Franca, Andre (2016): Quantum manybody effects in gravity and Bosonic theories. Dissertation, LMU München: Fakultät für Physik 

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Abstract
Manybody quantum effects play a crucial role in many domains of physics, from condensed matter to blackhole evaporation. The fundamental interest and difficulty in studying this class of systems is the fact that their effective coupling constant become rescaled by the number of particles involved $g= \alpha N$, and thus we observe a breakdown of perturbation theory even for small values of the $\ttt$ coupling constant. We will study three very different systems which share the property that their behaviour is dominated by nonperturbative effects. \\ The strong CP problem  the problem of why the $\theta$ angle of QCD is so small  can be solved by the PecceiQuinn mechanism, which promotes the $\theta$ angle to a physical particle, the axion. The essence of the PQ mechanism is that the coupling will generate a mass gap, and thus the expectation value of the axion will vanish at the vacuum. It has been suggested that topological effects in gravity can spoil the axion solution. By using the dual formulation of the PecceiQuinn mechanism, we are able to show that even in the presence of such dangerous contributions from gravity, the presence of light neutrinos can stabilize the axion potential. This effect also puts an upper bound on the lightest neutrino mass.\\ We know that at high energies, gravitational scattering is dominated by blackhole formation. The typical size of blackholes is a growing function of the total centerofmass energy involved in the scattering process. In the asymptotic future, these blackholes will decay into Hawking radiation, which has a typical wavelength of the size of the blackhole. Thus high energy gravitational scattering is dominated by low energy out states. It has been suggested that gravity is selfcomplete due to this effect, and that furthermore, there is a class of bosonic theories which can also be selfcomplete due to the formation of large classical field configurations: UV completion by Classicalization. \\ We explore the idea of Classicalization versus Wilsonian UV completion in derivatively coupled scalars. We seek to answer the following question: how does the theory decide which road to take at high energies? We find out that the information about the high energy behaviour of the theory is encoded in the sign of the quartic derivative coupling. There is one sign that allows for a consistent Wilsonian UVcompletion, and another sign that contains continuous classical field configurations for localized sources. \\ In the third part of the thesis we explore nonperturbative properties of black holes. We consider the model proposed by Dvali and Gomez where black holes are described as BoseEinstein condensates of $N$ gravitons. These gravitons are weakly interacting, however their collective coupling constant puts them exactly at the critical point of a quantum phase transition $\alpha N = 1$. We focus on a toy model which captures some of the features of information storage and processing of black holes. The carriers of information and entropy are the Bogoliubov modes, which we are able to map to pseuoGoldstone bosons of a broken SU(2) symmetry. At the quantum phase transition this gap becomes $1/N$, which implies that the cost of information storage disappears in the $\Ninf$ limit. Furthermore, the storage capacity and lifetime of the modes increases with $N$, becoming infinite in the $\Ninf$ limit.\\ The attractive Bose gas which we considered is integrable in 1+1d. All the eigenstates of the system can be constructed using the Bethe ansatz, which transforms the Hamiltonian eigenvalue problem into a set of algebraic equations  the Bethe equations  for $N$ parameters which play the role of generalize momenta. While the ground state and excitation spectrum are known in the repulsive regime, in the attractive case the system becomes more complicated due to the appearance of bound states. In order to solve the Bethe equations, we restrict ourselves to the $\Ninf$ limit and transform the algebraic equations into a constrained integral equation. By solving this integral equation, we are able to study the phase transition from the point of view of the Bethe ansatz. We observe that the phase transition happens precisely when the constraint is saturated, and manifests itself as a change in the functional form of the density of momenta. Furthermore, we are able to show that the ground state of this system can be mapped to the saddlepoint equation of 2dimensional YangMills on a sphere, with a gauge group U(N).
Dokumententyp:  Dissertation (Dissertation, LMU München) 

Themengebiete:  500 Naturwissenschaften und Mathematik
500 Naturwissenschaften und Mathematik > 530 Physik 
Fakultäten:  Fakultät für Physik 
Sprache der Dissertation:  Englisch 
Datum der mündlichen Prüfung:  13. Juli 2016 
1. Berichterstatter/in:  Dvali, Georgi 
URN des Dokumentes:  urn:nbn:de:bvb:19199564 
MD5 Prüfsumme der PDFDatei:  822ef17bc7fd51285b825397ccd521c7 
Signatur der gedruckten Ausgabe:  0001/UMC 24344 
ID Code:  19956 
Eingestellt am:  22. Dez. 2016 14:01 
Letzte Änderungen:  22. Dez. 2016 14:01 