PHY8042 : Quantum Fluids - Undergraduate Study

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

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 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 Activities	Lecture	40	1:00	40:00	Formal Lectures – Present in Person
Scheduled Learning And Teaching Activities	Lecture	4	1:00	4:00	Revision Lectures – Present in Person
Scheduled Learning And Teaching Activities	Lecture	10	1:00	10:00	Problem Classes – Synchronous On-Line
Guided Independent Study	Assessment preparation and completion	30	1:00	30:00	Completion of in course assessments
Guided Independent Study	Independent study	116	1:00	116:00	Preparation time for lectures, background reading, coursework review
Total				200:00

Jointly Taught With

Code	Title
MAS8812	Quantum 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

Exams

Description	Length	Semester	When Set	Percentage	Comment
Written Examination	90	2	A	60	N/A

Other Assessment

Description	Semester	When Set	Percentage	Comment
Prob solv exercises	1	M	8	Coursework assignment
Prob solv exercises	1	M	7	Coursework assignment
Prob solv exercises	2	M	5	Coursework assignment
Report	2	M	20	Technical 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

PHY8042's Reading List

Timetable

Timetable Website: www.ncl.ac.uk/timetable/
PHY8042's Timetable