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Module

PHY8042 : Quantum Fluids

  • Offered for Year: 2020/21
  • Module Leader(s): Professor Carlo Barenghi
  • Lecturer: Professor Nikolaos Proukakis
  • Owning School: Mathematics, Statistics and Physics
  • Teaching Location: Newcastle City Campus
Semesters
Semester 1 Credit Value: 10
Semester 2 Credit Value: 10
ECTS Credits: 10.0

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. Vortex lattices. Vortex tangles. 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 critical velocities. 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

Please note that module leaders are reviewing the module teaching and assessment methods for Semester 2 modules, in light of the Covid-19 restrictions. There may also be a few further changes to Semester 1 modules. Final information will be available by the end of August 2020 in for Semester 1 modules and the end of October 2020 for Semester 2 modules.

Teaching Activities
Category Activity Number Length Student Hours Comment
Structured Guided LearningLecture materials361:0036:00Non-Synchronous Activities
Guided Independent StudyAssessment preparation and completion301:0030:00N/A
Scheduled Learning And Teaching ActivitiesLecture91:009:00Present in Person (S2)
Scheduled Learning And Teaching ActivitiesLecture91:009:00Synchronous On-Line Material
Structured Guided LearningStructured non-synchronous discussion181:0018:00N/A
Scheduled Learning And Teaching ActivitiesDrop-in/surgery41:004:00Office Hour or Discussion Board Activity
Guided Independent StudyIndependent study941:0094:00N/A
Total200:00
Jointly Taught With
Code Title
MAS8812Quantum Fluids
Teaching Rationale And Relationship

Non-synchronous online materials are used for the delivery of theory and explanation of methods, illustrated with examples, and for giving general feedback on assessed work. Present-in-person and synchronous online sessions are used to help develop the students’ abilities at applying the theory to solving problems and to identify and resolve specific queries raised by students, and to allow students to receive individual feedback on marked work. Students who cannot attend a present-in-person session will be provided with an alternative activity allowing them to access the learning outcomes of that session. In addition, office hours/discussion board activity 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.

Alternatives will be offered to students unable to be present-in-person due to the prevailing C-19 circumstances.
Student’s should consult their individual timetable for up-to-date delivery information.

Assessment Methods

Please note that module leaders are reviewing the module teaching and assessment methods for Semester 2 modules, in light of the Covid-19 restrictions. There may also be a few further changes to Semester 1 modules. Final information will be available by the end of August 2020 in for Semester 1 modules and the end of October 2020 for Semester 2 modules.

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

Exams
Description Length Semester When Set Percentage Comment
Written Examination602A6024-hour exam
Other Assessment
Description Semester When Set Percentage Comment
Portfolio1M8Written exercises 1
Report2M20Technical report
Portfolio2M5written exercise 3
Portfolio1M7written exercise 2
Assessment Rationale And Relationship

A substantial formal examination is appropriate for the assessment of the material in this module. The course assessments will 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