Quantum Mechanical Aspects of Superfluidity

Abstract

Under certain conditions 4He undergoes a phase transition from a normal liquid to a superfluid state, with unique and remarkable characteristics. The statistical properties of an ideal Bose gas exhibit striking similarities to 4He, suggesting that the observed phase transition is associated with the condensation of atoms into the lowest energy state. Since 4He remains liquid at low temperatures, the normal modes of 4He cannot be expected to be strictly harmonic and other elementary excitations beyond phonons, Landau’s rotons, can be anticipated. In this work we discuss quantum aspects of the condensate and its wave function using the formalism of second quantization. The interacting system is studied developing the Hamiltonian in this formalism, finding the energy of the system in terms of the ground state energy plus excitations corresponding to the expected phonons. Introducing the theory of linear response and making use of the structure factor and general inequalities, again in the case of the weakly-interacting Bose gas, roton excitations are successfully described. Finally we briefly comment on the existence of quantized vortices