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MAS8812 : Quantum Fluids

  • Offered for Year: 2024/25
  • Module Leader(s): Professor Carlo Barenghi
  • Lecturer: Professor Nikolaos Proukakis
  • Owning School: Mathematics, Statistics and Physics
  • Teaching Location: Newcastle City Campus

Your programme is made up of credits, the total differs on programme to programme.

Semester 1 Credit Value: 10
Semester 2 Credit Value: 10
ECTS Credits: 10.0
European Credit Transfer System


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
Guided Independent StudyAssessment preparation and completion301:0030:00Completion of in course assessments
Scheduled Learning And Teaching ActivitiesLecture101:0010:00Problem Classes
Scheduled Learning And Teaching ActivitiesLecture21:002:00Revision Lectures
Scheduled Learning And Teaching ActivitiesLecture421:0042:00Formal Lectures
Guided Independent StudyIndependent study1161:00116:00Preparation time for lectures, background reading, coursework review
Jointly Taught With
Code Title
PHY8042Quantum Fluids
Teaching Rationale And Relationship

The teaching methods are appropriate to allow students to develop a wide range of skills, from understanding basic concepts and facts to higher-order thinking. 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
Exam Pairings
Module Code Module Title Semester Comment
Quantum Fluids2N/A
Other Assessment
Description Semester When Set Percentage Comment
Prob solv exercises1M15Problem-solving exercises assessment
Prob solv exercises2M5Problem-solving exercises assessment
Report2M20Technical report
Assessment Rationale And Relationship

A substantial formal unseen examination is appropriate for the assessment of the material in this module. The format of the examination will enable students to reliably demonstrate their own knowledge, understanding and application of learning outcomes. The assurance of academic integrity forms a necessary part of programme accreditation.

Examination problems may require a synthesis of concepts and strategies from different sections, while they may have more than one ways for solution. The examination time allows the students to test different strategies, work out examples and gather evidence for deciding on an effective strategy, while carefully articulating their ideas and explicitly citing the theory they are using.

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.

Reading Lists