse9PpB4adGCGiye6hE=">AAACIHicbZDLSsNAFIYn9VbrLerSTWgR6sKSiKAboagLlxXsBZpQJpNJO3ZmEmYmQgnZ+xw+gFt9BHfiUl/A13CaZmGrBwY+/v+cOTO/H1MilW1/GqWl5ZXVtfJ6ZWNza3vH3N3ryCgRCLdRRCPR86HElHDcVkRR3IsFhsynuOuPr6Z+9wELSSJ+pyYx9hgcchISBJWWBma1TlxJoRzhIL3OjtmRO4IqdWNJsosc77OBWbMbdl7WX3AKqIGiWgPz2w0ilDDMFdJXy75jx8pLoVAEUZxV3ETiGKIxHOK+Rg4Zll6a/yWzDrUSWGEk9OHKytXfEylkUk6YrzsZVCO56E3F/7x+osJzLyU8ThTmaLYoTKilImsajBUQgZGiEw0QCaLfaqERFBApHd/cliKvrKKTcRZz+Audk4ZjN5zb01rzssioDA5AFdSBA85AE9yAFmgDBB7BM3gBr8aT8Wa8Gx+z1pJRzOyDuTK+fgA/06QZ</latexit><latexit sha1_base64="Zk9Qseawpse9PpB4adGCGiye6hE=">AAACIHicbZDLSsNAFIYn9VbrLerSTWgR6sKSiKAboagLlxXsBZpQJpNJO3ZmEmYmQgnZ+xw+gFt9BHfiUl/A13CaZmGrBwY+/v+cOTO/H1MilW1/GqWl5ZXVtfJ6ZWNza3vH3N3ryCgRCLdRRCPR86HElHDcVkRR3IsFhsynuOuPr6Z+9wELSSJ+pyYx9hgcchISBJWWBma1TlxJoRzhIL3OjtmRO4IqdWNJsosc77OBWbMbdl7WX3AKqIGiWgPz2w0ilDDMFdJXy75jx8pLoVAEUZxV3ETiGKIxHOK+Rg4Zll6a/yWzDrUSWGEk9OHKytXfEylkUk6YrzsZVCO56E3F/7x+osJzLyU8ThTmaLYoTKilImsajBUQgZGiEw0QCaLfaqERFBApHd/cliKvrKKTcRZz+Audk4ZjN5zb01rzssioDA5AFdSBA85AE9yAFmgDBB7BM3gBr8aT8Wa8Gx+z1pJRzOyDuTK+fgA/06QZ</latexit>
J05
Anomalous transport in real time
B
Sphaleron transition in background B field
10
OutlookSphaleron transition rate enhanced during the early stages of HIC
Development of real-time lattice techniques to study pre-equilibrium dynamics of fermions
Successful microscopic description of anomalous transport phenomena in simplistic setup — framework set up for full back-reaction QED/QCD
Ongoing and planned studies of quark production and axial charge production for variety of gauge field configurations
Calculation of spectral functions, transport coefficients, etc.
First calculations of axial charge production based on weakly coupled pre-equilibrium dynamics
11
Fermion production in HIC — needed for full description of HIC thermalization
Non-perturbative study of QED Schwinger pair production — variety of space- and time-dependent electric fields
Study chirality transfer between gauge fields and fermions — chiral plasma instability MM, Mueller, Schlichting, Sharma, in prep
MM, Mueller, Schlichting, Sharma, in prep
Thanks!
12
BACKUP
Early stages of HICs
J+ J�E
⌘
B⌘
colliding nuclei Glasma flux tubes over-occupiedplasma
min-jets + soft bath equilibrium
time
classical-statistical lattice gauge theory eff. kinetic theory hydro
strong fields quasi particles 1-2 fm/c
Fig. S. Schlichting
Initial nuclei described as Color Glass
Condensates
Recent progress has lead to a relatively complete qualitative picture of weak coupling thermalization
Berges, Boguslavski, Schlichting Venugopalan Phys.Rev. D89 (2014) no.11, 114007, Epelbaum, Gelis PRL 111 (2013) 232301, Kurkela, Zhu PRL 115 (2015) 18, 182301 14
Real-time QFTs
• Longstanding goal of particle and nuclear physics is to access the real time dynamics of QCD
• Ex. Thermalization and transport properties of hot and dense QCD, parton distributions in nucleons,…
• Euclidean formulation works well for some static observables*
• For real-time (non-equilibrium) dynamics, formulate path-integral on Schwinger-Keldysh contour
• A sign problem prevents general computations, avoiding this is a grand challenge
* with well known caveats (like finite baryon chemical potential)
Schwinger, J. Math. Phys. 2, 407 (1961), Keldysh, Zh. Eksp. Teor. Fiz. 47, 1515 (1964)
e.g. Berges, Stamatescu PRL 95 (2005) 202003, Alexandru et al, PRL117, 081602 (2016)
15
Space-time evolution of HIC
Classical-Statistical Approximation
• Typical situation: weak coupling, large coherent field or highly occupied gauge fields → correspondence principle
• Systematic expansion of the 'quantum' fields around the 'classical' fields
‘Real-time’ partition function
ZC =
Z[dA]
Z[d d ]⇢(t0)exp(iSG + iSF )
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ZclC =
Z[dA]
Zd⇧0⇢W (A0,⇧0)�[@F [A]� j]
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A+µ,n = A+
µ,n +1
2A+
