Statistical Analysis and Computational Modelling of Superfluid Helium

Abstract Superfluidity as a state of matter is a complex phenomenon that can be studied from different perspectives. In this work the authors aim to describe superfluidity in Helium-4 through a microscopical computational approach. Through the quantum mechanical states of Helium a statistical model is created in order to transverse from the microscopical to the macroscopical spectrum. The Bose-Einstein statistics and the Maxwell-Boltzmann are then calculated for different temperatures to investigate the divergence between them in the microscopic view of the system, and explore the macroscopic system phase transitions to superfluidity. Through this computational model the probability distributions of the different energy states are presented, giving the ability to compare the statistical behavior of the ideal and non-ideal parts of superfluid Helium, and how superfluidity can be associated with the phenomenon of Bose-Einstein condensation computationally. The excitation spectrum of the superfluid is studied, through which the entropy of the excitations is shown to be the total entropy of the superfluid below the lambda line, connecting these finding with Landau’s quasiparticle approach. Through these computations the authors are now able to showcase this microscopical behavior directly, without making use of macroscopical thermodynamic data as done previously, and derive the basic thermodynamic behaviors of superfluid Helium-4 to near absolute zero without the need of experimental data.