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MAS8812 : Quantum Fluids

  • Offered for Year: 2022/23
  • Module Leader(s): Professor Carlo Barenghi
  • Lecturer: Professor Nikolaos Proukakis
  • Owning School: Mathematics, Statistics and Physics
  • Teaching Location: Newcastle City Campus
Semester 1 Credit Value: 10
Semester 2 Credit Value: 10
ECTS Credits: 10.0


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 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

Bose-Einstein condensation of an ideal gas. Condensate fraction. Liquid helium and superfluidity. The two-fluid model and its consequences (e.g. thermal counterflow, second sound, etc). Vortex lines in rotating superfluids. Quantisation of the circulation. Vortex lattices. Vortex tangles. The 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). Landau critical velocity. Nonlinear waves (dark and bright solitons) and vortices. 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
Scheduled Learning And Teaching ActivitiesLecture401:0040:00Formal Lectures – Present in Person
Scheduled Learning And Teaching ActivitiesLecture41:004:00Revision Lectures – Present in Person
Scheduled Learning And Teaching ActivitiesLecture101:0010:00Problem Classes – Synchronous On-Line
Guided Independent StudyAssessment preparation and completion301:0030:00Completion of in course assessments
Guided Independent StudyAssessment preparation and completion120:0020:00Revision for exam
Guided Independent StudyAssessment preparation and completion11:301:30Examination
Guided Independent StudyIndependent study194:3094:30Preparation time for lectures, background reading, coursework review
Jointly Taught With
Code Title
PHY8042Quantum 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. Problem Classes are used to help develop the students’ abilities at applying the theory to solving problems.

Assessment Methods

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

Description Length Semester When Set Percentage Comment
Written Examination902A60N/A
Other Assessment
Description Semester When Set Percentage Comment
Prob solv exercises1M7Coursework assignment
Prob solv exercises1M8Coursework assignment
Prob solv exercises2M5Coursework assignment
Report2M20Technical report
Assessment Rationale And Relationship

A substantial formal unseen examination is appropriate for the assessment of the material in this module. The coursework assignments 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.

In the event of on-campus examinations not being possible, an on-line alternative assessment will be used for written examination 1.

Reading Lists