No abstract

No 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

Hydrodynamic flow in classical and quantum fluids can be either laminar or turbulent. Vorticity in turbulent flow is often modelled with vortex filaments. While this represents an idealization in classical fluids, vortices are topologically stable quantized objects in superfluids. Superfluid turbulence is therefore thought to be important for the understanding of turbulence more generally. The fermionic 3He superfluids are attractive systems to study because their characteristics vary widely over the experimentally accessible temperature regime. Here we report nuclear magnetic resonance measurements and numerical simulations indicating the existence of sharp transition to turbulence in the B phase of superfluid 3He. Above 0.60T(c) (where T(c) is the transition temperature for superfluidity) the hydrodynamics are regular, while below this temperature we see turbulent behaviour. The transition is insensitive to the fluid velocity, in striking contrast to current textbook knowledge of turbulence. Rather, it is controlled by an intrinsic parameter of the superfluid: the mutual friction between the normal and superfluid components of the flow, which causes damping of the vortex motion.

Superconducting states with different internal topology are discussed for the layered high-T c materials. If the time inversion symmetry is broken, the superconductivity is determined not only by the symmetry of the superconducting state, but also by the topology of the ground state. The latter is determined the integer-valued momentumspace topological invariant N . The current carrying boundary between domains with different N (N 2 = N 1 ) is considered. The current is produced by fermion zero modes, which number per one layer is 2(N 2 − N 1 ).Recently a new phase transition in high temperature superconductor was reported on in Ni-doped Bi 2 Sr 2 CaCu 2 0 8 [1]. It occurs at low temperature, T ∼ 200 mK and seems to correspond to the opening of the gap in the superconductor which is gapless (contains lines of nodes) above transition. Since the gap usually appears in superconductor with lines of nodes if the time inversion (T ) symmetry is violated, this suggests that the spontaneous breaking of the T -symmetry occurs in the new transition. Such transition can be caused by interaction with magnetic impurities.Some evidence of the additional symmetry breaking with opening of the gap in a pure Bi 2 Sr 2 CaCu 2 0 8 in the presence of magnetic field was reported in [2]. The d x 2 −y 2 + id xy complex order parameter was suggested in [3] to describe this experiment. The possibility of the broken T -symmetry was discussed also within the grain boundaries and twin boundaries [4,5].Since the broken T -symmetry becomes popular now for the high temperature superconductors, we discuss some consequences of the broken Tsymmetry in D=2 spatial dimension relevant for layered superconductors. These consequences are similar to that in thin films of superfluid 3 He-A and other 2D systems where T -symmetry is broken. They are described in terms of the integer-valued topological invariant of the ground state [6,7,8,9,10], which gives rise to chiral edge states on the boundary of superconductor and in some cases to quantization of Hall conductivity. We dicuss here this topological invariant for the layered superconductors.

The first realization of instabilities in the shear flow between two superfluids is examined. The interface separating the A and B phases of superfluid 3 He is magnetically stabilized. With uniform rotation we create a state with discontinuous tangential velocities at the interface, supported by the difference in quantized vorticity in the two phases. This state remains stable and nondissipative to high relative velocities, but finally undergoes an instability when an interfacial mode is excited and some vortices cross the phase boundary. The measured properties of the instability are consistent with a modified Kelvin-Helmholtz theory.Instabilities in the shear flow between two layers of fluids [1] belong to a class of interfacial hydrodynamics which is attributed to many natural phenomena. Examples are wave generation by wind blowing over water [2], the flapping of a sail or flag in the wind [3,4], and even flow in granular beds [5]. In the hydrodynamics of inviscid and incompressible fluids the transition from calm to wavy interfaces is known as the Kelvin-Helmholtz (KH) instability [6,2]. Since Lord Kelvin's treatise in 1871, difficulties have plagued its description in ordinary fluids, which are viscous and dissipative. They also display a shear-flow instability, but its correspondence with that in the ideal limit is not straightforward. The tangential velocity discontinuity in the shear-flow instability is created by a vortex sheet. In a viscous fluid a planar vortex sheet is not a stable equilibrium state and not a solution of the hydrodynamic equations [7].Superfluids provide a close variation of the ideal inviscid limit considered by Lord Kelvin and thus an environment where the KH theory can be tested. The initial state is a non-dissipative vortex sheet -the interface between two superfluids brought into a state of relative shear flow. So far the only experimentally accessible case where this can be studied in stationary conditions, is the interface between 3 He-A and 3 He-B [8], where the order parameter changes symmetry and magnitude, but is continuous on the scale of the superfluid coherence length ξ ∼ 10 nm. We discuss an experiment, where the two phases slide with respect to each other in a rotating cryostat:3 He-A performs solid-body-like rotation while 3 He-B is in the vortex-free state and thus stationary in the laboratory frame. While increasing the rotation velocity Ω, we record the events when the AB phase boundary becomes unstable -when some circulation from the A-phase crosses the AB interface and vortex lines are introduced into the initially vortex-free B phase. On increasing the rotation further, the instability occurs repeatedly. Such a succession of instability events can be understood as a spin-up of 3 He-B by rotating 3 He-A. Our experimental setup is shown in Fig. 1. The AB boundary is forced against a magnetic barrier in a smooth-walled quartz container, by cooling the sample below T AB at constant pressure in a rotating refrigerator. The number of vortices in both phases is indepe...

No abstract

We suggest a procedure how to prepare the vortex with N = 1/2 winding number -the counterpart of the Alice string -in Bose-Einstein condensates. PACS numbers:Vortices with fractional winding number can exist in different condensed matter systems, see review paper [1]. Observation of atomic Bose-condensates with multicomponent order parameter in laser manipulated traps opens the possibility to create half-quantum vortices there. We discuss the N = 1/2 vortices in the Bosecondensate with the hyperfine spin F = 1, and also in the mixture of two Bose-condensates.The order parameter of F = 1 Bose-condensate consists of 3 complex components according to the number of the projections M = (+1, 0, −1). These components can be organized to form the complex vector a: