• Offered for Year: 2025/26

• Module Leader(s): Professor Nikolaos Proukakis

• Owning School: Mathematics, Statistics and Physics
• Teaching Location: Newcastle City Campus

Semesters

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

Aims

To introduce students to the exciting ubiquitous realm of quantum fluids and gases, spanning from diverse small-scale controlled laboratory atomic and condensed matter systems, to large-scale astrophysical and cosmological systems.

To describe the common underlying phenomenon of Bose-Einstein condensation emerging in all physical systems under appropriate conditions, focusing on the main mathematical and physical features of quantum fluids, and discuss its emergence and implications from the tiniest (atomic) to the largest (cosmological) scales, focusing primarily on systems of ultracold atomic gases, superfluid helium, neutron stars and dark matter, and the implications of the existence of such a state for physical (including astrophysical) observations.

Module Summary

The underlying mechanism and ubiquitous nature of Bose-Einstein condensation across the entire range of physical scales. The controlled experimental setting of atomic condensates and superfluid liquid helium. The fundamental mathematical equation used to describe a quantum gas/fluid, focusing on equilibrium solutions, linear perturbations and nonlinear excitations, such as solitons and vortices, and the importance of quantum-mechanical phase and quantum pressure. The evidence for, and implications of, the existence of a quantum fluid within neutron stars and as an emerging candidate for dark matter.

Outline Of Syllabus

The phenomenon of Bose-Einstein condensation: A historical overview, experimental evidence, and its uniquely ubiquitous nature across all physical scales; introduction to the main physical systems, from ultracold, magnetically-trapped, neutral atomic gases and superfluid helium, to neutron stars and dark matter. Condensate fraction and Phase-Space Density. The Nonlinear Schroedinger, or Gross- Pitaevskii, equation as the fundamental equation for a quantum fluid.

Fundamental Properties of the Gross-Pitaevskii Equation: The Madelung transformation and the fluid dynamics interpretation. The meaning of condensate phase and the important role of quantum pressure. 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 and Superfluidity. Nonlinear waves (dark and bright solitons) and vortices. Vortex dynamics in two (and three) dimensions and vortex lattices.

Applications of Gross-Pitaevskii equation to key systems in the lab and in the cosmos:

Key features and main findings in ultracold atomic and superfluid helium experiments, as validation of the underlying theoretical modelling. Extension to condensate mixtures and Josephson effects, and experimental relevance.

Evidence for the existence of quantum fluid behaviour in neutron stars: vortex dynamics and pulsar glitches.

Dark matter as an ultralight-particle superfluid: observational evidence for galactic cored halo formation and its interpretation as a detailed balance between gravitational attraction and quantum pressure.

Brief introduction to other current topical issues: cosmological analogues in the laboratory (e.g. analogue black holes) and controlled experiments paving the way for new quantum sensor technologies.

Teaching Methods

Teaching Activities

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. Problem Classes are used to help develop the students’ abilities at applying the theory to solving problems, and for giving General feedback on marked work.

Assessment Methods

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

Exams

Other Assessment

Assessment Rationale And Relationship

A substantial formal unseen examination is appropriate for the assessment of the material of 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 way 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 practice 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

• MSP8812's Reading List

Timetable

• Timetable Website: www.ncl.ac.uk/timetable/
• MSP8812's Timetable