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G. E. Volovik

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

At least 235 records · Page 13Linked to original sources
arXiv2002

Momentum space topology of fermion zero modes on brane

We discuss fermion zero modes within the 3+1 brain -- the domain wall between the two vacua in 4+1 spacetime. We do not assume relativistic invariance in 4+1 spacetime, or any special form of the 4+1 action. The only input is that the fermions in bulk are fully gapped and are described by nontrivial momentum-space topology. Then the 3+1 wall between such vacua contains chiral 3+1 fermions. The bosonic collective modes in the wall form the gauge and gravitational fields. In principle, this universality class of fermionic vacua can contain all the ingredients of the Standard Model and gravity.

gr-qc↗
arXiv2001

Fermionic microstates within Painlevé-Gullstrand black hole

We consider the quantum vacuum of fermionic field in the presence of a black-hole background as a possible candidate for the stabilized black hole. The stable vacuum state (as well as thermal equilibrium states with arbitrary temperature) can exist if we use the Painlevé-Gullstrand description of the black hole, and the superluminal dispersion of the particle spectrum at high energy, which is introduced in the free-falling frame. Such choice is inspired by the analogy between the quantum vacuum and the ground state of quantum liquid, in which the event horizon for the low-energy fermionic quasiparticles also can arise. The quantum vacuum is characterized by the Fermi surface, which appears behind the event horizon. We do not consider the back reaction, and thus there is no guarantee that the stable black hole exists. But if it does exist, the Fermi surface behind the horizon would be the necessary attribute of its vacuum state. We also consider exact discrete spectrum of fermions inside the horizon which allows us to discuss the problem of fermion zero modes.

gr-qc↗
arXiv2001

Fermion zero modes in Painlevé-Gullstrand black hole

Painleve-Gullstrand metric of the black hole allows to discuss the fermion zero modes inside the hole. The statistical mechanics of the fermionic microstates can be responsible for the black hole thermodynamics. Fermion zero modes also lead to quantization of the horizon area.

gr-qc↗
arXiv2001

Vacuum in quantum liquids and in general relativity

Quantum liquids, in which an effective Lorentzian metric and thus some kind of gravity gradually arise in the low-energy corner, are the objects where the problems related to the quantum vacuum can be investigated in detail. In particular, they provide the possible solution of the cosmological constant problem: why the vacuum energy is by 120 orders of magnitude smaller than the estimation from the relativistic quantum field theory. The almost complete cancellation of the cosmological constant does not require any fine tuning and comes from the fundamental ``trans-Planckian'' physics of quantum liquids. The remaining vacuum energy is generated by the perturbations of quantum vacuum caused by matter (quasiparticles), curvature, and other possible sources, such as smooth component -- the quintessence. This provides the possible solution of another cosmological constant problem: why the present cosmological constant is on the order of the present matter density of the Universe. We discuss here some properties of the quantum vacuum in quantum liquids: the vacuum energy under different conditions; excitations above the vacuum state and the effective acoustic metric for them provided by the motion of the vacuum; Casimir effect, etc.

gr-qc↗
arXiv2001

Vacuum energy and cosmological constant: View from condensed matter

The condensed matter examples, in which the effective gravity appears in the low-energy corner as one of the collective modes of quantum vacuum, provide a possible answer to the question, why the vacuum energy is so small. This answer comes from the fundamental ``trans-Planckian'' physics of quantum liquids. In the effective theory of the low energy degrees of freedom the vacuum energy density is proportional to the fourth power of the corresponding ``Planck'' energy appropriate for this effective theory. However, from the exact ``Theory of Everything'' of the quantum liquid it follows that its vacuum energy density is exactly zero without fine tuning, if: there are no external forces acting on the liquid; there are no quasiparticles which serve as matter; no space-time curvature; and no boundaries which give rise to the Casimir effect. Each of these four factors perturbs the vacuum state and induces the nonzero value of the vacuum energy density of order of energy density of the perturbation. This is the reason, why one must expect that in each epoch the vacuum energy density is of order of matter density of the Universe, or/and of its curvature, or/and of the energy density of smooth component -- the quintessence.

gr-qc↗
arXiv2001

Mesoscopic Casimir forces from effects of discrete particle number in the quantum vacuum

Traditionally it is assumed that the Casimir vacuum pressure does not depend on the ultraviolet cut-off. There are, however, some arguments that the effect actually depends on the regularization procedure and thus on the trans-Planckian physics. We provide the condensed matter example where the Casimir forces do explicitly depend on the microscopic (correspondingly trans-Planckian) physics due to the mesoscopic finite-N effects, where N is the number of bare particles in condensed matter (or correspondingly the number of the elements comprising the quantum vacuum). The finite-N effects lead to mesoscopic fluctuations of the vacuum pressure. The amplitude of the mesoscopic flustuations of the Casimir force in a system with linear dimension L is larger by the factor N^{1/3}\sim L/a than the traditional value of the Casimir force given by effective theory, where a is the interatomic distance which plays the role of the Planck length.