µ,n<latexit sha1_base64="g9LzmtwPEEvJt7MR4jpq1etqagI=">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</latexit><latexit sha1_base64="g9LzmtwPEEvJt7MR4jpq1etqagI=">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</latexit><latexit sha1_base64="g9LzmtwPEEvJt7MR4jpq1etqagI=">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</latexit><latexit sha1_base64="g9LzmtwPEEvJt7MR4jpq1etqagI=">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</latexit>
A�µ,n = A�
µ,n � 1
2A�
µ,n<latexit sha1_base64="F5/briopCh/yAsjremg77ED89hE=">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</latexit><latexit sha1_base64="F5/briopCh/yAsjremg77ED89hE=">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</latexit><latexit sha1_base64="F5/briopCh/yAsjremg77ED89hE=">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</latexit><latexit sha1_base64="F5/briopCh/yAsjremg77ED89hE=">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</latexit>
}
Fermion field integration
Wigner distribution over quantum ICs Classical EoMKeep first term in A<latexit sha1_base64="Sz5HXDUTi7FiyGmaAz27KJBGlZg=">AAACBXicbVDLSsNAFJ3UV62vqks3g0VwVRIRdFl147KCbZU2lMnkph06MwkzE6GErP0At/oJ7sSt3+EX+BtO2yxs64ELh3Pu5d57goQzbVz32ymtrK6tb5Q3K1vbO7t71f2Dto5TRaFFYx6rh4Bo4ExCyzDD4SFRQETAoROMbiZ+5wmUZrG8N+MEfEEGkkWMEmOlx55hPITsKu9Xa27dnQIvE68gNVSg2a/+9MKYpgKkoZxo3fXcxPgZUYZRDnmll2pICB2RAXQtlUSA9rPpwTk+sUqIo1jZkgZP1b8TGRFaj0VgOwUxQ73oTcT/vG5qoks/YzJJDUg6WxSlHJsYT77HIVNADR9bQqhi9lZMh0QRamxGc1u0fWoIYV6xyXiLOSyT9lndc+ve3XmtcV1kVEZH6BidIg9doAa6RU3UQhQJ9IJe0Zvz7Lw7H87nrLXkFDOHaA7O1y8F6JlU</latexit><latexit sha1_base64="Sz5HXDUTi7FiyGmaAz27KJBGlZg=">AAACBXicbVDLSsNAFJ3UV62vqks3g0VwVRIRdFl147KCbZU2lMnkph06MwkzE6GErP0At/oJ7sSt3+EX+BtO2yxs64ELh3Pu5d57goQzbVz32ymtrK6tb5Q3K1vbO7t71f2Dto5TRaFFYx6rh4Bo4ExCyzDD4SFRQETAoROMbiZ+5wmUZrG8N+MEfEEGkkWMEmOlx55hPITsKu9Xa27dnQIvE68gNVSg2a/+9MKYpgKkoZxo3fXcxPgZUYZRDnmll2pICB2RAXQtlUSA9rPpwTk+sUqIo1jZkgZP1b8TGRFaj0VgOwUxQ73oTcT/vG5qoks/YzJJDUg6WxSlHJsYT77HIVNADR9bQqhi9lZMh0QRamxGc1u0fWoIYV6xyXiLOSyT9lndc+ve3XmtcV1kVEZH6BidIg9doAa6RU3UQhQJ9IJe0Zvz7Lw7H87nrLXkFDOHaA7O1y8F6JlU</latexit><latexit sha1_base64="Sz5HXDUTi7FiyGmaAz27KJBGlZg=">AAACBXicbVDLSsNAFJ3UV62vqks3g0VwVRIRdFl147KCbZU2lMnkph06MwkzE6GErP0At/oJ7sSt3+EX+BtO2yxs64ELh3Pu5d57goQzbVz32ymtrK6tb5Q3K1vbO7t71f2Dto5TRaFFYx6rh4Bo4ExCyzDD4SFRQETAoROMbiZ+5wmUZrG8N+MEfEEGkkWMEmOlx55hPITsKu9Xa27dnQIvE68gNVSg2a/+9MKYpgKkoZxo3fXcxPgZUYZRDnmll2pICB2RAXQtlUSA9rPpwTk+sUqIo1jZkgZP1b8TGRFaj0VgOwUxQ73oTcT/vG5qoks/YzJJDUg6WxSlHJsYT77HIVNADR9bQqhi9lZMh0QRamxGc1u0fWoIYV6xyXiLOSyT9lndc+ve3XmtcV1kVEZH6BidIg9doAa6RU3UQhQJ9IJe0Zvz7Lw7H87nrLXkFDOHaA7O1y8F6JlU</latexit><latexit sha1_base64="Sz5HXDUTi7FiyGmaAz27KJBGlZg=">AAACBXicbVDLSsNAFJ3UV62vqks3g0VwVRIRdFl147KCbZU2lMnkph06MwkzE6GErP0At/oJ7sSt3+EX+BtO2yxs64ELh3Pu5d57goQzbVz32ymtrK6tb5Q3K1vbO7t71f2Dto5TRaFFYx6rh4Bo4ExCyzDD4SFRQETAoROMbiZ+5wmUZrG8N+MEfEEGkkWMEmOlx55hPITsKu9Xa27dnQIvE68gNVSg2a/+9MKYpgKkoZxo3fXcxPgZUYZRDnmll2pICB2RAXQtlUSA9rPpwTk+sUqIo1jZkgZP1b8TGRFaj0VgOwUxQ73oTcT/vG5qoks/YzJJDUg6WxSlHJsYT77HIVNADR9bQqhi9lZMh0QRamxGc1u0fWoIYV6xyXiLOSyT9lndc+ve3XmtcV1kVEZH6BidIg9doAa6RU3UQhQJ9IJe0Zvz7Lw7H87nrLXkFDOHaA7O1y8F6JlU</latexit>
� h�2iQ2
⇠ 1<latexit sha1_base64="AxMG8IVUOY57P2BFPXrub/lMzr4=">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</latexit><latexit sha1_base64="AxMG8IVUOY57P2BFPXrub/lMzr4=">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</latexit><latexit sha1_base64="AxMG8IVUOY57P2BFPXrub/lMzr4=">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</latexit><latexit sha1_base64="AxMG8IVUOY57P2BFPXrub/lMzr4=">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</latexit>
Coupling strength
field2 expectation value (vacuum/
thermal equilibrium/nonequilibrium)
characteristic energy/momentum2
Classical background
Quantum fluctuation
ZC =
Z[dA]
Z⇢G(A)exp(Tr log�C [A]�1 + iSG)
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Observables:
Kasper et al PRD 90 (2014) no.2, 025016
16hO[A]i =
Z[dA]
Zd⇧0⇢W (A0,⇧0)O[A]�[@F [A]� j]
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Where can we use this?
