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dc.contributor.advisorValiente, Doctor Manuel
dc.contributor.advisorOhberg, Professor Patrik
dc.contributor.authorPhillips, Lawrence
dc.date.accessioned2018-10-08T10:47:13Z
dc.date.available2018-10-08T10:47:13Z
dc.date.issued2017-10
dc.identifier.urihttp://hdl.handle.net/10399/3366
dc.description.abstractThis thesis presents results regarding one dimensional many-body quantum systems, obtained by considering the few-body physics of their constituent particles, and through use of traditional quantum mechanical techniques such as scattering theory and the variational principle. Choosing a perspective from which the connection between the microscopic behaviour of the systems’ constituents and its macroscopic properties is apparent, we investigate two one-dimensional many-body systems: a flat-banded optical lattice and a fermionic Luttinger liquid. Our choice of approach allows us to give a transparent description of the low-energy physics of both systems. For the former, we find that the low-energy eigenstates may be written down directly in terms of position space creation operators, and that they admit a simple and intuitive interpretation in terms of the position space behaviour of the atoms occupying the lattice. For the latter, we employ few-body scattering theory to investigate a long-held but (until now) untested belief about the parameters appearing in Luttinger’s model, a general effective low-energy description of one-dimensional quantum systems. We find this interpretation to be untenable, and give arguments as to how the parameters should correctly be regarded.en_US
dc.language.isoenen_US
dc.publisherHeriot-Watt Universityen_US
dc.publisherEngineering and Physical Sciencesen_US
dc.rightsAll items in ROS are protected by the Creative Commons copyright license (http://creativecommons.org/licenses/by-nc-nd/2.5/scotland/), with some rights reserved.
dc.titleFew-body approaches to one-dimensional many-body systemsen_US
dc.typeThesisen_US


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