Classical-statistical simulations and the Chiral Magnetic Effect
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- Clyde Cole
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1 Classical-statistical simulations and the Chiral Magnetic Effect Niklas Mueller Heidelberg University based on work together with: J. Berges, M. Mace, S. Schlichting, S. Sharma, N. Tanji, R. Venugopalan PRL 117 (2016) , PRD 93 (2016) , arxiv: , arxiv: th Workshop of the APS Topical Group on Hadronic Physics Washington DC / 02 / 02
2 Topology in Heavy Ion Collisions The Chiral Magnetic Effect (Kharzeev, McLerran, Warringa 2007; Kharzeev, Fukushima, Warringa 2008) 1
3 Topology in Heavy Ion Collisions The Chiral Magnetic Effect (Kharzeev, McLerran, Warringa 2007; Kharzeev, Fukushima, Warringa 2008) Topological Fluctuations (sphalerons) analogous to proposed 'electroweak baryogenesis' Review: Kharzeev et al, Prog. Nucl. Part. Phys 88 (2016) 1 1
4 Topology in Heavy Ion Collisions The Chiral Magnetic Effect (Kharzeev, McLerran, Warringa 2007; Kharzeev, Fukushima, Warringa 2008) Topological Fluctuations (sphalerons) analogous to proposed 'electroweak baryogenesis' The axial anomaly axial non-conservation vs. topological density Review: Kharzeev et al, Prog. Nucl. Part. Phys 88 (2016) 1 1
5 Topology in Heavy Ion Collisions The Chiral Magnetic Effect (Kharzeev, McLerran, Warringa 2007; Kharzeev, Fukushima, Warringa 2008) Topological Fluctuations (sphalerons) analogous to proposed 'electroweak baryogenesis' External Magnetic Fields 1018 Gauss, strongest ever produced in Lab! The axial anomaly axial non-conservation vs. topological density Review: Kharzeev et al, Prog. Nucl. Part. Phys 88 (2016) 1 1
6 Outline 1. Anomalous phenomena in heavy ion collisions 2. Why are early times so important? 3. Classical-statistical simulations 4. Towards kinetic theory and the bigger picture 5. Conclusions 2
7 1. Anomalous Phenomena in Heavy Ion Collisions CGC colliding nuclei flux tubes over-occupied plasma kinetic regime hydrodynamic regime S. Schlichting
8 1. Anomalous Phenomena in Heavy Ion Collisions CGC colliding nuclei flux tubes over-occupied plasma kinetic regime hydrodynamic regime S. Schlichting 2016 non-equilibrium anomalous fermion production from coherent fields (Tanji et al. 2016) and sphaleron transitions (Mace et al. 2016) 2
9 1. Anomalous Phenomena in Heavy Ion Collisions CGC colliding nuclei flux tubes over-occupied plasma kinetic regime hydrodynamic regime S. Schlichting 2016 non-equilibrium anomalous fermion production from coherent fields (Tanji et al. 2016) and sphaleron transitions (Mace et al. 2016) large magnetic fields present Anomalous Transport (CME, CSE and CMW)? 2
10 1. Anomalous Phenomena in Heavy Ion Collisions CGC colliding nuclei flux tubes over-occupied plasma kinetic regime hydrodynamic regime S. Schlichting 2016 non-equilibrium anomalous fermion production from coherent fields (Tanji et al. 2016) and sphaleron transitions (Mace et al. 2016) large magnetic fields present Anomalous Transport (CME, CSE and CMW)? Subsequent interactions in the fire ball, axial transport and relaxation weak to strong coupling 2
11 Anomalous Phenomena in Heavy Ion Collisions CGC colliding nuclei flux tubes over-occupied plasma kinetic regime hydrodynamic regime S. Schlichting 2016 non-equilibrium anomalous fermion production from coherent fields (Tanji et al. 2016) and sphaleron transitions (Mace et al. 2016) large magnetic fields present Anomalous Transport (CME, CSE and CMW)? Subsequent interactions in the fire ball, axial transport and relaxation weak to strong coupling Thermalization / Freezout 1. 2
12 1. Anomalous Phenomena in Heavy Ion Collisions CGC colliding nuclei flux tubes over-occupied plasma kinetic regime hydrodynamic regime non-equilibrium anomalous fermion production from coherent fields (Tanji et al. 2016) and sphaleron transitions (Mace et al. 2016) large magnetic fields present Anomalous Transport (CME, CSE and CMW)? Subsequent interactions in the fire ball, axial transport and relaxation weak to strong coupling Theory: classical statistical simulations + fermions chiral kinetic theory Thermalization / Freezout S. Schlichting 2016 anomalous hydrodynamics 2
