Superfluidity
Superfluidity (like its cousin, superconductivity) is a particularly striking and concrete manifestation of the wavelike nature of matter. In electromagnetism, it is often fruitful to use Maxwell’s equations, forgetting about the existence of photons. Similarly, we will describe matter by a classical (complex-valued) field, forgetting about the existence of particles. This unconventional approach greatly helps to understand and derive the fundamental concepts and relations of superfluidity, under very general conditions (for any temperature below the transition temperature, including in 2 dimensions —where there is no condensate— and in presence of disorder —where there is no Galilean invariance). Superfluidity appears to be the natural state of the classical field, which can only be destroyed by topological defects (vortices). More formally, superfluidity is associated to a topological order, characterized by an emergent constant of motion. This will allow us to derive key equations of two-fluid hydrodynamics, which will enable us to explain key phenoma such as the fountain effect, the Josephson effect, or supertransport of heat.
Chapters:
- historic overview of the discovery of superfluidity
- Neutral matter field and the Gross-Pitaevskii equation
- the topological origin of superfluidity
- Normal modes, Landau criterion and critical velocity
- Superfluidity at finite temperature
- Genuine long-range order and topological order
- The two-fluid picture and basics of two-fluid hydrodynamics
- Superfluid phase transition
Quantum mechanics
B. Svistunov, E. Babaev, N. Prokof’ev, Superfluid states of matter (Taylor & Francis, London, 2015)
I. M. Khalatnikov, An introduction to the theory of superfluidity (Benjamin, New York, 1965)
Written exam