Far-from-equilibrium universality classes In heavy-ion collisions and cosmology

Transcription

1 Far-from-equilibrium universality classes In heavy-ion collisions and cosmology Kirill Boguslavski J. Berges, KB, S. Schlichting and R. Venugopalan, PRD 92, (2015); PRL 114, (2015) Project: CGCglasmaQGP Particle Physics Day November 25, 2016 In collaboration with: Jürgen Berges Asier Piñeiro Orioli Sören Schlichting Raju Venugopalan Roland Walz A. Piñeiro Orioli, KB and J. Berges, PRD 92, (2015) An overview: KB, PhD thesis (2016) (linked e.g. via HEP-INSPIRE) University of Jyväskylä, Finland Kirill Boguslavski 1

2 Table of Contents 1. Introduction 2. Universality class: scalars in the IR 3. Universality class: expanding gauge & scalar theories 4. Conclusion University of Jyväskylä, Finland Kirill Boguslavski 2

3 Introduction: Motivation Systems far from equilibrium Heavy-ion collisions Inflationary cosmology Ultracold atoms ALICE (Expanding) non-abelian gauge theory NASA / WMAP Relativistic O(N) scalars TU VIENNA Nonrelativistic scalars For weak couplings: Universal properties? University of Jyväskylä, Finland Kirill Boguslavski 3

4 Distribution f Introduction: Nonthermal fixed points Typical IC: Over-occupation Nonthermal fixed point (NTFP) Micha & Tkachev, PRD 70, (2004) Berges, Rothkopf & Schmidt, PRL 101, (2008) Partial memory loss Time scale independence Self-similar dynamics (Single-particle) Distribution function: University of Jyväskylä, Finland Kirill Boguslavski 4

5 Introduction: Simulation method Weak couplings but large occupancies Classical-statistical simulations - Initialize fields or - Solve classical equations of motion on the lattice - Observables averaged over (quantum) IC Classicality condition: Aarts & Berges, PRL 88, (2002) Examples: Micha & Tkachev ; Smit & Tranberg; Nowak, Scholle, Sexty & Gasenzer ; Berges, KB, Schlichting & Venugopalan; Kurkela & Moore; University of Jyväskylä, Finland Kirill Boguslavski 5

6 Universality class: scalars in the IR Massless relativistic scalars O(N) symmetric, interaction Nonrelativistic scalars (Gross-Pitaevskii) Cosmology (inflaton), Higgs dynamics Ultracold atoms Micha & Tkachev, PRL 90, (2003) Berges, Rothkopf & Schmidt, PRL 101, (2008) A. Piñeiro Orioli, KB, and J. Berges, PRD 92, (2015) University of Jyväskylä, Finland Kirill Boguslavski 6

7 Universality class: scalars in the IR Self-similar evolution Self-similar evolution Pinerio Orioli, KB & Berges, PRD 92, (2015) Inverse particle cascade to infrared Scaling exponents Particle number conservation For nonrelativistic and relativistic O(N) symmetric scalars University of Jyväskylä, Finland Kirill Boguslavski 7

8 Universality class: scalars in the IR Self-similar evolution Universal scaling function Pinerio Orioli, KB & Berges, PRD 92, (2015) Same functional form with Universality class for: - non-relativistic Bose gases - O(N) symmetric scalars University of Jyväskylä, Finland Kirill Boguslavski 8

9 Universality class: scalars in the IR Explanation: Vertex-resummed kinetic theory Kinetic theory for elastic collisions At low momenta high occupancies resummation needed (because of interference of infinitely many scattering processes) 2 Berges, Rothkopf & Schmidt, PRL 101, (2008) Berges & Sexty, PRD 83, (2011) Leads to correct scaling exponents! Pinerio Orioli, KB & Berges, PRD 92, (2015) University of Jyväskylä, Finland Kirill Boguslavski 9