• In general, over-occupied and highly correlated systems
• Heavy ion collisions - initial fields strength A~1/g
• Pre-heating dynamics of the early universe
• Ultra-cold atoms far from equilibrium
• Can model quantum simulator systems
e.g. Berges, Boguslavski, Chatrchyan, Jaeckel PRD 96 (2017) no.7, 076020
eg. McLerran, Venugopalan PRD 49 2233 (1994), Venugopalan, Kransitz NPA 237 (1999) ,Berges, Boguslavski, Schlichting Venugopalan Phys.Rev. D89 (2014) no.11, 114007, MM et al…
c.f. J. Berges arXiv:1503.02907
e.g. Kasper et al Phys.Lett. B760 (2016) 742-746
Many of the methods discussed in this talk can be applied to a large variety of systems
e.g. Kasper et al New J.Phys. 19 (2017) no.2, 023030
17
High energy heavy ions• Heavy-ion collision experiments currently conducted at RHIC and the LHC
• Used to study many-body QCD in terms of quarks and gluons
• Formation of Quark Gluon Plasma (QGP)
• Possible to study QCD phase diagram, chiral symmetry restoration, transport properties of QCD, nuclear EoS,…
Difficult quantum many-body problem with phase transition, impossible to model entire evolution from first principles Can study initial times using high energy EFT of QCD
18
Photo taken 4/10/18 flying to UMD
Initial conditions of HICs
Problem can then be studied using effective theory of high energy QCD - Color Glass Condensate
Emergent semi-hard scale, Qs, becomes dominant scale of the problem
The initial nuclear wave function in high energy collisions dominated by gluons
Iancu and Venugopalan, QGP 249-3363; Iancu, Jalilian-Marian, Venugopalan, Ann. Rev. Nucl. Part. Sci. 60, 463 (2010)
↵S(Q2s) ⌧ 1
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Weakly coupled, but highly correlated system
Initially gluons highly over-occupied:f(p < Qs) ⇠ 1/↵S � 1
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19
Real-time simulations• Gauge field dynamics from Kogut-Susskind Hamiltonian
• From plasma instabilities, initial flux-tubes break up, over-occupied distribution up to scale Qs after timescale 1/Qs
H =a3
2
X
j,x
Eaj (x)E
aj (x) +
2
g2a
X
⇤ReTr
h1� U⇤
i
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Berges et al NPA 931 (2014) 348-353
f(p) = ✓(Qs � |p|)<latexit sha1_base64="pDswx1l7/0rFGOOIzcwNrv9ME8c=">AAACG3icbVDLSgNBEJz1GeMr6lGExSAkB8OuCHoRgl48JmAekA1hdtKbDJl9MNMrhE1Ofocf4FU/wZt49eAX+BtOkj2YxIKGoqqb7i43ElyhZX0bK6tr6xubma3s9s7u3n7u4LCuwlgyqLFQhLLpUgWCB1BDjgKakQTquwIa7uBu4jceQSoeBg84jKDt017APc4oaqmTO/EKUfHGwT4gLVQ76nzk+BT7rpdE41Gxk8tbJWsKc5nYKcmTFJVO7sfphiz2IUAmqFIt24qwnVCJnAkYZ51YQUTZgPagpWlAfVDtZPrG2DzTStf0QqkrQHOq/p1IqK/U0Hd15+RGtehNxP+8VozedTvhQRQjBGy2yIuFiaE5ycTscgkMxVATyiTXt5qsTyVlqJOb26L0U33ojrM6GXsxh2VSvyjZVsmuXubLt2lGGXJMTkmB2OSKlMk9qZAaYeSJvJBX8mY8G+/Gh/E5a10x0pkjMgfj6xcTc6FL</latexit><latexit sha1_base64="pDswx1l7/0rFGOOIzcwNrv9ME8c=">AAACG3icbVDLSgNBEJz1GeMr6lGExSAkB8OuCHoRgl48JmAekA1hdtKbDJl9MNMrhE1Ofocf4FU/wZt49eAX+BtOkj2YxIKGoqqb7i43ElyhZX0bK6tr6xubma3s9s7u3n7u4LCuwlgyqLFQhLLpUgWCB1BDjgKakQTquwIa7uBu4jceQSoeBg84jKDt017APc4oaqmTO/EKUfHGwT4gLVQ76nzk+BT7rpdE41Gxk8tbJWsKc5nYKcmTFJVO7sfphiz2IUAmqFIt24qwnVCJnAkYZ51YQUTZgPagpWlAfVDtZPrG2DzTStf0QqkrQHOq/p1IqK/U0Hd15+RGtehNxP+8VozedTvhQRQjBGy2yIuFiaE5ycTscgkMxVATyiTXt5qsTyVlqJOb26L0U33ojrM6GXsxh2VSvyjZVsmuXubLt2lGGXJMTkmB2OSKlMk9qZAaYeSJvJBX8mY8G+/Gh/E5a10x0pkjMgfj6xcTc6FL</latexit><latexit sha1_base64="pDswx1l7/0rFGOOIzcwNrv9ME8c=">AAACG3icbVDLSgNBEJz1GeMr6lGExSAkB8OuCHoRgl48JmAekA1hdtKbDJl9MNMrhE1Ofocf4FU/wZt49eAX+BtOkj2YxIKGoqqb7i43ElyhZX0bK6tr6xubma3s9s7u3n7u4LCuwlgyqLFQhLLpUgWCB1BDjgKakQTquwIa7uBu4jceQSoeBg84jKDt017APc4oaqmTO/EKUfHGwT4gLVQ76nzk+BT7rpdE41Gxk8tbJWsKc5nYKcmTFJVO7sfphiz2IUAmqFIt24qwnVCJnAkYZ51YQUTZgPagpWlAfVDtZPrG2DzTStf0QqkrQHOq/p1IqK/U0Hd15+RGtehNxP+8VozedTvhQRQjBGy2yIuFiaE5ycTscgkMxVATyiTXt5qsTyVlqJOb26L0U33ojrM6GXsxh2VSvyjZVsmuXubLt2lGGXJMTkmB2OSKlMk9qZAaYeSJvJBX8mY8G+/Gh/E5a10x0pkjMgfj6xcTc6FL</latexit><latexit