13 1. Anomalous Phenomena in Heavy Ion Collisions - condensed matter systems (Li, Kharzeev et al, Nature 2015) - heavy ions (charged particle correlations: RHIC 2009, LHC )? 3
14 1. Anomalous Phenomena in Heavy Ion Collisions - condensed matter systems (Li, Kharzeev et al, Nature 2015) - heavy ions (charged particle correlations: RHIC 2009, LHC )? Challenges: Signal How does the signal even look like? 3
15 1. Anomalous Phenomena in Heavy Ion Collisions - condensed matter systems (Li, Kharzeev et al, Nature 2015) - heavy ions (charged particle correlations: RHIC 2009, LHC )? Challenges: Signal How does the signal even look like? Background Apples to apples? CMS, arxiv
16 1. Anomalous Phenomena in Heavy Ion Collisions - condensed matter systems (Li, Kharzeev et al, Nature 2015) - heavy ions (charged particle correlations: RHIC 2009, LHC )? Challenges: Signal How does the signal even look like? Background Apples to apples? Earliest times! How long does the magnetic field live? CMS, arxiv
17 1. Anomalous Phenomena in Heavy Ion Collisions - condensed matter systems (Li, Kharzeev et al, Nature 2015) - heavy ions (charged particle correlations: RHIC 2009, LHC )? Challenges: Signal How does the signal even look like? Background Apples to apples? Earliest times! How long does the magnetic field live? CMS, arxiv Challenge for theorists: Quantitative Predictions needed at various stages of the collision: Production at early time --- chiral transport --- hydrodynamics and observables Clarification soon: Isobar run at RHIC! 3
18 2. Why are early times so important? Most important direct contribution to CME at early times! - (Abelian) magnetic field 'still alive' 4
19 2. Why are early times so important? Most important direct contribution to CME at early times! - (Abelian) magnetic field 'still alive' - Initial conditions via the Color Glass Condensate (CGC), from coherent longitudinal color fields to over-occupied plasma 4
20 2. Why are early times so important? Most important direct contribution to CME at early times! - (Abelian) magnetic field 'still alive' - Initial conditions via the Color Glass Condensate (CGC), from coherent longitudinal color fields to over-occupied plasma - Quark production large occupation numbers of gluons ~ 1/g quark production O(1) 4
21 2. Why are early times so important? Most important direct contribution to CME at early times! - (Abelian) magnetic field 'still alive' - Initial conditions via the Color Glass Condensate (CGC), from coherent longitudinal color fields to over-occupied plasma - Quark production large occupation numbers of gluons ~ 1/g quark production O(1) correspondence principle --- mapping onto classical-statistical ensemble possible 4
22 2. Why are early times so important? Most important direct contribution to CME at early times! - (Abelian) magnetic field 'still alive' - Initial conditions via the Color Glass Condensate (CGC), from coherent longitudinal color fields to over-occupied plasma - Quark production large occupation numbers of gluons ~ 1/g quark production O(1) correspondence principle --- mapping onto classical-statistical ensemble possible Classical-Statistical Simulations (see Kasper 2015 for an pedagogical introduction) Can be systematically derived within the Color Glass Framework (Mclerran, Venugopalan 1994) 4
23 2. Why are early times so important? Most important direct contribution to CME at early times! - (Abelian) magnetic field 'still alive' - Initial conditions via the Color Glass Condensate (CGC), from coherent longitudinal color fields to over-occupied plasma - Quark production large occupation numbers of gluons ~ 1/g quark production O(1) correspondence principle --- mapping onto classical-statistical ensemble possible Classical-Statistical Simulations (see Kasper 2015 for an pedagogical introduction) Can be systematically derived within the Color Glass Framework (Mclerran, Venugopalan 1994) replace gauge field operators by ensemble of classical Yang-Mills fields 4
