Download How does a Bohm particle localize?

Survey
yes no Was this document useful for you?
   Thank you for your participation!

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

Document related concepts

Quasi-set theory wikipedia, lookup

Standard Model wikipedia, lookup

Wave packet wikipedia, lookup

Matrix mechanics wikipedia, lookup

Photon polarization wikipedia, lookup

Ensemble interpretation wikipedia, lookup

Eigenstate thermalization hypothesis wikipedia, lookup

Supersymmetry wikipedia, lookup

Relativistic quantum mechanics wikipedia, lookup

Probability amplitude wikipedia, lookup

Coherent states wikipedia, lookup

Quantum electrodynamics wikipedia, lookup

Measurement in quantum mechanics wikipedia, lookup

Mathematical formulation of the Standard Model wikipedia, lookup

Path integral formulation wikipedia, lookup

Quantum tomography wikipedia, lookup

Theoretical and experimental justification for the Schrödinger equation wikipedia, lookup

Quantum entanglement wikipedia, lookup

Scalar field theory wikipedia, lookup

Topological quantum field theory wikipedia, lookup

Double-slit experiment wikipedia, lookup

Renormalization wikipedia, lookup

Quantum field theory wikipedia, lookup

Bell's theorem wikipedia, lookup

Quantum fiction wikipedia, lookup

Quantum mechanics wikipedia, lookup

Renormalization group wikipedia, lookup

Quantum tunnelling wikipedia, lookup

Symmetry in quantum mechanics wikipedia, lookup

Theory of everything wikipedia, lookup

Quantum machine learning wikipedia, lookup

Introduction to quantum mechanics wikipedia, lookup

Quantum teleportation wikipedia, lookup

Canonical quantum gravity wikipedia, lookup

Quantum key distribution wikipedia, lookup

Quantum gravity wikipedia, lookup

Quantum vacuum thruster wikipedia, lookup

Aharonov–Bohm effect wikipedia, lookup

Uncertainty principle wikipedia, lookup

Relational approach to quantum physics wikipedia, lookup

Quantum state wikipedia, lookup

EPR paradox wikipedia, lookup

Canonical quantization wikipedia, lookup

Old quantum theory wikipedia, lookup

Quantum potential wikipedia, lookup

Implicate and explicate order wikipedia, lookup

Quantum chaos wikipedia, lookup

Interpretations of quantum mechanics wikipedia, lookup

History of quantum field theory wikipedia, lookup

T-symmetry wikipedia, lookup

Quantum logic wikipedia, lookup

Hidden variable theory wikipedia, lookup

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]).