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Abstract
Universal dynamics of a dilute Bose gas is studied within the kinetic regime where the time evolution of the mode occupation number is governed by a waveBoltzmann equation. The universality manifests itself in the form of the dynamical evolution which can be a cascade in the context of KolmogorovZakharov wave turbulence or a selfsimilar shift in time and space. Which is the case depends on the relevant global conservation laws and on the particular range of scales in which the respective dynamics takes place. A nonperturbative kinetic equation is derived by applying the SchwingerKeldysh closedtime functional integral and the 2particleirreducible formalism to an action of complex scalar Bose fields with quartic interaction. The resulting dynamic equation for twopoint correlations are reduced to a waveBoltzmanntype kinetic equation with an effective $T$matrix which depends explicitly on the mode occupation numbers. This nonperturbative dependence on the solution occurs in the infrared regime where wave numbers are large and collective scattering of many particles prevails. Thus, the scaling analysis of wave turbulence theory can be applied. We explicitly calculate the effective $T$matrix analytically taking into account an infrared cutoff for dealing with the infrared divergences. Our results show that the scaling behaviour of the $T$matrix departs from the one predicted by naive dimensional counting due to the presence of the infrared cutoff. The KolmogorovZakharov and the selfsimilar exponents are evaluated by power counting using our $T$matrix and the results are confirmed by numerical integration of the waveBoltzmann scattering integral. The scaling exponents governing the time evolution are determined by means of the global conservation laws and the kinetic equation. Depending on the scaling properties of the quasiparticle spectrum, the momentum cutoff scale in the infrared evolves critically slowed in time. The respective scaling exponent is universal in the nonperturbative regime regardless of whether the process is an inverse cascade or a selfsimilar shift towards the infrared. Thus, our results provide a general framework for classifying nonthermal fixed points in dilute ultracold Bose gases. They pave the way to a straightforward generalisation and application to trapped systems in different dimensionalities and to systems with more than one internal degree of freedom. Our results furthermore provide a possible interpretation of recent experimental results on wave turbulence in an ultracold Bose gas. %We studied the universal dynamics of diluted Bose gas within the kinetic regime where time evolution of occupation number is governed by the Boltzmann's scattering integral. %There are three possible scenarios, depending on the scaling behaviour of occupation number. They are the particle and energy cascade which are the steady state of turbulence transport and selfsimilar evolution where local occupation evolves in time. %We evaluated the scaling exponents in both momentum and time scales in each case under the constraints of global number and energy conservation. Furthermore, we can go beyond the perturbative regime by employing the closedtimepath contour and the 2particleirreducible formalism to the GrossPitaevskii action. The kinetic equation is modified by an effective Tmatrix as a result of the resummation scheme. However, the structure of kinetic equation remains the same as in the perturbative case. Thus, all exponents in the nonperturbative regime depart from those in the perturbative regime because of the scaling of the effective Tmatrix.
Item Type:  Dissertation 

Supervisor:  Gasenzer, Prof. Dr. Thomas 
Date of thesis defense:  18 January 2018 
Date Deposited:  12 Mar 2018 08:45 
Date:  2018 
Faculties / Institutes:  The Faculty of Physics and Astronomy > Institute for Theoretical Physics The Faculty of Physics and Astronomy > Kirchhoff Institute for Physics 
Subjects:  530 Physics 
Controlled Keywords:  Kinetische Theorie, Vielteilchentheorie, Quantenfeldtheorie 
Uncontrolled Keywords:  Strong wave turbulence, Nonequilibrium quantum field theory 
Additional Information:  second version 
Available Versions of this Item

Strong Wave Turbulence and NonThermal Fixed Points in a Kinetic Theory. (deposited 02 Feb 2018 10:53)
 Strong Wave Turbulence and NonThermal Fixed Points in a Kinetic Theory. (deposited 12 Mar 2018 08:45) [Currently Displayed]