24 2. Why are early times so important? Most important direct contribution to CME at early times! - (Abelian) magnetic field 'still alive' - Initial conditions via the Color Glass Condensate (CGC), from coherent longitudinal color fields to over-occupied plasma - Quark production large occupation numbers of gluons ~ 1/g quark production O(1) correspondence principle --- mapping onto classical-statistical ensemble possible Classical-Statistical Simulations (see Kasper 2015 for an pedagogical introduction) Can be systematically derived within the Color Glass Framework (Mclerran, Venugopalan 1994) replace gauge field operators by ensemble of classical Yang-Mills fields Fermions: solve (operator-) Dirac equation 4
25 2. Real-time simulations Remarkable progress at early times classical statistical simulations 5
26 2. Real-time simulations Remarkable progress at early times classical statistical simulations - Identification of thermalization scenario (Berges, Boguslavski, Schlichting, Venugopalan 2014) PRD89 (2014)
27 2. Real-time simulations Remarkable progress at early times classical statistical simulations - Identification of thermalization scenario (Berges, Boguslavski, Schlichting, Venugopalan 2014) Instabilities and Turbulence Universal Physics far-from-equilibrium (recent connection to ultra-cold atoms PRL. 114 (2015) ) PRD89 (2014)
28 2. Real-time simulations Remarkable progress at early times classical statistical simulations - Identification of thermalization scenario (Berges, Boguslavski, Schlichting, Venugopalan 2014) Instabilities and Turbulence Universal Physics far-from-equilibrium PRD89 (2014) (recent connection to ultra-cold atoms PRL. 114 (2015) ) - Topological Transitions far-from-equilibrium (Mace, Schlichting, Venugopalan 2016, Moore 2011) PRD93 (2016)
29 2. Real-time simulations Remarkable progress at early times classical statistical simulations - Identification of thermalization scenario (Berges, Boguslavski, Schlichting, Venugopalan 2014) Instabilities and Turbulence Universal Physics far-from-equilibrium PRD89 (2014) (recent connection to ultra-cold atoms PRL. 114 (2015) ) - Topological Transitions far-from-equilibrium (Mace, Schlichting, Venugopalan 2016, Moore 2011) Fermions - EW & Higgs on a lattice (Saffin & Tranberg 2011) - Anomalous Effects in laser physics (NM, Hebenstreit, Berges PRL 117 (2016) ) PRD93 (2016) Many important contributions left out here --- my personal bias --- sorry! 5
30 2. Real-time simulations Remarkable progress at early times classical statistical simulations - Identification of thermalization scenario (Berges, Boguslavski, Schlichting, Venugopalan 2014) Instabilities and Turbulence Universal Physics far-from-equilibrium PRD89 (2014) (recent connection to ultra-cold atoms PRL. 114 (2015) ) - Topological Transitions far-from-equilibrium (Mace, Schlichting, Venugopalan 2016, Moore 2011) Fermions - EW & Higgs on a lattice (Saffin & Tranberg 2011) - Anomalous Effects in laser physics (NM, Hebenstreit, Berges PRL 117 (2016) ) PRD93 (2016) Real-time simulations of the Chiral Magnetic Effect and Anomalous Dynamics (QCD+QED) (Tanji, NM, Berges PRD93 (2016) ; Mace, NM, Schlichting, Sharma PRL 117 (2016) & arxiv: ) Many important contributions left out here --- my personal bias --- sorry! 5
31 Will show you today: Far-from-equilibrium anomalous and topological dynamics in HI collisions can be understood quantitative and from first principles, using real-time lattice simulations in the classical statistical regime
32 3. Real-time simulations Anomalous fermion dynamics during a topologicial transition Clean test case for the development of our tools. 5
33 3. Real-time simulations Anomalous fermion dynamics during a topologicial transition Clean test case for the development of our tools. simplified situation: setting up an isolated sphaleron transition Mace et al
34 3. Real-time simulations Anomalous fermion dynamics during a topologicial transition Clean test case for the development of our tools. simplified situation: setting up an isolated sphaleron transition Mace et al