sha1_base64="pDswx1l7/0rFGOOIzcwNrv9ME8c=">AAACG3icbVDLSgNBEJz1GeMr6lGExSAkB8OuCHoRgl48JmAekA1hdtKbDJl9MNMrhE1Ofocf4FU/wZt49eAX+BtOkj2YxIKGoqqb7i43ElyhZX0bK6tr6xubma3s9s7u3n7u4LCuwlgyqLFQhLLpUgWCB1BDjgKakQTquwIa7uBu4jceQSoeBg84jKDt017APc4oaqmTO/EKUfHGwT4gLVQ76nzk+BT7rpdE41Gxk8tbJWsKc5nYKcmTFJVO7sfphiz2IUAmqFIt24qwnVCJnAkYZ51YQUTZgPagpWlAfVDtZPrG2DzTStf0QqkrQHOq/p1IqK/U0Hd15+RGtehNxP+8VozedTvhQRQjBGy2yIuFiaE5ycTscgkMxVATyiTXt5qsTyVlqJOb26L0U33ojrM6GXsxh2VSvyjZVsmuXubLt2lGGXJMTkmB2OSKlMk9qZAaYeSJvJBX8mY8G+/Gh/E5a10x0pkjMgfj6xcTc6FL</latexit>
Consider an over-occupied plasma
20
Over-occupied QCD plasma• Loss of memory of initial
conditions
• System eneters a turbulent cascade
• Direct energy cascade, inverse particle number cascade
• Kinetic scenario can be identified from simulations
• Emergent scales from initial scale Q
Berges, Boguslavski, Schlichting Venugopalan Phys.Rev. D89 (2014) no.11, 114007,
21
Other effects and discovery• Chiral Separation Effect:
• Chiral Magnetic Wave: collective gapless excitation from the coupling between density waves of electric and chiral chargesKharzeev & Yee, PRD 83, 085007; Newman JHEP 0601 2006
Son & Zhitnitsky, PRD 70, 074018; Metlitski & Zhitnitsky, PRD 72, 045011ja ⇠ nV B
• Predicted and obseverd in Dirac and Weyl semi-metals
• Effects under intense search at RHIC (right now!) and LHC
• Tantalizing hints from RHIC, but many experimental and theory uncertainties
First found in ZrTe5: Kharzeev et al. Nature Physics 2016
22STAR, B. I. Abelev et al., Phys. Rev. Lett. 103, 251601 (2009), 0909.1739; ALICE, B. Abelev et al., Phys. Rev. Lett. 110, 012301 (2013), STAR, L. Adamczyk et al., Phys. Rev. Lett. 113, 052302 (2014), 1404.1433
The Chiral Magnetic Effect• Chiral Magnetic Effect: jV ⇠ n5B
Kharzeev, McLerran, Warringa NPA 803 2008; Fukushima, Kharzeev, Warringa PRD 78 2008
New kind of parity odd conductivity, non-dissipative
jV =e2
2⇡2µ5B
P-odd T-odd
P-even T-odd
P-odd T-even
Coefficient fixed from the anomaly• Anomalously produced axial charge — connection between
topology of QCD vacuum
• Tells us about confinement and chiral symmetry transition: deconfinement and chiral symmetry restoration needed
Red=momentum Blue=spin
Macroscopic electric current from quark chirality imbalance, n5, in external B field
23
Open question: Where does n5 come from? How much is created?Real-time information needed!
Universal dynamics
• Initial particle production leads to universal scaling
• Reaches non-thermal fixed point, self-similar evolution
Berges, MM, Schlichting PRL 118 (2017) no.19, 192005
Berges, Boguslavski, Schlichting, Venugopalan PRL114 (2015)
f(t,p) = s↵/�f(s�1/�t, sp)<latexit sha1_base64="1bJzPtVFbUxb6uj48Aj1jlUBf6k=">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</latexit><latexit sha1_base64="1bJzPtVFbUxb6uj48Aj1jlUBf6k=">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</latexit><latexit sha1_base64="1bJzPtVFbUxb6uj48Aj1jlUBf6k=">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</latexit><latexit sha1_base64="1bJzPtVFbUxb6uj48Aj1jlUBf6k=">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</latexit>
