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Transcript

ROEMER THEO/NUM How does a Bohm particle localize? Space In recent years, our continued lack of progress in finding a convincing theory beyond the standard model, one which would unify gravity and quantum physics, has led many colleagues to speculate that it may be precisely an incomplete understanding of quantum physics which is a root cause of the problem. And there is indeed a renewed wider interest in the field: Recent theoretical developments include physical axioms for quantum theory, new formalisms without background causal structure, the application of collapse theories and hidden-variables theories to cosmology, and new perspectives on black-hole information loss. During the project work, we would concentrate on using our knowledge of the standard quantum mechanics of disordered solid states systems – Anderson localization – and reinterpret it within the context of alternative approaches to the quantum world. We will employ the de Broglie-Bohm theory in the Anderson localization context and study the Bohm particle trajectories for wave packets in the localized, critical and diffusive phases (see picture). It will be quite instructive to see how spatial localization and multifractality arises without internal contradictions as the Bohm trajectories are not allowed to cross each other. The comparison of the trajectories to the semi-classical characteristics such as scar states, etc., should also be most interesting, particularly their variation with magnetic flux. In a fully localized one-dimensional disordered chain, it will also be instructive to treat the trajectories as in standard non-linear dynamics and measure their Lyapunov exponents if these exist. These projects are clearly feasible and might lead to publishable results which are of interest to both the condensed matter as well as the foundations community. In addition, they might lead to new techniques for studying quantum systems based on the Bohm trajectories as has recently happened in quantum chemistry. I would like to stress that I have concentrated here on the perhaps best developed "alternative" approach to quantum mechanics due to de Broglie-Bohm. Similar questions we might intend to ask in later stages within Cramer’s “transactional interpretation” with “offer” and “confirmation” waves. It will be particularly interesting to compute the proposed avoidance of the wave function collapse via interference of offer and confirmation. This project will give the student a flavour of theoretical and computational techniques in quantum physics and nanoscience, and so will be ideal for a student contemplating research in this area. A strong background in programming is recommended. For more information please contact Rudolf Roemer ([email protected]).