35 3. Real-time simulations Anomalous fermion dynamics during a topologicial transition Clean test case for the development of our tools. simplified situation: setting up an isolated sphaleron transition Mace et al
36 3. Real-time simulations Anomalous fermion dynamics during a topologicial transition Clean test case for the development of our tools. simplified situation: setting up an isolated sphaleron transition Mace et al 2016 Fermions: Challenging! Solving Dirac operator equation in mode-function expansion 5
37 3. Real-time simulations Anomalous fermion dynamics during a topologicial transition Clean test case for the development of our tools. simplified situation: setting up an isolated sphaleron transition Mace et al 2016 Fermions: Challenging! Solving Dirac operator equation in mode-function expansion extremely costly (~N6) big obstacle so far and many attempts at reducing price (e.g. 'low-cost' techniques) 5
38 3. Real-time simulations Chiral Magnetic and Chiral Separation Effect Chiral Magnetic Waves NM, Schlichting, Sharma, PRL 117 (2016) ; Mace, NM, Schlichting, Sharma, arxiv:
39 3. Real-time simulations Chiral Magnetic and Chiral Separation Effect Chiral Magnetic Waves NM, Schlichting, Sharma, PRL 117 (2016) ; Mace, NM, Schlichting, Sharma, arxiv: lattice size:24x24x64 6
40 3. Real-time simulations Chiral Magnetic and Chiral Separation Effect Chiral Magnetic Waves NM, Schlichting, Sharma, PRL 117 (2016) ; Mace, NM, Schlichting, Sharma, arxiv: lattice size:24x24x64 B abelian magnetic field along z Initially: Vacuum (no fermions, no axial charge) 6
41 3. Real-time simulations Chiral Magnetic and Chiral Separation Effect Chiral Magnetic Waves NM, Schlichting, Sharma, PRL 117 (2016) ; Mace, NM, Schlichting, Sharma, arxiv: lattice size:24x24x64 B abelian magnetic field along z sphaleron transition (time) Initially: Vacuum (no fermions, no axial charge) 6
42 3. Real-time simulations Chiral Magnetic and Chiral Separation Effect Chiral Magnetic Waves NM, Schlichting, Sharma, PRL 117 (2016) ; Mace, NM, Schlichting, Sharma, arxiv: lattice size:24x24x64 B abelian magnetic field along z sphaleron transition (time) Initially: Vacuum (no fermions, no axial charge) 6
43 3. Real-time simulations Chiral Magnetic and Chiral Separation Effect Chiral Magnetic Waves NM, Schlichting, Sharma, PRL 117 (2016) ; Mace, NM, Schlichting, Sharma, arxiv: lattice size:24x24x64 B abelian magnetic field along z sphaleron transition (time) Initially: Vacuum (no fermions, no axial charge) 6
44 3. Real-time simulations Chiral Magnetic and Chiral Separation Effect Chiral Magnetic Waves NM, Schlichting, Sharma, PRL 117 (2016) ; Mace, NM, Schlichting, Sharma, arxiv: lattice size:24x24x64 B abelian magnetic field along z sphaleron transition (time) Initially: Vacuum (no fermions, no axial charge) 6
45 3. Real-time simulations Chiral Magnetic and Chiral Separation Effect Chiral Magnetic Waves NM, Schlichting, Sharma, PRL 117 (2016) ; Mace, NM, Schlichting, Sharma, arxiv: lattice size:24x24x64 B abelian magnetic field along z sphaleron transition (time) Initially: Vacuum (no fermions, no axial charge) 6
46 3. Real-time simulations Chiral Magnetic and Chiral Separation Effect Chiral Magnetic Waves NM, Schlichting, Sharma, PRL 117 (2016) ; Mace, NM, Schlichting, Sharma, arxiv: lattice size:24x24x64 B abelian magnetic field along z sphaleron transition (time) Initially: Vacuum (no fermions, no axial charge) 6
47 3. Real-time simulations Chiral Magnetic and Chiral Separation Effect Chiral Magnetic Waves NM, Schlichting, Sharma, PRL 117 (2016) ; Mace, NM, Schlichting, Sharma, arxiv: lattice size:24x24x64 B abelian magnetic field along z sphaleron transition (time) Initially: Vacuum (no fermions, no axial charge) Chiral Magnetic Effect: Chiral Separation Effect: Electric current generated due to axial charge produced Axial current generated due to electric charge 6
48 3. Real-time simulations 7
49 3. Real-time simulations asymptotic limit, simple estimates work 7
50 3. Real-time simulations asymptotic limit, simple estimates work finite magnetic field: important deviations from 'ideal' picture of CME 7
51 3. Real-time simulations 8