10 Rescaled distribution: Universality class: scalars in the IR Explanation: Vertex-resummed kinetic theory Nonrelativistic scalars in VR kinetic theory Self-similar evolution Effective kinetic theory also captures scaling form! R. Walz, KB and J. Berges, Preliminary with Rescaled momentum: University of Jyväskylä, Finland Kirill Boguslavski 10

11 Universality class: expanding gauge & scalar theories Massless scalar field theory (O(N)) Non-Abelian gauge theory (SU(2)) Heavy-ion collisions at early times (weak-coupling limit ) Bjorken coordinates: Metric in Bjorken coordinates: longitudinal expansion (in beam direction) Little Bang by P. Sorensen and C. Shen Self-similar evolution: J. Berges, KB, S. Schlichting and R. Venugopalan: PRL 114, (2015) ; PRD 92, (2015) University of Jyväskylä, Finland Kirill Boguslavski 11

12 Universality class: expanding gauge & scalar theories Longitudinal dynamics Reminder: Self-similar evolution Shared universality class Dynamical exponents Gaussian scaling form Same exponents and scaling function in gauge and scalar theories! Gauge attractor from elastic scatterings Baier, Mueller, Schiff & Son, PLB 502, 51 (2001) Berges, KB, Schlichting, Venugopalan, PRD 89, (2014) University of Jyväskylä, Finland Kirill Boguslavski 12

13 Universality class: expanding gauge & scalar theories Where is shared scaling region? i) scalar fields ii) iii) gauge fields ii) - Scaling range ii) is the universal region. - Exponents and form largely insensitive to initial conditions (memory loss), see J. Berges, KB, S. Schlichting, and R. Venugopalan: PRD 89, (2014) ; PRD 92, (2015) University of Jyväskylä, Finland Kirill Boguslavski 13

14 Expanding scalars linking universal features Link between the world s hottest and coldest matter Scalar fields infrared scaling region: i) Longitudinally expanding scalars i) scalar fields ii) iii) Broad universality class Explanation: vertex-resummed kinetic theory i. Cold atoms, inflationary cosmology ii. Heavy-ion collisions Berges, KB, Schlichting & Venugopalan, PRD 92, (2015) See also: KB, PhD thesis (2016) University of Jyväskylä, Finland Kirill Boguslavski 14

15 Conclusion Over-occupied quantum systems may approach nonthermal fixed-points Scalar systems lie in the same infrared universality class Expanding scalar and gauge systems share a universality class Outlook Possibility of accessing infrared in inflationary cosmology with ultracold atoms Simulation of inflaton evolution with resummed kinetic theory? How can far-from-equilibrium universality classes be classified? Our results hint at a nontrivial infrared region in gauge theories description? Thank you for your attention! University of Jyväskylä, Finland Kirill Boguslavski 15

16 BACKUP SLIDES University of Jyväskylä, Finland Kirill Boguslavski 16

17 Details on vertex-resummation University of Jyväskylä, Finland Kirill Boguslavski 17

18 University of Jyväskylä, Finland Kirill Boguslavski 18

19 Expanding scalars linking universal features The entire attractor in longitudinally expanding scalars Reminder: Self-similar evolution i) scalar fields ii) iii) Berges, KB, Schlichting & Venugopalan, PRD 92, (2015) Scaling regions i) ii) iii) Institut for Theoretical Physics, Uni Heidelberg Kirill Boguslavski 19

20 Expanding scalars linking universal features Pressure ratio: Parametrically: P u z z l e s Berges, KB, Schlichting, Venugopalan, PRD 92, (2015) Visible discrepancies! P L : important contributions from IR modes, Described by vertex-resummed kinetic theory (scalars) Results challenge kinetic description of non-abelian gauge theory. IR in non-abelian plasmas isotropic? Enhanced? Transient condensation? Nontrivial topological structure? Vertex-resummations required? Institut for Theoretical Physics, Uni Heidelberg Kirill Boguslavski 20