s�1/�t = 1<latexit sha1_base64="6LGfsVNMB+Lo+YVKtUGRIUdNJMY=">AAACDXicbVBLSgNBEO2Jvxg/GXXpZjAIbowzIuhGCLpxGcF8IBlDT09N0qTnQ3eNEIY5gwdwq0dwJ249gyfwGnY+C5P4oODxXhVV9bxEcIW2/W0UVlbX1jeKm6Wt7Z3dsrm331RxKhk0WCxi2faoAsEjaCBHAe1EAg09AS1veDv2W08gFY+jBxwl4Ia0H/GAM4pa6pll9ZidOmddD5DmeO30zIpdtSewlokzIxUyQ71n/nT9mKUhRMgEVarj2Am6GZXImYC81E0VJJQNaR86mkY0BOVmk8Nz61grvhXEUleE1kT9O5HRUKlR6OnOkOJALXpj8T+vk2Jw5WY8SlKEiE0XBamwMLbGKVg+l8BQjDShTHJ9q8UGVFKGOqu5LUo/NQA/L+lknMUclknzvOrYVef+olK7mWVUJIfkiJwQh1ySGrkjddIgjKTkhbySN+PZeDc+jM9pa8GYzRyQORhfv+iam0o=</latexit><latexit sha1_base64="6LGfsVNMB+Lo+YVKtUGRIUdNJMY=">AAACDXicbVBLSgNBEO2Jvxg/GXXpZjAIbowzIuhGCLpxGcF8IBlDT09N0qTnQ3eNEIY5gwdwq0dwJ249gyfwGnY+C5P4oODxXhVV9bxEcIW2/W0UVlbX1jeKm6Wt7Z3dsrm331RxKhk0WCxi2faoAsEjaCBHAe1EAg09AS1veDv2W08gFY+jBxwl4Ia0H/GAM4pa6pll9ZidOmddD5DmeO30zIpdtSewlokzIxUyQ71n/nT9mKUhRMgEVarj2Am6GZXImYC81E0VJJQNaR86mkY0BOVmk8Nz61grvhXEUleE1kT9O5HRUKlR6OnOkOJALXpj8T+vk2Jw5WY8SlKEiE0XBamwMLbGKVg+l8BQjDShTHJ9q8UGVFKGOqu5LUo/NQA/L+lknMUclknzvOrYVef+olK7mWVUJIfkiJwQh1ySGrkjddIgjKTkhbySN+PZeDc+jM9pa8GYzRyQORhfv+iam0o=</latexit><latexit sha1_base64="6LGfsVNMB+Lo+YVKtUGRIUdNJMY=">AAACDXicbVBLSgNBEO2Jvxg/GXXpZjAIbowzIuhGCLpxGcF8IBlDT09N0qTnQ3eNEIY5gwdwq0dwJ249gyfwGnY+C5P4oODxXhVV9bxEcIW2/W0UVlbX1jeKm6Wt7Z3dsrm331RxKhk0WCxi2faoAsEjaCBHAe1EAg09AS1veDv2W08gFY+jBxwl4Ia0H/GAM4pa6pll9ZidOmddD5DmeO30zIpdtSewlokzIxUyQ71n/nT9mKUhRMgEVarj2Am6GZXImYC81E0VJJQNaR86mkY0BOVmk8Nz61grvhXEUleE1kT9O5HRUKlR6OnOkOJALXpj8T+vk2Jw5WY8SlKEiE0XBamwMLbGKVg+l8BQjDShTHJ9q8UGVFKGOqu5LUo/NQA/L+lknMUclknzvOrYVef+olK7mWVUJIfkiJwQh1ySGrkjddIgjKTkhbySN+PZeDc+jM9pa8GYzRyQORhfv+iam0o=</latexit><latexit sha1_base64="6LGfsVNMB+Lo+YVKtUGRIUdNJMY=">AAACDXicbVBLSgNBEO2Jvxg/GXXpZjAIbowzIuhGCLpxGcF8IBlDT09N0qTnQ3eNEIY5gwdwq0dwJ249gyfwGnY+C5P4oODxXhVV9bxEcIW2/W0UVlbX1jeKm6Wt7Z3dsrm331RxKhk0WCxi2faoAsEjaCBHAe1EAg09AS1veDv2W08gFY+jBxwl4Ia0H/GAM4pa6pll9ZidOmddD5DmeO30zIpdtSewlokzIxUyQ71n/nT9mKUhRMgEVarj2Am6GZXImYC81E0VJJQNaR86mkY0BOVmk8Nz61grvhXEUleE1kT9O5HRUKlR6OnOkOJALXpj8T+vk2Jw5WY8SlKEiE0XBamwMLbGKVg+l8BQjDShTHJ9q8UGVFKGOqu5LUo/NQA/L+lknMUclknzvOrYVef+olK7mWVUJIfkiJwQh1ySGrkjddIgjKTkhbySN+PZeDc+jM9pa8GYzRyQORhfv+iam0o=</latexit>
f(t,p) = t↵fs(t�p)
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• Self similarity observed for distribution function seen between scalars and gauge theory
0
0.05
0.1
0.15
0.2
0 1 2 3
Mo
men
t: (p
/Q)3 g
2 f(p,
t)
Momentum: p/Q
tQNc2=450
tQNc2=900
tQNc2=1800
tQNc2=3600
0 1 2 3 0
0.05
0.1
0.15
0.2
0.25
Scale
d: (
t/t0
Nc2 )-β
(p/Q
)3 g2 f(
p,t)
SU(3)SU(2)
Qt0=100
Scaled: (t/t0Nc2)β p/Q
24Berges et al PRL114 (2015)
Universal dynamics
0 0.5
1 1.5
2 2.5
3 3.5
4 4.5
5
0 20 40 60 80 100 120 140 160 180 200
ζ=3/5 | t0Q=100
SU(2) SU(3)
Wilso
n L
oo
p: -
1/C
F lo
g(〈W
(t,A)〉)
Scaled Area: (t/t0)-ζ A Q2/Nc
tQ=200tQ=400tQ=600tQ=800
0 0.5
1 1.5
2 2.5
3 3.5
4 4.5
5
0 20 40 60 80 100 120 140 160 180 200
ζ=3/5 | t0Q=100
SU(2) SU(3)
Wilso
n L
oo
p: -
1/C
F lo
g(〈W
(t,A)〉)
Scaled Area: (t/t0)-ζ A Q2/Nc
Berges, MM, Schlichting PRL 118 (2017) no.19, 192005
1
Ha
rd S
ca
le:
10-2
10-1
102 103
Λ(t)
2 / Q
2m
D(t)
2 / (N
c Q2 )
(tQ)2/7
(tQ)-2/7
SU(2) SU(3)
1
De
by
e S
ca
le:
Time: t Q Nc2
• In gauge theories, universal, self-similar scaling for a large range of scales, including IR, which controls topological transitions
0
0.5
1
1.5
2
2.5
3
3.5
0 20 40 60 80 100 120 140 160 180 200
SU(2) SU(3)Wil
so
n L
oo
p: -
1/C
F lo
g(〈W
(t,A)〉)
Area: A Q2/Nc
tQ=200tQ=400tQ=600tQ=800
25
W =1
NcTrPeig
Hc dxµAµ(x)
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Dynamical separation of scales
MM, Schlichting, Venugopalan PRD 074036 (2016)
Hard Scale
Electric Screening
Magnetic Screening
meqD ⇠ gT
⇤eq ⇠ T
⇤eqs ⇠
p� ⇠ g2T
Initially one scale , dynamically generate scales
QsIn equilibrium, hierarchy of scales
�neqsph(t) = 2⇥ 10�2�2(t)Identify that sphaleron transition rate:
Qua
ntum
True approach to equilibrium needs quantum treatment
26
Sphaleron transition in action
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
