Numerical methods for holographic thermalization

Numerical methods for holographic thermalization

Lecture series during the week 5-9 May 2014, HIP seminar room Physicum A315

Michał Heller, University of Amsterdam

Abstract: Holography is an exploratory tool for studying time-dependent processes in strongly coupled gauge theories. The most interesting setups, such as creation of the quark-gluon plasma or its relaxation from a state having significant pressure anisotropy, require the use of numerical relativity methods. The course will present basic theoretical and numerical know-how that allow to address such questions. The ultimate goal will be to understand how to write a Mathematica code that reproduces the results of arXiv:1202.0981 and 1304.5172. Pre-requisite skills are Mathematica programming, general relativity and the basics of quantum field theory.

Active participation in the course corresponds to 3 credits for graduate students.

Program

1. Monday 5 May 10.15-12, 15.15-16 (Tommi Markkanen defends his thesis at 12.15- )

[lecture] Setting up goals for the course; Bottom-up approach to holography; black holes in anti-de Sitter space (3×45 min.);

Tuesday 6 May 10.15- . Michał Heller will give a HIP colloquium: Gauge fields out of equilibrium – a holographic approach

Abstract: Ultra-relativistic heavy ion collision programs at RHIC and LHC probe the properties of matter under extreme conditions in which quarks and gluons are liberated from hadrons and form the quark-gluon plasma. I will discuss the progress on theoretical understanding of the formation of the quark-gluon plasma in heavy ion collisions, and related questions, coming from the first principle calculations in the models of strong interactions solvable using holography. This leads to a fascinating connection with gravitational physics, in particular black hole formation and dynamics, which I will discuss in detail.

2. Tuesday 6 May 12.15-14.00

[lecture/workshop] Black hole perturbations and quasinormal modes; the ingoing Eddington-Finkelstein coordinates and the characteristic formulation; basics of numerics in Mathematica (3×45 min.);

3. Wednesday 7 May 10.15-12, 15.15-16

[workshop] Numerical solutions of harmonic oscillator equations: finite differences vs. spectral methods (3×45 min.);

4. Thursday 8 May 12.15-14, 15.15-16

Nick Evans will give a HIP colloquium (10.15-11).
[workshop] Solving the wave equation; solving linearized Einstein’s equations, as in arXiv:1202.0981 and 1304.5172 (3×45 min.);

5. Friday 9 May 10.15-16

[workshop] Writing simple nonlinear code for holographic thermalization (4-6×45 min.);