2020 Superfluidity

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Academic unit or major
Graduate major in Physics
Okuma Satoshi 
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Course description and aims

When liquid helium is cooled to an extremely low temperature, the liquid enters a superfluid state in which it flows without viscosity. This superfluid state is an example of a quantum phenomena appearing on the macroscopic level. This course will give an overview of the physics of superfluids, and go over how it can be understood and described as a quantum many-body problem. Specifically, students will learn about the properties of the superfluid state, Bose-Einstein condensate, quantized vortex/elemental excitation, the two-fluid model/sound waves, two-dimensional superfluids, etc.

Student learning outcomes

By completing this course, students will be able to:
1) Study how the superfluidity, which is a macroscopic quantum phenomenon seen at low temperatures, can be explained in terms of a physics of quantum many-body problem.
2) Understand that liquid helium shows the superfluidity at very low temperatures, in which the helium behaves a fluid with zero viscosity.
3) Understand and explain how the physics of the superfluidity is described as a quantum effect on a macroscopic scale.


Bose-Einstein condensation, superfluidity, phase diagram, quantized vortex, elementary excitation, sound waves, two-fluid model

Competencies that will be developed

Specialist skills Intercultural skills Communication skills Critical thinking skills Practical and/or problem-solving skills

Class flow

Handouts will be distributed at the beginning of each class. Students are given exercise problems related to the lecture to better understand the contents. The midterm exam (50 min) is scheduled during the regular lecture period.

Course schedule/Required learning

  Course schedule Required learning
Class 1 Phase diagram of helium Explain the phase diagram of helium 3 and helium 4.
Class 2 Basic properties of superfluidity Explain basic properties of superfluidity.
Class 3 Bose-Einstein condensation Explain Bose-Einstein condensation.
Class 4 Quantized vortex and elementary excitation Explain the relation between elementary excitations and superfluidity.
Class 5 Two-fluid model and sound waves Explain the various sound waves in helium 4.
Class 6 Two dimensional superfluidity Describe the characteristic of two dimensional superfluidity.
Class 7 Other topics related to superfluidity Describe the other topics related to superfluidity you are interested in.

Out-of-Class Study Time (Preparation and Review)

To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.


To be specified by the instructor.

Reference books, course materials, etc.

To be specified by the instructor. Handouts will be distributed. 

Assessment criteria and methods

Based on exams and reports. → Based on a final report.

Related courses

  • ZUB.Q204 : Quantum Mechanics I
  • ZUB.Q206 : Quantum Mechanics II
  • ZUB.S205 : Thermodynamics and Statistical Mechanics I
  • ZUB.S310 : Thermodynamics and Statistical Mechanics II
  • PHY.S440 : Statistical Mechanics III
  • PHY.Q438 : Quantum Mechanics of Many-Body Systems
  • PHY.C443 : Superconductivity

Prerequisites (i.e., required knowledge, skills, courses, etc.)

No prerequisites are necessary, but enrollment in the related courses is desirable.

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