8 10 12 14 16
NC
S
Time: t
UncooledCooled τc=4
27
@Aai (x)
@⌧= � @H
@Aai (x)
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Ea ·Ba<latexit sha1_base64="cNaFPOh/cfWjHSgVzMh61P6DkIg=">AAACG3icbVDLSsNAFJ34rPUVdSnCYBFclUQEXZaK4LKCfUATw2QyaYdOMmFmIpSQld/hB7jVT3Anbl34Bf6GkzaCbT1w4XDOvdx7j58wKpVlfRlLyyura+uVjerm1vbOrrm335E8FZi0MWdc9HwkCaMxaSuqGOklgqDIZ6Trj64Kv/tAhKQ8vlPjhLgRGsQ0pBgpLXnmkRMhNfTD7Dq/Rw4OuPoVmrmHPLNm1a0J4CKxS1IDJVqe+e0EHKcRiRVmSMq+bSXKzZBQFDOSV51UkgThERqQvqYxioh0s8kbOTzRSgBDLnTFCk7UvxMZiqQcR77uLG6U814h/uf1UxVeuhmNk1SRGE8XhSmDisMiExhQQbBiY00QFlTfCvEQCYSVTm5mi9RPDUmQV3Uy9nwOi6RzVretun17Xms0y4wq4BAcg1NggwvQADegBdoAg0fwDF7Aq/FkvBnvxse0dckoZw7ADIzPH6zRoj4=</latexit><latexit sha1_base64="cNaFPOh/cfWjHSgVzMh61P6DkIg=">AAACG3icbVDLSsNAFJ34rPUVdSnCYBFclUQEXZaK4LKCfUATw2QyaYdOMmFmIpSQld/hB7jVT3Anbl34Bf6GkzaCbT1w4XDOvdx7j58wKpVlfRlLyyura+uVjerm1vbOrrm335E8FZi0MWdc9HwkCaMxaSuqGOklgqDIZ6Trj64Kv/tAhKQ8vlPjhLgRGsQ0pBgpLXnmkRMhNfTD7Dq/Rw4OuPoVmrmHPLNm1a0J4CKxS1IDJVqe+e0EHKcRiRVmSMq+bSXKzZBQFDOSV51UkgThERqQvqYxioh0s8kbOTzRSgBDLnTFCk7UvxMZiqQcR77uLG6U814h/uf1UxVeuhmNk1SRGE8XhSmDisMiExhQQbBiY00QFlTfCvEQCYSVTm5mi9RPDUmQV3Uy9nwOi6RzVretun17Xms0y4wq4BAcg1NggwvQADegBdoAg0fwDF7Aq/FkvBnvxse0dckoZw7ADIzPH6zRoj4=</latexit><latexit sha1_base64="cNaFPOh/cfWjHSgVzMh61P6DkIg=">AAACG3icbVDLSsNAFJ34rPUVdSnCYBFclUQEXZaK4LKCfUATw2QyaYdOMmFmIpSQld/hB7jVT3Anbl34Bf6GkzaCbT1w4XDOvdx7j58wKpVlfRlLyyura+uVjerm1vbOrrm335E8FZi0MWdc9HwkCaMxaSuqGOklgqDIZ6Trj64Kv/tAhKQ8vlPjhLgRGsQ0pBgpLXnmkRMhNfTD7Dq/Rw4OuPoVmrmHPLNm1a0J4CKxS1IDJVqe+e0EHKcRiRVmSMq+bSXKzZBQFDOSV51UkgThERqQvqYxioh0s8kbOTzRSgBDLnTFCk7UvxMZiqQcR77uLG6U814h/uf1UxVeuhmNk1SRGE8XhSmDisMiExhQQbBiY00QFlTfCvEQCYSVTm5mi9RPDUmQV3Uy9nwOi6RzVretun17Xms0y4wq4BAcg1NggwvQADegBdoAg0fwDF7Aq/FkvBnvxse0dckoZw7ADIzPH6zRoj4=</latexit><latexit sha1_base64="cNaFPOh/cfWjHSgVzMh61P6DkIg=">AAACG3icbVDLSsNAFJ34rPUVdSnCYBFclUQEXZaK4LKCfUATw2QyaYdOMmFmIpSQld/hB7jVT3Anbl34Bf6GkzaCbT1w4XDOvdx7j58wKpVlfRlLyyura+uVjerm1vbOrrm335E8FZi0MWdc9HwkCaMxaSuqGOklgqDIZ6Trj64Kv/tAhKQ8vlPjhLgRGsQ0pBgpLXnmkRMhNfTD7Dq/Rw4OuPoVmrmHPLNm1a0J4CKxS1IDJVqe+e0EHKcRiRVmSMq+bSXKzZBQFDOSV51UkgThERqQvqYxioh0s8kbOTzRSgBDLnTFCk7UvxMZiqQcR77uLG6U814h/uf1UxVeuhmNk1SRGE8XhSmDisMiExhQQbBiY00QFlTfCvEQCYSVTm5mi9RPDUmQV3Uy9nwOi6RzVretun17Xms0y4wq4BAcg1NggwvQADegBdoAg0fwDF7Aq/FkvBnvxse0dckoZw7ADIzPH6zRoj4=</latexit>
Real-time Lattice QCDTo study full CME dynamics, need to extend non-equilibrium gauge field studies to include fermions
Cannot resort to classical approximation for fermions because of Pauli principle
Expand initial fermion field in operator basis, evolve wave function by solving Dirac equation
Measure operator expectation values, i.e
Fermions in HIC are nearly chiral, want chiral formulations
Work in quenched limited (no fermion backreaction) for first study
SU(Nc)+U(1) x(t) =1pV
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Kasper et al PRD 90 (2014) no.2, 025016, MM, Mueller, Schlichting, Sharma PRD 95 2017
i�0@t x = (�i /DsW +m) x ,
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A0=0 3+1D
28
Fermions on the lattice
Overlap Fermions:
Exact Chiral symmetry. Separate chiral and continuum limit. Can be massless. Extremely numerically expensive. First Minkowski study in 3+1D.
Narayanan & Neuberger PRL71 3251, Neuberger PLB417 141
Karsten & Smit NPB 183 (1983)
Simulate with both as a cross check
Wilson (tree level-improved):
Add term to action to remove doublers. Explicitly breaks chiral symmetry, only recovered in continuum limit. Has own anomaly relation
In the classical-statistical limit mass renormalized perturbatively, Wilson fermions arbitrary close to massless limit
�i /Dsov = M
1+
�0HW (M)pHW (M)2
!
