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Project Title: Complex behaviour of Bose-Einstein Condensates, Cold Atoms and Arrays of Optical Waveguides
Differential equations are one of the main study tools in theoretical physics. They show how physical systems evolve in time, and can be solved numerically using computational simulations. The topic of my research is the investigation of the Non-Linear Schrödinger Equation, both through analytical methods, and through computational simulations. The Non-Linear Schrödinger equation describes the evolution of Bose-Einstein Condensates (an exotic state of matter) in optical lattices, but also the propagation of light through arrays of optical waveguides. The equation predicts the existence of intrinsic localised modes, also known as breathers. This type of localised solutions also characterise other discrete non-linear systems, such as DNA and RNA molecules, polymers, proteins or crystals in solid state physics. They are therefore important in understanding quantum transport phenomena, which today are studied not only in physics, but also in quantum biology and quantum chemistry. The focus of my work is to determine how breathers inhibit or enhance quantum transport, and how they interact with the systems they appear in.
Awarded: Carnegie PhD Scholarship
University: University of Strathclyde