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G. E. Volovik

Publications and source records attributed to G. E. Volovik.

At least 253 records · Page 14Linked to original sources
arXiv1999

Fermion zero modes on vortices in chiral superconductors

The energy levels of the fermions bound to the vortex core are considered for the general case of chiral superconductors. There are two classes of chiral superconductivity: in the superconducting state of class I the axisymmetric singly quantized vortex has the same energy spectrum of bound states as in s-wave superconductor: E=(n+1/2)ω_0 with integral n. In the class II the corresponding spectrum is E=nω_0 and thus contains the state with exactly zero energy. The effect of a single impurity on the spectrum of bound state is also considered. For the class I the spectrum acquires the double period ΔE=2ω_0 and consists of two equidistant sets of levels in accordance with A.I. Larkin and Yu.N. Ovchinnikov, Phys. Rev. B57 (1998) 5457. The spectrum is not influenced by a single impurity if the same approximation is applied for vortices in the class II superconducting states.

cond-mat↗
arXiv1999

Momentum-Space Topology of Standard Model

The momentum-space topological invariants, which characterize the ground state of the Standard Model, are continuous functions of two parameters, generated by the hypercharge and by the weak charge. These invariants provide the absence of the mass of the elementary fermionic particles in the symmetric phase above the electroweak transition (the mass protection). All the invariants become zero in the broken symmetry phase, as a result all the elementary fermions become massive. Relation of the momentum-space invariants to chiral anomaly is also discussed.

hep-ph↗
arXiv1999

Fermions in the vortex core in chiral superconductors

Using the semiclassical approach to the energy levels of the fermions bound to the vortex core, we found the difference between the states in nonchiral and chiral superconductors, determined by the Berry phase. The bound states of fermions in the singly quantized vortex in the layered superconductor with the symmetry of superfluid 3He-A is E=nω_0 (as distinct from E=(n+1/2)ω_0 in s-wave superconductor) and thus contains the state with exactly zero energy. This is in accordance with the result obtained in microscopic theory by Kopnin and Salomaa. Using this approach for calculations of the effect of impurities on the spectrum of bound state we reproduced the Larkin-Ovchinnikov result for single impurity in s-wave vortex: the spectrum has the double period ΔE=2ω_0 and consists of two equdistant sets of levels. The same approach however shows that the single impurity does not change the spectrum E=nω_0 in the p-wave vortex .

cond-mat.supr-con↗
arXiv1999

Defect formation in inhomogeneous 2-nd order phase transition: theory and experiment

The status quo in our understanding of defect formation during a rapid transition into the broken symmetry state in condensed matter and cosmology is discussed. An observation of vortex nucleation in neutron absorption experiments in superfluid 3He-B is interpreted in terms of defect formation during inhomogeneous cooling through T_c. Due to the temperature gradient in the locally heated region the superfluid phase transition occurs as a propagating front. The theoretical considerations of vortex formation at the propagating front are based on work by Kibble-Volovik, Kopnin-Thuneberg, and Aranson-Kopnin-Vinokur.

cond-mat↗
arXiv1999

On induced CPT-odd Chern-Simons terms in 3+1 effective action

This paper was originally designated as Comment to the paper by R. Jackiw and V. Alan Kostelecky (hep-ph/9901358). We provide an example of the fermionic system, the superfluid 3He-A, in which the CPT-odd Chern-Simons terms in the effective action are unambiguously induced by chiral fermions. In this system the Lorentz and gauge invariances both are violated at high energy, but the behavior of the system beyond the cut-off is known. This allows us to construct the CPT-odd action, which combines the conventional 3+1 Chern-Simons term and the mixed axial-gravitational Chern-Simons term discussed in hep-ph/9905460. The influence of Chern-Simons term on the dynamics of the effective gauge field has been experimentally observed in rotating 3He-A.

