D á niel Ber ényi Wigner RCP of the HAS , Budapest

1. Describing pair production in inhomogeneous external fieldswith the Dirac-Heisenberg-Wigner formalism DánielBerényiWigner RCP of the HAS, Budapest with Sándor Varró, Vladimir Skokovand Péter Lévai Wigner 111 Budapest, 12. november 2013.

2. Pair Production from vacuum • One of the most interesting predictions of QED!Predicted by Sauter and first calculated by Schwinger: Dániel Berényi Pair Production

3. Phenomenologic view from the Dirac Sea Tunneling… Dániel Berényi Pair Production

4. The onset of pair production The necessary field strength is extreme: Do we have any chance to see it? Dániel Berényi Pair Production

5. Pair production sources • Rapid development of laser technology!We are still few orders of magnitude below the Schwinger limit,but the progress is promising! ELI @ Szeged, Hungary T. Tajima G. Mourou Dániel Berényi Pair Production

6. Pair production sources • Pair production can also happen in QCD: Separating quarks create a flux tube in between, that produce quark-anti quark pairs! new pair The QCD formulas are analogous to the QED case! This model is particularly successful: employed at LHC too! Dániel Berényi Pair Production

7. Describing pair production To be able to • make calculations to give predictions and • build devices to observe pair productionTheoretical models are needed!In the last 30 years important developments have been made with contributions from many people now here at Wigner111! Dániel Berényi Pair Production

8. Dániel Berényi Pair Production

9. The Wigner quasi-probability function Jenő Wigner wanted to calculate quantum corrections to statistical physics.His distribution function since became a fundamental tool in the investigation of pair production! • Most importantproperties: • Describes a quantumsystemwithquasi-classicaltimeevolution • negativevaluesindicatequantumphenomena Dániel Berényi Pair Production

10. The Wigner quasi-probability function Relativistic definition for spinor fields in terms of the wave function: Dániel Berényi Pair Production

11. Evolution equation for the Wigner function The time evolution equations in compact form: Dániel Berényi Pair Production

12. Evolution equation for the Wigner function The cost of including arbitrary E and B field is:16 equations in 3+3+1 dimensions and non-local differential equations… Dániel Berényi Pair Production

13. Interpretations of the QED Wigner function Dániel Berényi Pair Production

14. Initial conditions of the QED Wigner function Dániel Berényi Pair Production

15. Pair production characteristics • What we know about pair production so far?First results were analytic, but arbitrary fields need numerical solutions… Dániel Berényi Pair Production

16. Pair production characteristics Static constant electric field: Schwinger-rate: Dániel Berényi Pair Production

17. Pair production characteristics Time dependent, homogeneous electric field (Sauter-pulse): Dániel Berényi Pair Production

18. Pair production analogue process A very similar analogue process that can be calculated with only time dependent E field: Ionization from bound state with a strong, ultra short laser pulseThis is a real, time resolved measurement performed at Max Planck Institute, GermanyBelow is a calculation for vacuum pair production. Dániel Berényi Pair Production

19. Pair production characteristics For the QCD applications:Power-law like fields generate power law like transverse spectra!The SU(N) Wigner function can be constructed, but behaviour is very similar to the QED case! Dániel Berényi Pair Production Péter Lévai, Vladimir Skokov

20. Pair production characteristics • So far only spatially homogeneous fields…But what about finite size effects?What happen at the edges of a gluon string?Or at the edge of a strong laser pulse?The required numerics are cumbersome but slowly became feasible! Dániel Berényi Pair Production

21. Pair production ininhomogeneousfields • We are investigating the following QED toy model of the QCD color string: Dániel Berényi Pair Production

22. Pair production ininhomogeneousfields Wefind a largeexcess of pairsattheedgeswhilereproducing thehomogeneousresultsinthemiddle. Dániel Berényi Pair Production

23. Pair production ininhomogeneousfields Dániel Berényi Pair Production

24. Pair production ininhomogeneousfields Pulse widthdependencecomparedtothehomogeneouscase: Inhomogeneousfield Homogeneousreference Dániel Berényi Pair Production

25. Pair production ininhomogeneousfields Plateuwidth dependence of particleyieldcomparedtohomogeneousreference: Inhomogeneousfield Sameslope!!! Homogeneousreference Dániel Berényi Pair Production

26. Pair production ininhomogeneousfields What does these results mean? • Inhomogeneity enhances the particle yield • The enhancement is proportional to the elapsed time • The enhancement does not scale with the volume, but instead scales with the surface!We thus support the prediction of Heisenberg from 1934, that inhomogeneity is a genuine surface effect in pair production! Dániel Berényi Pair Production

27. Hardware • Our numerical method is based on pseudo-spectral collocation. • Scalable: dense matrix problem Ideal for GPUs! Further investigations will be performed at theGPU lab at the Wigner RCP. Dániel Berényi Pair Production

28. Summary • Wigner formalism is an effective tool for investigating pair production in arbitrary external fields in QED and QCD. • We developed a numerical solvers for the 16 component 3+1 dimensional QED Wigner function that was not considered before. • We are investigating the effect of inhomogeneity that seems to play an important role on long time scales. • Consequences may extend to the parameters of next gen laser facilities as well more precise models of QCD string fragmentation Dániel Berényi Pair Production