Quantum transport and the phase space structure of the Wightman functions
- PDF / 1,725,431 Bytes
- 28 Pages / 595.276 x 841.89 pts (A4) Page_size
- 63 Downloads / 158 Views
Springer
Received: October 30, 2019 Accepted: December 16, 2019 Published: January 3, 2020
Henri Jukkala,a,b Kimmo Kainulainena,b,c and Olli Koskivaaraa,b a
Department of Physics, University of Jyv¨ askyl¨ a, P.O. Box 35 (YFL), FI-40014 Jyv¨ askyl¨ a, Finland b Helsinki Institute of Physics, University of Helsinki, P.O. Box 64, FI-00014 Helsinki, Finland c Theoretical Physics Department, CERN, 1211 Geneva 23, Switzerland
E-mail: [email protected], [email protected], [email protected] Abstract: We study the phase space structure of exact quantum Wightman functions in spatially homogeneous, temporally varying systems. In addition to the usual mass shells, the Wightman functions display additional coherence shells around zero frequency k0 = 0, which carry the information of the local quantum coherence of particle-antiparticle pairs. We find also other structures, which encode non-local correlations in time, and discuss their role and decoherence. We give a simple derivation of the cQPA formalism, a set of quantum transport equations, that can be used to study interacting systems including the local quantum coherence. We compute quantum currents created by a temporal change in a particle’s mass, comparing the exact Wightman function approach, the cQPA and the semiclassical methods. We find that the semiclassical approximation, which is fully encompassed by the cQPA, works surprisingly well even for very sharp temporal features. This is encouraging for the application of semiclassical methods in electroweak baryogenesis with strong phase transitions. Keywords: Thermal Field Theory, CP violation, Quantum Dissipative Systems ArXiv ePrint: 1910.10979
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP01(2020)012
JHEP01(2020)012
Quantum transport and the phase space structure of the Wightman functions
Contents 1
2 Wightman functions and cQPA 2.1 cQPA-solution in a spatially homogeneous system
3 4
3 Constructing the exact Wightman function 3.1 Non-interacting Wightman function 3.2 Including damping 3.3 Explicit solutions for mode functions
7 7 8 9
4 Phase space of the exact Wightman function 4.1 Non-local coherence in time 4.2 Physical and practical significance of the phase space structures
12 14 15
5 Currents and connection to the semiclassical limit 5.1 Collisionless case 5.2 Semiclassical approximation 5.3 Range of validity of the different formalism
15 16 17 18
6 cQPA with collisions 6.1 A numerical example
20 22
7 Conclusions and outlook
23
1
Introduction
Quantum coherence plays an important role in many physical problems in cosmology. Examples include CP-violating particle-wall interactions during the electroweak phase transition, out-of-equilibrium decay of nearly degenerate heavy neutrinos during leptogenesis, particle production during phase transitions and reheating at the end of inflation. The key quantity in the analysis of such intrinsically quantum systems is the two-point correlation function, whose evolution is descri
Data Loading...
