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Quantum Mechanics in Phase Space

Project Description

Reference: PH/ME-Un2/2019
School: School of Science
Location: Loughborough
UK/EU Fee band: Research Band 1 Classroom Based (£4,327)
International Fee band: Research Band 1 Classroom Based (£21,100)
Full Time Duration: 3 years
Part Time Duration: 6 years

Phase space provides an alternative view of quantum mechanics from the traditional Schrödinger (wave functions/functionals), Heisenberg (matrix mechanics) or Feynman (path integral) views. Since the very early days of quantum theory there have been numerous attempts to interpret quantum mechanics in phase space, but finite dimensional systems have historically been an issue. In recent work we have completed the phase-space formulation of quantum mechanics — extending work by Wigner, Weyl, Moyal and others to any quantum system — and related the Wigner and Weyl distributions to classical statistical physics.

A number of tasks remain outstanding, such as demonstrating applications to statistical physics and quantum thermodynamics, generalising the framework beyond non-relativistic quantum mechanics (e.g. to systems whose underlying group structure is SU(N,M), O(N), E8 etc), expressing quantum dynamics in point rather than integral form and application to open quantum systems.

Applications are welcome for students interested in any of these areas of study.

Links to find out more:
General approach to quantum mechanics as a statistical theory [open access version]

Simple procedure for phase-space measurement and entanglement validation [open access]

Wigner Functions for Arbitrary Quantum Systems [open access version]

Entry requirements

Applicants should have, or expect to achieve, at least a 2:1 Honours degree (or equivalent) in Physics and/or Mathematics.

A relevant Master's degree and / or experience in one or more of the following will be an advantage: theoretical and/or mathematical physics, especially knowledge of the theory of continuous groups. All students must also meet the minimum English Language requirements (

How to apply

All applications are made online, please select the school/department name under the programme name section and include the quote reference number:

Programme name (to be included on the application form): Physics
Reference: PH/ME-Un2/2019

Funding Notes

This is an open call for candidates who are sponsored or who have their own funding. If you do not have funding, you may still apply, however Institutional funding is not guaranteed. Outstanding candidates (UK/EU/International) without funding will be considered for funding opportunities which may become available in the School.

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