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The aim of the course is to give a mathematical introduction to superfluids and superfluid turbulence. Some of the existing mathematical models used to describe superfluid liquid Helium and Bose-Einstein condensates of dilute gases will be devised. Experimental and numerical experiments will also complement the course as examples. More details on the course topics are given in the Syllabus.


Spring 2018 (Monday, January 22 to Friday, March 16; Monday, April 23 to Friday, May 4)


  • Fri 09:05 - 09:55


Calculus, partial differential equation, general concepts of mechanics and fluid mechanics. A basic knowledge of quantum mechanics would be preferable.


Syllabus: - brief history of superfluidity, introduction to different types of superfluids; - Landau’s two-fluid model; - the Biot-Savart model and the Euler equation; - the local induction approximation limit; - Hasimoto’s transformations and some of the nonlinear Schroedinger equation solutions; - Bose-Einstein condensates and the Gross-Pitaevskii equation; - Bogoliubov excitations and quantised vortices; - vortex reconnections; - introduction to classical turbulence and Kolmogorov’s -5/3 law; - superfluid turbulence phenomenology.


Davide Proment
Phone 01603 591642


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A Primer on Quantum FluidsCarlo F. Barenghi & Nick G. Parker
Bose-Einstein CondensationLev. P. Pitaevskii & Sandro Stringari
Quantized Vortex Dynamics and Superfluid TurbulenceBarenghi, C.F., Donnelly, R.J., Vinen, W.F. (Eds.)
Quantized Vortices in Helium IIDonnelly
Superconductivity, Superfluids and CondensatesAnnett


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