Download Localization, interaction and the modern interpretation(s) of quantum mechanics

ROEMER
PhD
Localization, interaction and the modern interpretation(s) of quantum
mechanics
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
physicists 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 such fundamental approaches: recent 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. On the experimental side, among many we have new
fundamental tests such as the three-slit experiment, tests of contextuality, and remarkable
fluid-mechanical analogues of elementary quantum phenomena. During the studentship,
we will concentrate on using the knowledge of quantum disordered and interacting manybody systems within the context of alternative interpretations of quantum mechanics.
Here we can contribute the most to these discussions by reevaluating non-trivial quantum
mechanical systems from condensed matter within the alternative interpretations. We
intend to study three separate themes within the de Broglie-Bohm formulation, namely,
(i) Anderson localisation in one-, two-, and three-dimensional systems, (ii) two-particle
short-range interacting systems on nano-rings, i.e. the excitonic Aharonov-Bohm effect,
and (iii) the integrable quantum many-body systems with long-ranged 1/r2 interaction.
Localization: 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. It will be quite instructive to see how spatial localization and
multifractality arise 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.
Many-body interactions: We intent to compute the two-interacting particle problem of
excitons in an Aharonov-Bohm quantum ring where the magnetic field induced quantum
interference of the tails of a bound state with itself gives rise to non-trivial but
experimentally accessible quantum oscillations.
Integrable many-body physics: Models such as Hubbard, Heisenberg and 1/r2 chains
are known to be integrable. This integrability severely restricts to degrees of freedom of
these systems. Particularly for the continuous 1/r2 chains, where the classical limit is well
known, this should also severely restrict the Bohm trajectories. How the classical
trajectories emerge from the quantum trajectories will be very interesting. Also, the
interpretation of the integrals of motion is not clear, perhaps here the alternative
approaches can help to elucidate their meaning.
These projects are clearly feasible and will 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. In this proposal, we have
concentrated here on the perhaps best-developed "alternative" approach to quantum
mechanics due to de Broglie-Bohm. Similar questions shall be asked 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.
For further information, see http://www.warwick.ac.uk/go/DisQS. The work will be done
together with Dr. M Hadley.
References:
1. D. Bohm, “A Suggested Interpretation of the Quantum Theory in Terms of "Hidden" Variables”,
Phys. Rev. 85, 166 (1952); ibid, 180 (1952)
2. John G. Cramer, “The Transactional Interpretation of Quantum Mechanics”, Rev. Mod. Phys. 58,
3.
4.
5.
647-688, July (1986)
A. J. Leggett, “Realism and the physical world”, Rep. Prog. Phys. 71, 022001 (2008).
Rodriguez, A., Vasquez, L. J., Slevin, K. & Römer, R. A. Multifractal finite-size scaling and
universality at the Anderson transition. Phys. Rev. Lett. 84, 134209 (2011).
Römer, R. A. & Raikh, M. E. Aharonov-Bohm effect for an exciton. Phys. Rev. B 62, 7045–7049
(2000).