Field theory in superfluid ³ He: What are the lessons for particle physics, gravity, and high-temperature superconductivity?

Abstract

There are several classes of homogeneous Fermi systems that are characterized by the topology of the energy spectrum of fermionic quasiparticles: (i) gapless systems with a Fermi surface, (ii) systems with a gap in their spectrum, (iii) gapless systems with topologically stable point nodes (Fermi points), and (iv) gapless systems with topologically unstable lines of nodes (Fermi lines). Superf luid 3 He-A and electroweak vacuum belong to the universality class 3. The fermionic quasiparticles (particles) in this class are chiral: they are left-handed or right-handed. The collective bosonic modes of systems of class 3 are the effective gauge and gravitational fields. The great advantage of superf luid 3 He-A is that we can perform experiments by using this condensed matter and thereby simulate many phenomena in high energy physics, including axial anomaly, baryoproduction, and magnetogenesis.3 He-A textures induce a nontrivial effective metrics of the space, where the free quasiparticles move along geodesics. With 3 He-A one can simulate event horizons, Hawking radiation, rotating vacuum, etc. High-temperature superconductors are believed to belong to class 4. They have gapless fermionic quasiparticles with a ''relativistic'' spectrum close to gap nodes, which allows application of ideas developed for superf luid 3 He-A.It is now well understood that the universe and its symmetrybroken ground state, the physical vacuum, may behave like a condensed matter system with a complicated and possibly degenerate ground state (1-5). If the analogy of the quantum mechanical physical vacuum with condensed matter systems is taken seriously, the first question that arises is: which system of condensed matter reproduces most closely the properties of the quantum vacuum? Because particle physics deals with interacting Fermi and Bose quantum fields, the system should be fermionic. This requirement excludes superfluid 4 He, which contains only Bose fields. In Fermi systems, such as metals, superconductors, and normal and superfluid 3 He, in addition to the fermionic degrees of freedom that come from the bare fermions, electrons, and 3 He-atoms, the quantum Bose fields appear as low-energy collective modes. Therefore, these systems do represent interacting Fermi and Bose quantum fields.Which Fermi system is the best? To answer this question we first must realize that the main feature that differentiates between various Fermi systems is the topology of the quasiparticle spectrum in the low energy (infra-red) corner. I will consider only systems whose ground state is spatially homogeneous, which is one of the least disputed properties of the physical vacuum. When the topology of the quasiparticle spectrum is taken into account, the homogeneous Fermi systems can be organized into very few classes (see Fig. 1).

Superfluid analogies of cosmological phenomena

“…(1) and (4) can be obtained from the Hamiltonian formalism using the energy in Eq. (5) as Hamiltonian and the following Poisson brackets {v s (r 1 ), n(r 2 )} = 1 m ∇δ(r 1 − r 2 ) , {n(r 1 ), n(r 2 )} = {v s (r 1 ), v s (r 2 )} = 0 .…”

“…The vacuum is characterized by the equilibrium value of the particle number density n 0 (µ) at given chemical potential µ, which is determined by the minimization of the energyǫ(n) which enters the functional in Eq. (5): dǫ/dn = 0. This energy is related to the pressure in the liquid created by external sources provided by the environment.…”

Quantum gravity: a progress report

“…Tests may be possible in the not-toodistant future in Bose-Einstein condensates [347], superfluid helium 3 [348], and "slow light" in dielectrics [349].…”

Nuclear orientation and nuclear cooling experiements in Oxford and Helsinki Part 3. Progress from 1975 to 2001

“…Over the past 20 years nuclear refrigeration has been used for many studies at ultra-low temperatures, both in Helsinki and elsewhere, particularly for investigations on superfluid 3 He, including studies of the rotating liquid (reviewed by Lounasmaa and Thuneberg 15 ) and the possible implications of the 3 He data for explaining the 'Big Bang' that occurred in the early Universe. 16 A review by Oja and Lounasmaa 17 gives a comprehensive picture of nuclear ordering experiments by the Helsinki group and its Danish and German associates. Experimental techniques are described and magnetic susceptibility and neutron diffraction data are discussed in detail.…”