hep-th↗
arXiv1999

3He and Universe parallelism

We discuss topological properties of the ground state of spatially homogeneous ensemble of fermions. There are several classes of topologically different fermionic vacua; in each case the momentum space topology of the vacuum determines the low-energy (infrared) properties of the fermionic energy spectrum. Among them there is a class of the gapless systems which is characterized by the Fermi-hypersurface, which is the topologically stable singularity in momentum space. This class contains the conventional Landau Fermi-liquid and also the non-Landau Luttinger Fermi-liquid. Another important class of gapless systems is characterized by the topologically stable point nodes (Fermi points). Superfluid 3He-A and electroweak vacuum belong to this universality class. The fermionic quasiparticles (particles) in this class are chiral: close to the Fermi points they are left-handed or right-handed massless relativistic particles. Since the spectrum becomes relativistic at low energy, the symmetry of the system is enhanced in the low-energy edge. The low-energy dynamics acquires local invariance, Lorentz invariance and general covariance, which become better and better when the energy decreases. Interaction of the fermions near the Fermi point leads to collective bosonic modes, which look like effective gauge and gravitational fields. Since the vacuum of superfluid 3He-A and electroweak vacuum are topologically similar, we can use 3He-A for simulation of many phenomena in high energy physics, including axial anomaly. 3He-A textures induce a nontrivial effective metrics of the space, where the free quasiparticles move along geodesics. Possible simulation in 3He-A of event horizon, Hawking radiation, rotating vacuum and conical space are discussed.

cond-mat↗
arXiv1999

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

There are several classes of homogeneous Fermi-systems which are characterized by the topology of the energy spectrum of fermionic quasiparticles: (1) Gapless systems with a Fermi-surface; (2) Systems with a gap in their spectrum; (3) Gapless systems with topologically stable point nodes (Fermi points); and (4) Gapless systems with topologically unstable lines of nodes (Fermi lines). Superfluid 3He-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 superfluid 3He-A is that we can perform experiments using this condensed matter and thereby simulate many phenomena in high energy physics, including axial anomaly, baryoproduction, and magnetogenesis. 3He-A textures induce a nontrivial effective metrics of the space, where the free quasiparticles move along geodesics. With 3He-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 superfluid 3He-A.

cond-mat↗
arXiv1999

Rotational quantum friction in superfluids: Radiation from object rotating in superfluid vacuum

We discuss the friction experienced by the body rotating in superfluid liquid at T=0. The effect is analogous to the amplification of electromagnetic radiation and spontaneous emission by the body or black hole rotating in quantum vacuum, first discussed by Zel'dovich and Starobinsky. The friction is caused by the interaction of the part of the liquid, which is rigidly connected with the rotating body and thus represents the comoving detector, with the "Minkowski" vacuum outside the body. The emission process is the quantum tunneling of quasiparticles from the detector to the ergoregion, where the energy of quasiparticles is negative in the rotating frame. This quantum rotational friction caused by the emission of quasiparticles is estimated for phonons and rotons in superfluid 4He and for Bogoliubov fermions in superfluid 3He.

cond-mat↗
arXiv1998

Effective spacetime and Hawking radiation from moving domain wall in thin film of 3He-A

An event horizon for "relativistic" fermionic quasiparticles can be constructed in a thin film of superfluid 3He-A. The quasiparticles see an effective "gravitational" field which is induced by a topological soliton of the order parameter. Within the soliton the "speed of light" crosses zero and changes sign. When the soliton moves, two planar event horizons (black hole and white hole) appear, with a curvature singularity between them. Aside from the singularity, the effective spacetime is incomplete at future and past boundaries, but the quasiparticles cannot escape there because the nonrelativistic corrections become important as the blueshift grows, yielding "superluminal" trajectories. The question of Hawking radiation from the moving soliton is discussed but not resolved.

gr-qc↗
arXiv1998

Energy-momentum tensor of quasiparticles in the effective gravity in superfluids

The problem of the energy-momentum conservation for matter in the gravitational field is discussed on the example of the effective gravity, which arises in superfluids. The "gravitational" field experienced by the relativistic-like massless quasiparticles which form the "matter" (phonons in superfluid 4He and low-energy fermions in superfluid 3He-A), is induced by the flow of the superfluid "vacuum". It appears that the energy-momentum conservation law for quasiparticles, has the covariant form T^μ_{ν;μ}=0. "Pseudotensor" of the energy-momentum for the "gravitational field" (superfluid condensate) appears to depend on "matter". In the presence of the stationary "gravitational" (superfluid) field the real thermodynamic temperature T is constant in the true dissipationless equilibrium state with no entropy production, while the "relativistic" temperature T/\sqrt{g_{00}} is space dependent in agreement with Tolman's law. In the presence of the event horizon the true dissipationless equilibrium state does not exist. The quasiequilibrium dissipative motion across the horizon is considered. The inflationary stage of the expansion of the Universe can be modelled using the expanding Bose-condendsate.

gr-qc↗
arXiv1998

Critical Velocity in 3He-B Vibrating Wire Experiments as Analog of Vacuum Instability in a Slowly Oscillating Electric Field

The Lancaster experiments with a cylindrical wire moving in superfluid 3He-B are discussed, where the measured critical velocity of pair creation is much below the Landau critical velocity. The phenomenon is shown to be analogous to the instability of the electron-positron vacuum in an adiabatically alternating strong electric potential of both signs, where the positive- and negative-root levels cross and thus the instability treshold is twice less than in the conventional case of a single static potential well.

cond-mat↗
arXiv1998

Axial anomaly in 3He-A: Simulation of baryogenesis and generation of primordial magnetic field in Manchester and Helsinki

The gapless fermionic excitations in superfluid 3He-A have a "relativistic" spectrum close to the gap nodes. They are the counterpart of the chiral particles (left-handed and right-handed) in high energy physics above the electroweak transition. We discuss the effective gravity and effective gauge fields, induced by these massless fermions in the low-energy corner. The interaction of the chiral fermions with the gauge field in 3He-A is discussed in detail. It gives rise to the effect of axial anomaly: conversion of the charge from the coherent motion of the condensate (vacuum) to the quasiparticles (matter). The charge of the quasiparticles is thus not conserved: In other words, matter can be created without creating antimatter. This effect is instrumental for the vortex dynamics, in which the vortex is the mediator of conversion of linear momentum from the condensate to the normal component via the spectral flow in the vortex core. The same effect leads to the instability of the counterflow in 3He-A, in which the flow of the normal component (incoherent degrees of freedom) is transformed to the order parameter texture (coherent degrees of freedom). We discuss the analogs of these phenomena in high energy physics. The conversion of the momentum from the vortex to the heat bath is equivalent to the nonconservation of baryon number in the presence of textures and cosmic strings. The counterflow instability is equivalent to the generation of the hypermagnetic field via the axial anomaly. We discuss also an analog of axions and different sources of the mass of the "hyperphoton" in 3He-A.

cond-mat↗
arXiv1998

Induced Gravity in Superfluid 3He

The gapless fermionic excitations in superfluid 3He-A have the "relativistic" spectrum close to the gap nodes. This allowed us to model the modern cosmological scenaria of baryogenesis and magnetogenesis. The same massless fermions induce another low-energy property of the quantum vacuum -- the gravitation. The effective metric of the space, in which the free quasiparticles move along geodesics, is not generally flat. Different order parameter textures correspond to curved effective space and produce many different exotic metrics, which are theoretically discussed in quantum gravity and cosmology. This includes the condensed matter analog of the black hole and event horizon, which can be realized in the moving soliton. This will allow us to simulate and thus experimentally investigate such quantum phenomena as the Hawking radiation from the horizon, the Bekenstein entropy of the black hole, and the structure of the quantum vacuum behind the horizon. One can also simulate the conical singularities produced by cosmic strings and monopoles; inflation; temperature dependence of the cosmological and Newton constants, etc.

cond-mat↗
arXiv1998

Event horizons and ergoregions in 3He

Event horizons for fermion quasiparticles naturally arise in moving textures in superconductors and Fermi superfluids. We discuss the example of a planar soliton moving in superfluid 3He-A, which is closely analogous to a charged rotating black hole. The moving soliton will radiate quasiparticles via the Hawking effect at a temperature of about 5 μK, and via vacuum polarization induced by the effective `electromagnetic field' and `ergoregion'. Superfluid 3He-A thus appears to be a useful system for experimental and theoretical simulations of quantum effects related to event horizons and ergoregions.

cond-mat↗
arXiv1998

Superflow-Stabilized Nonlinear NMR in Rotating 3He-B

Nonlinear spin precession has been observed in 3He-B in large counterflow of the normal and superfluid fractions. The new precessing state is stabilized at high rf excitation level and displays frequency-locked precession over a large range of frequency shifts, with the magnetization at its equilibrium value. Comparison to analytical and numerical calculation indicates that in this state the orbital angular momentum L of the Cooper pairs is oriented transverse to the external magnetic field in a ``non-Leggett'' configuration with broken spin-orbit coupling. The resonance shift depends on the tipping angle theta of the magnetization as omega - omega_L = (Omega_B^2 / 2 omega_L)(cos(theta) - 1/5). The phase diagram of the precessing modes with arbitrary orientation of L is constructed.

cond-mat↗