52 3. Real-time simulations 8
53 3. Real-time simulations finite quark mass effects anomalous transport suppressed for heavy quarks 8
54 3. Real-time simulations Simulating chiral fermions in real-time: Overlap fermions 9
55 3. Real-time simulations Simulating chiral fermions in real-time: Overlap fermions Lattice simulations: exactly chiral fermions challenging (at least in strong coupling regime) 9
56 3. Real-time simulations Simulating chiral fermions in real-time: Overlap fermions Lattice simulations: exactly chiral fermions challenging (at least in strong coupling regime) - in the classical-statistical limit mass renormalized perturbatively Wilson fermions arbitrary close to massless limit 9
57 3. Real-time simulations Simulating chiral fermions in real-time: Overlap fermions Lattice simulations: exactly chiral fermions challenging (at least in strong coupling regime) - in the classical-statistical limit mass renormalized perturbatively Wilson fermions arbitrary close to massless limit Benchmark: Wilson-fermions vs. Overlap fermions - mass matters! chiral instabilities (Yamamoto, Akamatsu, Kaplan, Reddy, Sen, Dvornikov...) - real-time evolutio beyond early time 9
58 3. Real-time simulations Simulating chiral fermions in real-time: Overlap fermions Lattice simulations: exactly chiral fermions challenging (at least in strong coupling regime) - in the classical-statistical limit mass renormalized perturbatively Wilson fermions arbitrary close to massless limit Benchmark: Wilson-fermions vs. Overlap fermions - mass matters! chiral instabilities (Yamamoto, Akamatsu, Kaplan, Reddy, Sen, Dvornikov...) - real-time evolutio beyond early time 9
59 3. Real-time simulations How this became possible Technical breakthroughs The challenge with fermions 10
60 3. Real-time simulations How this became possible Technical breakthroughs The challenge with fermions Evolution of the fermion operators extremely costly due to mode-function expansion (cost with lattice size: N6 for fermions vs. N3 for 'YM only') 10
61 3. Real-time simulations How this became possible Technical breakthroughs The challenge with fermions Evolution of the fermion operators extremely costly due to mode-function expansion (cost with lattice size: N6 for fermions vs. N3 for 'YM only') stochastic descriptions have been put forward early on: 'low-cost fermions' (Borsányi and Hindmarsh 2009, Berges, Gelfand) 10
62 3. Real-time simulations How this became possible Technical breakthroughs The challenge with fermions Evolution of the fermion operators extremely costly due to mode-function expansion (cost with lattice size: N6 for fermions vs. N3 for 'YM only') stochastic descriptions have been put forward early on: 'low-cost fermions' (Borsányi and Hindmarsh 2009, Berges, Gelfand) converge in a number of cases, unfortunately not in many others, especially for anomalous dynamics! 10
63 3. Real-time simulations How this became possible Technical breakthroughs The challenge with fermions Evolution of the fermion operators extremely costly due to mode-function expansion (cost with lattice size: N6 for fermions vs. N3 for 'YM only') stochastic descriptions have been put forward early on: 'low-cost fermions' (Borsányi and Hindmarsh 2009, Berges, Gelfand) converge in a number of cases, unfortunately not in many others, especially for anomalous dynamics! Our approach: - tree-level operator improvements (Eguchi and N. Kawamoto 1984) - Wilson-averaging works extremely well, convergence already on small lattices 16x16x16 for smooth gauge fields 10
64 3. Real-time simulations How this became possible Technical breakthroughs The challenge with fermions Evolution of the fermion operators extremely costly due to mode-function expansion (cost with lattice size: N6 for fermions vs. N3 for 'YM only') stochastic descriptions have been put forward early on: 'low-cost fermions' (Borsányi and Hindmarsh 2009, Berges, Gelfand) converge in a number of cases, unfortunately not in many others, especially for anomalous dynamics! Our approach: - tree-level operator improvements (Eguchi and N. Kawamoto 1984) - Wilson-averaging works extremely well, convergence already on small lattices 16x16x16 for smooth gauge fields Computational Ressources: 10
65 3. Real-time simulations How this became possible Technical breakthroughs The challenge with fermions Evolution of the fermion operators extremely costly due to mode-function expansion (cost with lattice size: N6 for fermions vs. N3 for 'YM only') stochastic descriptions have been put forward early on: 'low-cost fermions' (Borsányi and Hindmarsh 2009, Berges, Gelfand) converge in a number of cases, unfortunately not in many others, especially for anomalous dynamics! Our approach: - tree-level operator improvements (Eguchi and N. Kawamoto 1984) - Wilson-averaging works extremely well, convergence already on small lattices 16x16x16 for smooth gauge fields Computational Ressources: Check arxiv: for the current state-of-art! 10
66 4. Relativistic Chiral Kinetic Theory The limits of classical statistical simulations CGC colliding nuclei flux tubes over-occupied plasma kinetic regime hydrodynamic regime S. Schlichting 2016 classical statistical simulations + fermions chiral kinetic theory anomalous hydrodynamics 11
67 4. Relativistic Chiral Kinetic Theory The limits of classical statistical simulations CGC colliding nuclei flux tubes over-occupied plasma kinetic regime hydrodynamic regime S. Schlichting 2016 classical statistical simulations + fermions chiral kinetic theory anomalous hydrodynamics 11
68 4. Relativistic Chiral Kinetic Theory The limits of classical statistical simulations CGC colliding nuclei flux tubes over-occupied plasma kinetic regime hydrodynamic regime S. Schlichting 2016 classical statistical simulations + fermions chiral kinetic theory anomalous hydrodynamics classical-statistical simulations become inaccurate as occupation numbers drop subsequent evolution of chiral and vector currents influenced by medium: 11
69 4. Relativistic Chiral Kinetic Theory The limits of classical statistical simulations CGC colliding nuclei flux tubes over-occupied plasma kinetic regime hydrodynamic regime S. Schlichting 2016 classical statistical simulations + fermions chiral kinetic theory anomalous hydrodynamics classical-statistical simulations become inaccurate as occupation numbers drop subsequent evolution of chiral and vector currents influenced by medium: scattering of topological domains axial transport E&M conductivity 11
70 4. Relativistic Chiral Kinetic Theory The limits of classical statistical simulations CGC colliding nuclei flux tubes over-occupied plasma kinetic regime hydrodynamic regime S. Schlichting 2016 classical statistical simulations + fermions chiral kinetic theory anomalous hydrodynamics classical-statistical simulations become inaccurate as occupation numbers drop subsequent evolution of chiral and vector currents influenced by medium: scattering of topological domains axial transport Need to connect early time E&M conductivity and hydrodynamic evolution! 11
71 4. Relativistic Chiral Kinetic Theory Chiral Kinetic Theory talk by Jinfeng Liao Connection between Berry phase (adiabatic limit) and quantum anomalies 12
72 4. Relativistic Chiral Kinetic Theory Chiral Kinetic Theory talk by Jinfeng Liao Connection between Berry phase (adiabatic limit) and quantum anomalies massless fermions, large chemical potential 12
73 4. Relativistic Chiral Kinetic Theory talk by Jinfeng Liao Chiral Kinetic Theory Connection between Berry phase (adiabatic limit) and quantum anomalies massless fermions, large chemical potential Son,Yamamoto, PRL109 (2012), ; PRD87 (2013) Stephanov, Yin, PRL109 (2012) Chen, Son, Stephanov, Yee, Yin, PRL 113 (2014) Chen, Son, Stephanov, PRL115 (2015) Chen,Pu,Wang,Wang, PRL110 (2013) Gao,Liang,Pu,Wang,Wang, PRL109 (2012) Stone,Dwivedi,Zhou, PRD91 (2015) Zahed, PRL109 (2012) ; Basar, Kharzeev,Zahed, PRL111 (2013) Stephanov,Yi,Yin,PRD91 (2015) Manuel, Torres-Rincon, PRD 90, (2014) 12
