Solving the homogeneous Boltzmann equation with arbitrary scattering kernel

Hohenegger, Andreas

doi:10.1103/physrevd.79.063502

Cited by 10 publications

(15 citation statements)

References 28 publications

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“…We give in appendix A the final reduced integrals and, as an example, the full reduction procedure applied to the s-channel collisional integral for tracking the RHN following the method of [31,32]. A general treatment of scattering kernels in kinetic equations can be found in [33]. Figure 5 shows snapshots of the RHN distribution function in Case S2 relative to an equilibrium Fermi-Dirac distribution at time z = 0.2, 1, 5, as well as the RHN number density normalised to its equilibrium value as a function of z for an interaction strength of K = 0.1.…”

Section: Case S2: Complete Mode Equations Including Scatteringmentioning

confidence: 99%

Full Boltzmann equations for leptogenesis including scattering

Hahn-Woernle

Plümacher

Wong

2009

J. Cosmol. Astropart. Phys.

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We study the evolution of a cosmological baryon asymmetry produced via leptogenesis by means of the full classical Boltzmann equations, without the assumption of kinetic equilibrium and including all quantum statistical factors. Beginning with the full mode equations, we derive the usual equations of motion for the right-handed neutrino number density and integrated lepton asymmetry, and show explicitly the impact of each assumption on these quantities. For the first time, we investigate also the effects of scattering of the right-handed neutrino with the top quark to leading order in the Yukawa couplings by means of the full Boltzmann equations. We find that in our full Boltzmann treatment the final lepton asymmetry can be suppressed by as much as a factor of ∼ 1.5 in the weak wash-out regime (K 1), compared to the usual integrated approach which assumes kinetic equilibrium and neglects quantum statistics. This suppression is in contrast with the enhancement seen in some previous studies that considered only decay and inverse decay of the right-handed neutrino. However, this suppression quickly decreases as we increase K. In the strong wash-out regime (K 1), the full Boltzmann treatment and the integrated approach give nearly identical final lepton asymmetries (within 10% of each other at K > 3). Finally, we show that the opposing effects of quantum statistics on decays/inverse decays and the scattering processes tend to reduce the net importance of scattering on leptogenesis in the full treatment compared to the integrated approach. Basic set-upWe concentrate on the simplest case of "vanilla-leptogenesis", in which a lepton asymmetry is established from the decay and scattering of the lightest heavy right-handed neutrino N 1 . We neglect the decay of the two heavier neutrino states N 2,3 [22], assuming that any lepton asymmetry pro-

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Section: Case S2: Complete Mode Equations Including Scatteringmentioning

confidence: 99%

Full Boltzmann equations for leptogenesis including scattering

Hahn-Woernle

Plümacher

Wong

2009

J. Cosmol. Astropart. Phys.

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“…Sakharov realized that a baryon asymmetry could be produced dynamically in the evolution of the universe if three conditions are satisfied: 1 • Baryon number violation…”

Section: The Sakharov Conditionsmentioning

confidence: 99%

“…Since the procedure for the λϕ 4 theory is well known in Minkowski space-time it will be easy to compare it with the results obtained in [35,[41][42][43][44] and elsewhere. 1 Beginning with the generating functional for connected Green's functions in covariant form, the individual steps are roughly:…”

Section: Schwinger-keldysh Formalism In Curved Space-timementioning

confidence: 99%

Finite density aspects of leptogenesis

Hohenegger¹

2010

J. Phys.: Conf. Ser.

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Leptogenese ist ein Modell zur dynamischen Erklärung der Materie-Antimaterie Asymmetrie. Dieser Prozess findet im frühen Universum bei hohen Temperaturen statt und eine Abweichung vom Gleichgewicht ist fundamentale Voraussetzung für die Erzeugung der Asymmetrie. Die Beschreibung dieses Prozesses basiert auf klassischen Boltzmann Gleichungen (BGn). Diese wurden durch die Verwendung thermaler Propagatoren verfeinert. In Anbetracht der grundlegenden Beschränkungen dieser Gleichungen erscheint es wünschenswert einen systematischen Ansatz zu entwickeln der auf Nicht-Gleichgewichts QFT beruht. In dieser Arbeit werden modifizierte BGn verwendet die aus ersten Prinzipien innerhalb des Kadanoff-Baym Formalismus hergeleitet werden. Dies wird für ein einfaches Toy-Modell durchgeführt welches ausreichend komplex ist um populäre Szenarien wie das der thermalen Leptogenese in Analogie untersuchen zu können. Dieser Ansatz legt die Struktur der korrigierten BGn offen und führt zu einem neuen Ergebnis für die thermalen Beiträge zum CP-verletzenden Parameter, sodass die gängige Form überdacht werden muss. Es stellt sich heraus, dass die verschiedenen Ansätze in Einklang gebracht werden können. Die neuen Ergebnisse sagen eine Verstärkung der Asymmetrie vorher. Die Grösse der Korrekturen innerhalb des Toy-Modells wird durch numerische Lösung der vollen BGn bestimmt. Finite Density Aspects of LeptogenesisLeptogenesis is a model for the dynamical generation of the matter-antimatter asymmetry. This process takes place in the early universe at very high temperatures and a deviation from equilibrium is a fundamental requirement for the formation of the asymmetry. The equations used for its description originate from classical Boltzmann equations (BEs), which were refined using thermal propagators. In view of the basic restrictions of BEs, it is desirable to develop a systematic approach which uses non-equilibrium QFT as starting point. In this thesis modified BEs are used which are derived from first principles in the Kadanoff-Baym formalism. This is done for a simple toy model which is sufficiently intricate to study popular scenarios such as thermal leptogenesis in analogy to the phenomenological theory. This approach uncovers the structure of the corrected BEs and leads to a new result for the form of the thermal contributions to the CP-violating parameter, so that the established one must be reconsidered. It turns out that the different approaches can be reconciled. The new form predicts an enhancement of the asymmetry. The quantitative implications of the medium corrections within the toy model are studied numerically in terms of the full BEs.

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“…Since f 0 depends only on the modulus of p, but not on n, the angular integrations over n 2 , n 3 and n 4 in the expression for C 22 [f 0 ] n may be performed using a method devised in Ref. 23. The expression for I d [f 0 ] can be written in the form…”

Section: B Collision Integralmentioning

confidence: 99%

Kinetics of the disordered Bose gas with collisions

Schwiete

Finkel’stein

2013

Phys. Rev. A

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We discuss the kinetics of the disordered interacting Bose gas using the Boltzmann transport equation. The theory may serve as a unifying framework for studying questions of dynamics of the expanding Bose gas at different stages of the expansion. We show that the transport theory allows us to straightforwardly reproduce and generalize a number of results previously obtained from microscopic models in different formalisms. Based on estimates for the interparticle scattering rates, we discuss the relevance of interaction effects for the localization problem in the interacting disordered Bose gas. We argue that, if the number of particles is large enough, the size of the expanding cloud may exceed the localization length. We describe the spreading of the wave packet in this regime as collision-induced diffusion and compare the obtained rate of expansion to known results on subdiffusive spreading in nonlinear disordered lattices.Comment: 7 page

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Solving the homogeneous Boltzmann equation with arbitrary scattering kernel

Cited by 10 publications

References 28 publications

Full Boltzmann equations for leptogenesis including scattering

Full Boltzmann equations for leptogenesis including scattering

Finite density aspects of leptogenesis

Kinetics of the disordered Bose gas with collisions

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