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How does a Bohm particle localize?
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]).