74 4. Relativistic Chiral Kinetic Theory talk by Jinfeng Liao Chiral Kinetic Theory Connection between Berry phase (adiabatic limit) and quantum anomalies massless fermions, large chemical potential Son,Yamamoto, PRL109 (2012), ; PRD87 (2013) Stephanov, Yin, PRL109 (2012) Chen, Son, Stephanov, Yee, Yin, PRL 113 (2014) Chen, Son, Stephanov, PRL115 (2015) Chen,Pu,Wang,Wang, PRL110 (2013) Gao,Liang,Pu,Wang,Wang, PRL109 (2012) Stone,Dwivedi,Zhou, PRD91 (2015) Zahed, PRL109 (2012) ; Basar, Kharzeev,Zahed, PRL111 (2013) Stephanov,Yi,Yin,PRD91 (2015) Manuel, Torres-Rincon, PRD 90, (2014) - Absence of level crossings (adiabaticity) vs. anomaly? 12
75 4. Relativistic Chiral Kinetic Theory talk by Jinfeng Liao Chiral Kinetic Theory Connection between Berry phase (adiabatic limit) and quantum anomalies massless fermions, large chemical potential Son,Yamamoto, PRL109 (2012), ; PRD87 (2013) Stephanov, Yin, PRL109 (2012) Chen, Son, Stephanov, Yee, Yin, PRL 113 (2014) Chen, Son, Stephanov, PRL115 (2015) Chen,Pu,Wang,Wang, PRL110 (2013) Gao,Liang,Pu,Wang,Wang, PRL109 (2012) Stone,Dwivedi,Zhou, PRD91 (2015) Zahed, PRL109 (2012) ; Basar, Kharzeev,Zahed, PRL111 (2013) Stephanov,Yi,Yin,PRD91 (2015) Manuel, Torres-Rincon, PRD 90, (2014) - Absence of level crossings (adiabaticity) vs. anomaly? - topology of Berry's phase vs. topology of the anomaly? (Fujikawa 2005) 12
76 4. Relativistic Chiral Kinetic Theory talk by Jinfeng Liao Chiral Kinetic Theory Connection between Berry phase (adiabatic limit) and quantum anomalies massless fermions, large chemical potential Son,Yamamoto, PRL109 (2012), ; PRD87 (2013) Stephanov, Yin, PRL109 (2012) Chen, Son, Stephanov, Yee, Yin, PRL 113 (2014) Chen, Son, Stephanov, PRL115 (2015) Chen,Pu,Wang,Wang, PRL110 (2013) Gao,Liang,Pu,Wang,Wang, PRL109 (2012) Stone,Dwivedi,Zhou, PRD91 (2015) Zahed, PRL109 (2012) ; Basar, Kharzeev,Zahed, PRL111 (2013) Stephanov,Yi,Yin,PRD91 (2015) Manuel, Torres-Rincon, PRD 90, (2014) - Absence of level crossings (adiabaticity) vs. anomaly? - topology of Berry's phase vs. topology of the anomaly? (Fujikawa 2005) - adiabatic approximation in heavy ion collision? 12
77 4. Relativistic Chiral Kinetic Theory talk by Jinfeng Liao Chiral Kinetic Theory Connection between Berry phase (adiabatic limit) and quantum anomalies massless fermions, large chemical potential Son,Yamamoto, PRL109 (2012), ; PRD87 (2013) Stephanov, Yin, PRL109 (2012) Chen, Son, Stephanov, Yee, Yin, PRL 113 (2014) Chen, Son, Stephanov, PRL115 (2015) Chen,Pu,Wang,Wang, PRL110 (2013) Gao,Liang,Pu,Wang,Wang, PRL109 (2012) Stone,Dwivedi,Zhou, PRD91 (2015) Zahed, PRL109 (2012) ; Basar, Kharzeev,Zahed, PRL111 (2013) Stephanov,Yi,Yin,PRD91 (2015) Manuel, Torres-Rincon, PRD 90, (2014) - Absence of level crossings (adiabaticity) vs. anomaly? - topology of Berry's phase vs. topology of the anomaly? (Fujikawa 2005) - adiabatic approximation in heavy ion collision? - Lorentz covariance (side jumps?) 12
78 4. Relativistic Chiral Kinetic Theory Chiral Kinetic Theory just a teaser 12a
79 4. Relativistic Chiral Kinetic Theory Chiral Kinetic Theory just a teaser We understand the anomaly very well in second quantization (Fujikawa 1979) How can this understanding be extended to first quantization (x,p,...) from first principles? 12a
80 4. Relativistic Chiral Kinetic Theory Chiral Kinetic Theory just a teaser We understand the anomaly very well in second quantization (Fujikawa 1979) How can this understanding be extended to first quantization (x,p,...) from first principles? World line quantization (Schwinger, Feynman, Bern, Kosower, Strassler ) 12a
81 4. Relativistic Chiral Kinetic Theory Chiral Kinetic Theory just a teaser We understand the anomaly very well in second quantization (Fujikawa 1979) How can this understanding be extended to first quantization (x,p,...) from first principles? World line quantization (Schwinger, Feynman, Bern, Kosower, Strassler ) - fermionic determinant and anomalies Witten & Alvarez-Gaume 1983, D'Hoker & Gagne a
82 4. Relativistic Chiral Kinetic Theory Chiral Kinetic Theory just a teaser We understand the anomaly very well in second quantization (Fujikawa 1979) How can this understanding be extended to first quantization (x,p,...) from first principles? World line quantization (Schwinger, Feynman, Bern, Kosower, Strassler ) - fermionic determinant and anomalies Witten & Alvarez-Gaume 1983, D'Hoker & Gagne natural quasi-classical limit, (Lorentz covariant, no requirement of adiabaticity) 12a
