Superfluid analogies of cosmological phenomena

Abstract

Superfluid 3He-A gives example of how chirality, Weyl fermions, gauge fields and gravity appear in low energy corner together with corresponding symmetries, including Lorentz symmetry and local SU(N). This supports idea that quantum field theory (Standard Model or GUT) is effective theory describing low-energy phenomena. * Momentum space topology of fermionic vacuum provides topological stability of universality class of systems, where above properties appear. * BCS scheme for 3He-A incorporates both ``relativistic'' infrared regime and ultraviolet ``transplanckian'' range: subtle issues of cut-off in quantum field theory and anomalies can be resolved on physical grounds. This allows to separate ``renormalizable'' terms in action, treated by effective theory, from those obtained only in ``transPlanckian'' physics. * Energy density of superfluid vacuum within effective theory is ~ E_{Planck}^4. Stability analysis of ground state beyond effective theory leads to exact nullification of vacuum energy: equilibrium vacuum is not gravitating. In nonequilibrium, vacuum energy is of order energy density of matter. * 3He-A provides experimental prove for anomalous nucleation of fermionic charge according to Adler-Bell-Jackiw. * Helical instability in 3He-A is described by the same equations as formation of magnetic field by right electrons in Joyce-Shaposhnikov scenario. * Macroscopic parity violating effect and angular momentum paradox are both desribed by axial gravitational Chern-Simons action. * High energy dispersion of quasiparticle spectrum allow to treat problems of vacuum in presence of event horizon, etc.Comment: draft of review for Physics Reports, RevTex file, 113 pages, 26 figures; new sections and references are adde

Unconventional interaction between vortices in a polarized Fermi gas

“…[35]. This is consistent with a quite general argument that the transformation properties for quasiparticles in the lowenergy effective theories should not depend on the quantities such as the bare particle mass m. [48] As a by-product of this transformation law, the Bogoliubov-quasiparticle current j is invariant under Galilean boosts, which is also consistent with the invariance of the quasiparticle momentum.…”

“…In what follows, we employ formula (48) to determine the superfluid (number) density n s = ρ s /(m ↑ + m ↓ ) at zero temperature in the special case of an equal mass system of interest in the present work.…”

“…In order to determine how the Bogoliubov quasiparticle field transforms under the Galilean transformation, we recall that the momentum of a quasiparticle is invariant under the Galilean transformation while the quasiparticle energy is Doppler-shifted (to leading order in the boost velocity): [48] …”

Vortices and type-I superconductivity in neutron stars

“…Actually, it can be shown by using the equations of motion obtained from the free energy (1) that for most potentials V , which are approximately invariant under the U (2) symmetry, it is impossible for the ψ 2 field to remain constant when the ψ 1 field varies in space. On the other hand, from the energetic point of view, given that the potential V can be written approximately as V ≈ U (|ψ 1 | 2 + |ψ 2 | 2 ), one can argue (in part based on previous work [5,6,7,8,9,10,11]) that it is favorable for the ψ 2 field to increase its magnitude in the vortex core to compensate the decrease in the magnitude of ψ 1 . So, anticipating a non-trivial behavior of the neutron field ψ 2 , let's adopt the following cylindrically symmetric ansatz for the fields describing a proton vortex with a unit winding number:…”

Running of the spectral index and violation of the consistency relation between tensor and scalar spectra from trans-Planckian physics

“…Similar methods were employed to investigate the same phenomenon in the context of black hole physics [5,6]. These modifications were inspired by higher dimensional models of the universe [7] or from condensed matter analogs of gravity [8]. It was shown that the prediction of a thermal Hawking spectrum is insensitive to modifications of the physics at the trans-Planckian end of the spectrum.…”