Effective Theory Of Superfluidity

Abstract

Abstract This chapter discusses how the effective theory incorporates the low-energy dynamics of the superfluid vacuum and the dynamics of the system of quasiparticles in Bose liquids. The effective theory of two-fluid hydrodynamics was developed by Lev Landau. According to the general ideas of Landau, a weakly excited state of the quantum system can be considered as a small number of elementary excitations. Applying this to the quantum liquid 4He, the dense system of strongly interacting 4Heatoms can be represented in the low-energy corner by a dilute system of weakly interacting quasiparticles (phonons and rotons). In addition, the state without excitations — the ground state or the quantum vacuum — has its own degrees of freedom: it can experience the coherent collective motion. This motion is described by continuity and London equations for superfluid velocity and density. Since superfluid velocity and density of liquid produce effective acoustic metric for quasiparticles, the continuity and London equations represent an analog of Einstein equations for effective gravity in quantum liquids, while quasiparticles represent matter on the background of quantum vacuum. The chapter also considers the role of Galilean transformation, two reference frames for quasiparticles (co-moving and absolute), effect of frame dragging produced by superfluid velocity, and whether the speed of light is a fundamental constant.