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MM, Mueller, Schlichting, Sharma PRD 95 2017
MM, Mueller, Schlichting, Sharma PRD 95 2017
29
Magnetic field dependence
MM, Mueller, Schlichting, Sharma PRD 95 (2017)
finite magnetic field: → important deviations
from ‘ideal' picture of CME
0
0.2
0.4
0.6
0.8
1
0 1 2 3 4 5 6 7
Vect
or c
harg
e se
para
tion:
Δ
J0 V
Magnetic field: qBrsph2
maxt/tsph=1.5
-0.6-0.4-0.2
0 0.2 0.4
-5 -4 -3 -2 -1 0 1 2 3 4 5z/rsph
t = 2.67 tsph
qB = 0.8 rsph-2
qB = 1.6 rsph-2
-0.6-0.4-0.2
0 0.2 0.4
Vector density Axial density
t = 1.67 tsph
-0.6-0.4-0.2
0 0.2 0.4 jv
0(z,t)
t = 0.67 tsph
0 0.2 0.4 0.6 0.8
1
-5 -4 -3 -2 -1 0 1 2 3 4 5
qB = 3.5 rsph-2
qB = 7 rsph-2
0 0.2 0.4 0.6 0.8
1 0
0.2 0.4 0.6 0.8
1 ja0(z,t)
asymptotic limit
“simple” estimates work
30
Quark mass dependence
MM, Mueller, Schlichting, Sharma PRD 95 (2017)
0
0.2
0.4
0.6
0.8
1
0 0.5 1
Cha
rge
sepa
ratio
n
ΔJV0
Quark mass: mrsph
maxt/tsph=1.5
0 0.5 1
ΔJA0
finite quark mass effects → anomalous transport
suppressed for heavy quarks
31
Chiral magnetic effect
Non-zero magnetic field -> vector current is generated jzVBz
With addition of B field, sphaleron transition induces local imbalance
of axial charge density
Vector current leads to separation of electric charges along the B-field direction
j0VjzV
j05
xz
y
B
32(MM, Mueller, Schlichting, Sharma PRD 95 2017)
Vector charge j0VVector current jzVAxial charge j05
(Slide adapted from S. Schlichting CERN 2016)
Non-zero magnetic field -> vector current is generated jzVBz
Sphaleron transition induces local imbalance of axial charge density j05
Vector current leads to separation of electric charges along the B-field direction
j0VjzV
Chiral magnetic effect
33(MM, Mueller, Schlichting, Sharma PRD 95 2017)
Vector charge j0VVector current jzVAxial charge j05
xz
y
B
(Slide adapted from S. Schlichting CERN 2016)
Chiral magnetic wave
Vector charge j0VVector current jzVAxial charge j05
Vector charge imbalance generates an axial current so that axial charge also flows along the B-field direction
j0V jz5
Shock-wave of vector charge and axial charge propagating along B-field direction
34
xz
y
B
(MM, Mueller, Schlichting, Sharma PRD 95 2017)(Slide adapted from S. Schlichting CERN 2016)
Vector charge j0VVector current jzVAxial charge j05
Vector charge imbalance generates an axial current so that axial charge also flows along the B-field direction
j0V jz5
Shock-wave of vector charge and axial charge propagating along B-field direction
Chiral magnetic wave
35
xz
y
B
(MM, Mueller, Schlichting, Sharma PRD 95 2017)(Slide adapted from S. Schlichting CERN 2016)
Vector charge j0VVector current jzVAxial charge j05
Vector charge imbalance generates an axial current so that axial charge also flows along the B-field direction
j0V jz5
Shock-wave of vector charge and axial charge propagating along B-field direction
Chiral magnetic wave
36
xz
y
B
(MM, Mueller, Schlichting, Sharma PRD 95 2017)(Slide adapted from S. Schlichting CERN 2016)
LI ET AL, NATURE PHYSICS, DOI: 10.1038/NPHYS3648 STAR, B. I. ABELEV ET AL., PHYS. REV. LETT. 103, 251601 (2009), 0909.1739; ALICE, B. ABELEV ET AL., PHYS. REV. LETT. 110, 012301 (2013), STAR, L. ADAMCZYK ET AL., PHYS. REV. LETT. 113, 052302 (2014), 1404.1433 S. PRATT, S. SCHLICHTING, AND S. GAVIN, PHYS. REV. C84, 024909 (2011), 1011.6053.; Y. HATTA, A. MONNAI, AND B.-W. XIAO, (2015), 1507.04690.
CHIRAL MAGNETIC EFFECT IN REALITY▸ In heavy ion collisions
▸ STAR, ALICE published results in line with CME (and other anomalous transport phenomena) predictions
▸ Alternative explanations exist
▸ Local charge conservation
▸ Viscous hydrodynamics
▸ Recent discovery in condensed matter systems
Image from H. Ke’s RHIC/AGS 2015 users meeting talk
37
Sphalerons in the glasma
• Non-equilibrium, over occupied gluons
• Initially only one scale,
• Classical-Statistical framework: sample over ensemble of stochastic initial conditions
Qs
38
(MM, Schlichting, Venugopalan PRD 074036)
Dynamical scales at a glance• Hard scale
• Average typical momentum of hard modes
• Electric screening scale
• Appeal to perturbative formula
• Magnetic screening scale
• Measure spatial string tension
• Large area fall limit of spatial Wilson loop
⇤eqs ⇠
p� ⇠ g2T
⇤eq ⇠ T
meqD ⇠ gT
Qs
Qs
Qs
hW (A, t)i ⇡ exp(��A)
Kurkela and Moore, JHEP 1112, 044 (2011); Schlichting PRD86, 065008 (2012)
Dumitru, Lappi, and Nara, PLB734, 7 (2014)
Kurkela and Moore, PRD86, 056008 (2012)m2
D = 4g2Nc
Zd3p
(2⇡)3f(p)
p
⇤(t)2 =2
3
Rd3p p3 f(p)Rd3p p f(p)
Non-equilibrium sphaleron transition rate
-1
0
1
2
3
4
5
6
7
40 60 80 100 120 140 160 180 200 220
x 10-3
Γne
qsp
h / σ
2
Time: Qs t
Qs2τc=36
• In equilibrium, sphaleron rate controlled by magnetic modes
• From dynamical separation of scales, non-equilibrium sphaleron rate controlled by modes of order magnetic screening
• Same scaling exponent expected for SU(2) and SU(3), greater coefficient for SU(3)
(MM, Schlichting, Venugopalan PRD 93 2016)
�neqsph(t) = 2⇥ 10�2�2(t)
�2(t) ⇡ Q2s(Qst)
�2/3
40
(Berges, MM, Schlichting arXiv:1703.00697)
Transport
• Mass, B dependence on charge separation
0
0.5
1
1.5
0 0.5 1 1.5 2Δ
J vz / Δ
J a0 (t)t/tsph
2
4
6
8
10
ΔJ az /
ΔJ v0 (t)
qB = 0.8 rsph-2
qB = 1.6 rsph-2
qB = 3.5 rsph-2
qB = 7 rsph-2
• B dep. for ratios of charge separation
Nontrivial behavior away from asymptotic limit
Vector charge separation vanishes for large m
�Jzv (t)
�J0a(t)
�Jza (t)
�J0v (t)
MM, Mueller, Schlichting, Sharma PRD 95 2017Finite “relaxation time” should be taken into account
0
0.2
0.4
0.6
0.8
1
0 1 2 3 4 5 6 7
Vect
or c
harg
e se
para
tion Δ
J V0
qBr2sph
maxt/tsph=1.5
0 0.5 1mrsph
Application: Pair production in strong field
QED
42
Schwinger pair production• Above a critical field strength, F=me2/e=1018 V/m,
classical electrodynamics breaks down
• Produce fermion pairs from vacuum due to non-linearities in QED
• Many analytical/numerical results, however including full backreaction of fermions difficult
• Large coherent field highly amenable to classical-statistical approximation
e.g. Cooper, Mottola PRD 40 (1989), Kluger, Eisenberg, Svetitsky, Cooper, Mottola PRD 45 (1992), …, Dunne et al…
