Quantum many-body correlations in low-dimensional systems

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dc.contributor.authorPelwan, Chad
dc.date.accessioned2021-04-26T11:39:39Z
dc.date.available2021-04-26T11:39:39Z
dc.date.issued2020
dc.descriptionA thesis submitted to the Faulty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the degree of Doctor of Philosophy. September 2020en_ZA
dc.description.abstractIn Part I, we consider a quantum quench from the strongly correlated ground state of the Kondo model to a Fermi sea. We calculate the overlap between the ground states before and after the quench, as well as the Loschmidt echo, that is, the transition amplitude between the initial state and the evolved state at a time t after the quench. The overlap is known to determine the dynamics of the echo at large times. We show, in addition, that the overlap depends algebraically on the emergent Kondo length, with a power-law exponent that is the difference of long-and short-time contributions that appear in the echo. Our result suggests that in general, there may be more information contained in the overlap than previously. In Part II, we study the effects of increasing modulation instability and random fluctuations on the onset times of rogue waves in a waveguide array as described by the discrete unstable nonlinear Schrödinger equation (UNLSE). We analytically determine regions of instability, where rogue waves are likely to occur in the UNLSE and then we use numerical techniques to study the time evolution of these systems. We find that the effects of the fluctuations are prominent on the onset times of rogue waves only for small modulation instability, but otherwise large modulation instability dominated the onset time behaviouren_ZA
dc.description.librarianCK2021en_ZA
dc.facultyFaculty of Scienceen_ZA
dc.identifier.urihttps://hdl.handle.net/10539/31004
dc.language.isoenen_ZA
dc.phd.titlePhDen_ZA
dc.schoolSchool of Physicsen_ZA
dc.titleQuantum many-body correlations in low-dimensional systemsen_ZA
dc.typeThesisen_ZA
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