Superfluidity and Bose-Einstein condensation in ⁴He
"In 1938, Pyotr Kapitsa, John Allen and Don Misener discovered that helium-4 became a new kind of fluid, now known as a superfluid, at temperatures less than 2.17 K (the lambda point). Superfluid helium has many unusual properties, including zero viscosity (the ability to flow without dissipating energy) and the existence of quantized vortices. It was quickly believed that the superfluidity was due to partial Bose–Einstein condensation of the liquid. In fact, many properties of superfluid helium also appear in gaseous condensates created by Cornell, Wieman and Ketterle. Superfluid helium-4 is a liquid rather than a gas, which means that the interactions between the atoms are relatively strong; the original theory of Bose–Einstein condensation must be heavily modified in order to describe it. Bose–Einstein condensation remains, however, fundamental to the superfluid properties of helium-4. Note that helium-3, a fermion, also enters a superfluid phase (at a much lower temperature) which can be explained by the formation of bosonic Cooper pairs of two atoms (see also fermionic condensate)."
--Source: https://en.wikipedia.org/wiki/Superfluid_helium-4
The relatively strong interaction between ⁴He atoms makes impossible to study the system with the usual methods applied to generic weakly interacting Bose-Einstein condensates so we need some methods that are able to deal with the strong correlations in this system. This fact is what motivates the use of quantum Monte Carlo methods as the most accurate techniques to microscopically study the ground state (T=0 K) and finite temperature of ⁴He.
The most accurate interaction potential between ⁴He atoms is the so-called HFD-B(HE) (or simply Axiz II) potential, given by:
where
In the following you will be able to study the equation of state of liquid ⁴He modelled using the Aziz II potential. In this hands-on we will be trying to reproduce the results obtained in the following paper (https://journals.aps.org/prb/abstract/10.1103/PhysRevB.49.8920) in the most efficient way using the computational resources of the CSUC managed by Slurm.
Quantum Monte Carlo methods
In the following document you can find a description of ground states Quantum Monte Carlo methods, two of them, Variational (VMC) and Diffusion (DMC) Monte Carlo will be used along this hands-on.
If you are interested in a finite temperature description of condensed ⁴He you can find a very detailed description of the usual and most successful method (Path Integral Monte Carlo) in the following link: https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.67.279