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Bose-Hubbard chains as models for mesoscopic environments and systems

James Anglin

This theoretical project will construct and evaluate simplified models for the dynamics of large quantum systems, based on treating parts of the system as reservoirs for each other. The ultimate vision is to develop the theory of small, open systems (in general) into a tool for understanding and controlling larger systems (as generally as possible). This vision is motivated by the basic OSCAR premise that the open system perspective is not merely something to which one is forced, for poorly isolated systems, but a powerful tool. The project considers a specific class of model systems: Bose-Hubbard systems. Bose-Hubbard models can be realized with trapped quantum gases, but they are selected here for two theoretical reasons. Firstly, they are highly versatile as models – arguably even more so than spin systems, for example, which are widely used as models. A very wide range of physical features can be represented qualitatively within some Bose-Hubbard model; rather as one can make a Lego model for almost any real object, some form of Bose-Hubbard system can represent a large class of real systems, at least in cartoon form. And secondly, Bose-Hubbard systems are tractable. With so many parameter regimes, they offer many instructive limiting cases that can be solved, at least approximately, either numerically or analytically.


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