<p>The study of the quantum dynamics of many-particle systems has recently become the subject of intensive research, stimulated in part by enormous progress in experimental techniques, particularly the manipulation of ultracold atomic gases, which allow high tunability of artificial systems with decoherence and dissipation strongly suppressed. One of the simplest protocols for out of equilibrium dynamics is a quantum quench where the time-scale associated with an external variation is much smaller than the typical relaxation time of the system. Here we first study in detail the dynamics after a quantum quench in the one-dimensional sine-Gordon model in the phase where the boson spectrum remains gapless. We construct a Dyson equation to leading order in the cosine potential and show that the resulting quantum kinetic equation is atypical in that it involves multi-particle scattering processes. We also show that using an effective action, which generates the Dyson equation by a variational principle, the conserved stress-momentum tensor can be constructed. We solve the dynamics numerically by making a quasi-classical approximation that makes the quantum kinetic equation local in time while retaining the multi-particle nature of the scattering processes. At long times the system is found to thermalize, with a thermalization time that depends in a non-monotonic way on the amount of energy injected into the system by the quench. This non-monotonic behavior arises due to the competing effect of an increase of phase space for scattering on the one hand, and an enhancement of the orthogonality catastrophe on the other hand as the quench amplitude is increased. The approach to equilibrium is found to be purely exponential for large quench amplitudes but more complex for smaller ones. In the following chapter, the dynamics of interacting bosons in one dimension after a sudden switching on of a weak disordered potential is investigated. We find that on time scales before quasiparticles scatter, which correspond to the prethermalization regime, the dephasing from random elastic forward scattering causes the correlations to decay exponentially fast, while the system remains far from thermal equilibrium. For longer times however, the combined effect of disorder and interactions gives rise to inelastic scattering which eventually leads to thermalization. A novel quantum kinetic equation taking into account both disorder and interactions is employed to study the dynamics. It is found that thermalization becomes most effective close to the superfluid-Bose glass critical point where nonlinearities become increasingly important. The thermalization times obtained numerically are found to agree well with analytic estimates. In the last chapter we investigate the dynamics of a scalar field theory in spatial dimension d=4 after a quench close to a critical point, using renormalization-group methods. We show that after the system is quenched, but before eventually thermalizing due to dissipative effects, it approaches a different, thermal-like regime associated with a fixed-point describing a dynamical scaling behaviour. Within this regime the time dependence of the dynamical correlations is characterized by a novel short-time universal exponent. </p>
| Identifer | oai:union.ndltd.org:PROQUEST/oai:pqdtoai.proquest.com:3716614 |
| Date | 11 September 2015 |
| Creators | Tavora, Marco |
| Publisher | New York University |
| Source Sets | ProQuest.com |
| Language | English |
| Detected Language | English |
| Type | thesis |
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