83 4. Relativistic Chiral Kinetic Theory Chiral Kinetic Theory just a teaser We understand the anomaly very well in second quantization (Fujikawa 1979) How can this understanding be extended to first quantization (x,p,...) from first principles? World line quantization (Schwinger, Feynman, Bern, Kosower, Strassler ) - fermionic determinant and anomalies Witten & Alvarez-Gaume 1983, D'Hoker & Gagne natural quasi-classical limit, (Lorentz covariant, no requirement of adiabaticity) see NM, R. Venugopalan, arxiv: (+ longer paper very very soon); and NM, R. Venugopalan, Y.Yin, in prep. 12a
84 5. Conclusions - I have shown you real-time classical statistical simulations of fermion production during sphaleron transitions in background magnetic fields - Axial anomaly realized in lattice simulations using Wilson fermions - Chiral Magnetic and Chiral Separation Effect emerge dynamically - Observation of the Chiral Magnetic Wave - Have investigated finite mass and magnetic field dependence. Finite quark mass plays an important role: dissipation of anomalous currents - Simulated chiral lattice fermions in real-time overlap! 13
85 What's next? The techniques are established for the quantitative first principle simulation of farfrom-equilibrium dynamics of fermions and gauge fields! Realistic heavy ion collision CGC initial conditions & expansion (work in progress with J. Berges, M. Mace, S.Schlichting, S. Sharma, N. Tanji ) chiral plasma instabilities (with M. Mace, S.Schlichting, S. Sharma) provide initial conditions for hydrodynamics electromagnetic properties of the Glasma, how long does the magnetic field live? connection to chiral kinetic theory & anomalous hydrodynamics (with R. Venugopalan, Y. Yin) non-thermal photons and the direct photon puzzle (with J. Berges, O. Garcia-Montero, N. Tanji) 14
86 Thanks for your attention and thanks to
87 A. Backup Classical Statistical Simulations (see for example Kasper et al. Phys.Rev. D90 (2014) 2, ) typical situation: large coherent or highly occupied gauge fields correspondence principle - initial stages of a heavy ion collision: A ~ 1/g - colliding laser beams large and coherent fields The classical-statistical approximation is a systematic expansion of the 'quantum' fields around the 'classical' fields 'classical' 'quantum' Fermions are never classical Exact description via modefunctions up to 24x24x64 lattices 7
88 B. Backup Algorithmic Improvements Fermions: Exact description via modefunctions up to 24x24x64 lattices Improved operators (NM, S.Schlichting, S.Sharma, arxiv: , arxiv: ) Wilson-averaging (M.Mace, NM, S.Schlichting, S.Sharma, arxiv: ) improvement of chiral properties extremely important for larger fermion masses average fermionic observables over Wilson parameters with opposite sign leading order errors in the anomaly equation cancel
89 C. Backup Magnetic Fields on the lattice Magnetic fields break translation invariance magnetic translation group - Magnetic fields on a torus very non-trivial (see Al-Hashimi & Wiese Accidental Symmetries, also Bali et al.) - Intriguing lattice artefacts! spoil the low-cost method --- while there probably are field configurations where low-cost works, this is certainly not the case in magnetic fields
90 D. Backup Anomaly Realization on the Lattice Chiral Symmetry + Fermion doubling + Chiral Anomaly = one of the prettiest connections I have ever seen - The axial anomaly and the fermion doubling problem are intimately related - Lattice theory regularized on the basis of the action already - Anomaly comes from the non-trivial continuum limit of any regulator you put in to remove doublers preliminary
Chiral magnetic effect and anomalous transport from real-time lattice simulations
Chiral magnetic effect and anomalous transport from real-time lattice simulations Niklas Mueller Heidelberg University based on work together with: J. Berges, M. Mace, S. Schlichting, S. Sharma, N. Tanji
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