Postgraduate

Modules

Modules

PHY8029 : Quantum Fluids

Semesters
Semester 1 Credit Value: 15
ECTS Credits: 8.0

Aims

To describe the phenomenon of Bose-Einstein condensation and the main mathematical and physical features of quantum fluids (e.g. atomic gases, superfluid helium, etc).

Module Summary
The distinction between classical statistics and quantum statistics. The mechanism of Bose-Einstein condensation in its most elementary form for ideal gases. The main phenomenology of atomic condensates and superfluid liquid helium. The mathematical models which are used to determine the ground state and linear/nonlinear excitations, such as solitons and vortices.

Outline Of Syllabus

Quantum mechanics of many-particles. Maxwell-Boltzmann, Fermi-Dirac and Bose-Einstein statistics. Bose-Einstein condensation of an ideal gas. Condensate fraction. Liquid helium and superfluidity.
Landau critical velocity. The two-fluid model and its consequences (e.g. thermal counterflow, second sound, etc). Vortex lines in rotating superfluids. The Nonlinear Schrodinger, or Gross-Pitaevskii, equation. The Madelung transformation and the fluid dynamics interpretation of the Gross-Pitaevskii equation. The Thomas-Fermi approximation and the ground state. Stability of Gross-Pitaevskii equation and the energy functional. The dispersion relation and linear waves (phonons). Nonlinear waves (dark and bright solitons), vortices and lattices. Vortex dynamics in two and three dimensions. Overview of relevant experimental findings. Quantum turbulence, Josephson effects, or other topics of current research (e.g. two-component condensates, dipolar condensates, polariton condensates, etc).

Teaching Methods

Teaching Activities
Category Activity Number Length Student Hours Comment
Guided Independent StudyAssessment preparation and completion120:0020:00Project
Guided Independent StudyAssessment preparation and completion115:0015:00Revision for unseen exam
Guided Independent StudyAssessment preparation and completion12:002:00Unseen exam
Scheduled Learning And Teaching ActivitiesLecture21:002:00Revision lectures
Scheduled Learning And Teaching ActivitiesLecture331:0033:00Formal lectures
Scheduled Learning And Teaching ActivitiesDrop-in/surgery120:102:00Office hours
Guided Independent StudyIndependent study153:0053:00Studying, practising, and gaining understanding of course material
Guided Independent StudyIndependent study23:006:00Review of coursework assignments
Guided Independent StudyIndependent study26:0012:00Preparation for coursework assignments
Guided Independent StudyIndependent study15:005:00Review of project
Total150:00
Jointly Taught With
Code Title
MAS8851Quantum Fluids
Teaching Rationale And Relationship

Lectures are used for the delivery of theory and explanation of methods, illustrated with examples, and for giving general feedback on marked work. Tutorials (within lectures) are used to discuss the course material, identify and resolve specific queries raised by students and to allow students to receive individual feedback on marked work. In addition, office hours (two per week) will provide an opportunity for more direct contact between individual students and the lecturer: a typical student might spend a total of one or two hours over the course of the module, either individually or as part of a group.

Assessment Methods

The format of resits will be determined by the Board of Examiners

Exams
Description Length Semester When Set Percentage Comment
Written Examination1201A70N/A
Exam Pairings
Module Code Module Title Semester Comment
MAS8851Quantum Fluids1N/A
Other Assessment
Description Semester When Set Percentage Comment
Prob solv exercises1M5Coursework assignments
Prof skill assessmnt1M25A technical report or numerical project
Assessment Rationale And Relationship

A substantial formal unseen examination is appropriate for the assessment of the material in this module. The coursework assignments are expected to consist of two written assignments of equal weight: the exact nature of assessment will be explained at the start of the module. The coursework assignments and the project or report allow the students to develop their problem solving techniques, to practise the methods learnt in the module, to assess their progress and to receive feedback; these assessments have a secondary formative purpose as well as their primary summative purpose.

Reading Lists

Timetable