Strong E and B fields in HIC also above limit
J. S. Schwinger, Phys. Rev. 82, 664 (1951).
Kasper et al PRD 90 (2014) no.2, 025016
May be accessible in next generation of high intensity user experiments (ELI)
43
Schwinger pair production• Without back-reaction able to
reproduce continuum pair production rate
• Novel dynamics begin when including fermion back-reaction
MM, Schlichting, Sharma, in progress
0.015
0.02
0.025
0.03
0.035
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
Schw
inge
r pai
r pro
duct
ion
rate
: d/d
t dN
/d3 x
[m4 ]
Lattice spacing: maT
Wilson (LO): VTm2=36cont. extrapolation: s0 + s1(maT) + s2 (maT)2
Wilson (LO): VTm2=81cont. extrapolation: s0 + s1(maT) + s2 (maT)2
Wilson (NLO): VTm2=36cont. extrapolation: s0 + s0 (maT)2
continuum result
Narozhny et al Phys. Lett. A 330, 1 (2004); JETP Lett. 80, 382 (2004); JETP 129, 14 (2006).
dN
dtd3x=
e2E2s
4⇡2✏⌘ coth
⇣⇡⌘✏
⌘exp
⇣�⇡
✏
⌘
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-3
-2
-1
0
1
2
3
0 20 40 60 80 100 120 140
Elec
tric
field
: eE/
me2
Evolution time: me t
r-Avg Wilson (NLO) NT=16 NL=40 maT= 0.375 maL=0.05
e2Nf=1
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
0 20 40 60 80 100 120 140
e+ e- pai
r den
sity
: dN
e+ e- /d3 x
[me3 ]
Evolution time: me t
r-Avg Wilson (NLO) NT=16 NL=40 maT= 0.375 maL=0.05
e2Nf=1 rW=+1e2Nf=1 rW= -1
e2Nf=1No BR
limit
44
Real-time dynamics
45
MM, S. SCHLICHTING, R. VENUGOPALAN ARXIV:1601.07342 [HEP-PH]
COOLING: A CARTOON46
real-time evolution
cooling
calib
ratio
n
NCS(t2) - NCS(t1) NCS(t3) - NCS(t2)
NC
S(t 1
) - N
CS(
t 1)
Vac
NC
S(t 3
) - N
CS(
t 3)
Vac
τ=0
τ=τc
τ=∞ vacuum
t2t1 t3
@Aai (x)
@⌧= � @H
@Aai (x)
TOPOLOGY ON THE LATTICE▸
▸ On the lattice,
47
dNCS
dt' g2
8⇡2
X
x2lattice,i
(Eai (x, t+ �t/2) + Ea
i (x, t� �t/2))
22X
8⇤tr(
i⌧aU⇤(x)4
)
Ez(x, t+ �t/2)� Ez(x, t� �t/2)
2Bz
dNCS(t)
dt=
Zd3x
g2
8⇡2Ea
i Bai
INDEPENDENT TEST
▸ Can compute the change in Chern-Simons number with two completely independent methods which agree well
48
*Shifted curves for
clarity
MM, S. SCHLICHTING, R. VENUGOPALAN ARXIV:1601.07342 [HEP-PH]
ROBUSTNESS OF OUR RESULTS 49
0
5x10-7
1x10-6
1.5x10-6
2x10-6
2.5x10-6
3x10-6
0 10 20 30 40 50 60 70 80
Qst=50
<(N
CS(
t+δt
)-NC
S(t))
2 >/(Q
s3 V)
Qsδt
N=64, Qsa=1, Qs2τc=12
N=128, Qsa=0.5, Qs2τc=12
N=96, Qsa=1, Qs2τc=12
N=192, Qsa=0.5, Qs2τc=12
0
5x10-7
1x10-6
1.5x10-6
2x10-6
2.5x10-6
0 10 20 30 40 50 60 70 80
<(N
CS(
t+δt
)-NC
S(t))
2 >/(Q
s3 V)
Qsδt
N=96, Qs2τc=12
N=128, Qs2τc=12
N=192, Qs2τc=12
Volume independence (for two cooling lengths)
Lattice spacing independence
0 2x10-8 4x10-8 6x10-8 8x10-8 1x10-7
1.2x10-7 1.4x10-7 1.6x10-7 1.8x10-7
2x10-7
0 10 20 30 40 50 60 70 80
<(N
CS(
t+δt
)-NC
S(t))
2 >/(Q
s3 V)
Qsδt
N=64, Qs2τc=324
N=96, Qs2τc=324
MM, S. SCHLICHTING, R. VENUGOPALAN ARXIV:1601.07342 [HEP-PH]