gr-qc↗
arXiv2001

Reentrant violation of special relativity in the low-energy corner

In the effective relativistic quantum field theories the energy region, where the special relativity holds, can be sandwiched from both the high and low energies sides by domains where the special relativity is violated. An example is provided by 3He-A where the relativistic quantum field theory emerges as the effective theory. The reentrant violation of the special relativity in the ultralow energy corner is accompanied by the redistribution of the momentum-space topological charges between the fermionic flavors. At this ultralow energy an exotic massless fermion with the topological charge $N_3=2$ arises, whose energy spectrum mixes the classical and relativistic behavior. This effect can lead to neutrino oscillations if neutrino flavors are still massless at this energy scale.

hep-ph↗
arXiv2000

What can superconductivity learn from quantized vorticity in He-3 superfluids?

In He-3 superfluids quantized vorticity can take many different forms: It can appear as distributed periodic textures, as sheets, or as lines. In the anisotropic He-3A phase in most cases the amplitude of the order parameter remains constant throughout the vortex structure and only its orientation changes in space. In the quasi-isotropic He-3B phase vortex lines have a hard core where the order parameter has reduced, but finite amplitude. The different structures have been firmly identified, based on both measurement and calculation. What parallels can be drawn from this information to the new unconventional superconductors or Bose-Einstein condensates?

cond-mat↗
arXiv2000

Interplay of real space and momentum space topologies in strongly correlated fermionic systems

We discuss the momentum-space topology of 3+1 and 2+1 strongly correlated fermionic systems. For the 3+1 systems the important universality class is determined by the topologically stable Fermi points in momentum space. In the extreme limit of low energy the condensed matter system of this universality class acquires all the symmetries, which we know today in high energy physics: Lorentz invariance, gauge invariance, general covariance, etc. The chiral fermions as well as gauge bosons and gravity field arise as fermionic and bosonic collective modes of the system. This introduces the conceptual similarity between such condensed matter and the quantum vacuum of Standard Model, which also contains the Fermi point. For the 2+1 fermionic systems the momentum space topology gives rise to the quantization of different physical parameters, such as Hall conducivity and spin-Hall conductivity, and to quantum phase transitions with the abrupt change of the momentum-space topology. The combined p-space and r-space topology determines in particular the topology of the energy spectrum of fermion zero modes living within the topological defects; fermionic charges of the topologically nontrivial extended objects; axial anomaly; etc.

cond-mat↗
arXiv2000

Superfluid analogies of cosmological phenomena

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.

gr-qc↗
arXiv2000

Composite defect extends cosmology - 3He analogy

Spin-mass vortices have been observed to form in rotating superfluid 3He-B following the absorption of a thermal neutron and a rapid transition from the normal to superfluid state. The spin-mass vortex is a composite defect which consists of a planar soliton (wall) which terminates on a linear core (string). This observation fits well within the framework of a cosmological scenario for defect formation, known as the Kibble-Zurek mechanism. It suggests that in the early Universe analogous cosmological defects might have formed.

cond-mat↗
arXiv2000

Vortices observed and to be observed

Linear defects are generic in continuous media. In quantum systems they appear as topological line defects which are associated with a circulating persistent current. In relativistic quantum vacuum they are known as cosmic strings, in superconductors as quantized flux lines, and in superfluids and low-density atomic Bose-Einstein condensates as quantized vortex lines. We discuss unconventional vortices in unconventional superfluids and superconductors, which have been observed or have to be observed, such as continuous singly and doubly quantized vortices in 3He-A and chiral Bose condensates; half-quantum vortices (Alice strings) in 3He-A and in nonchiral Bose condensates; Abrikosov vortices with fractional magnetic flux in chiral and d-wave superconductors; vortex sheets in 3He-A and chiral superconductors; the nexus -- combined object formed by vortices and monopoles. Some properties of vortices related to fermionic quasiparticles living in the vortex core are also discussed.

cond-mat↗
arXiv2000

Macroscopic parity violating effects and 3He-A

We discuss parity violating effects in relativistic quantum theory and their analogues in effective field theory of superfluid 3He-A. A mixed axial-gravitational Chern-Simons term in the relativistic effective action and its condensed matter analog are responsible for the chiral fermion flux along the rotation axis of the heat bath in relativistic system and for the unusual Omega-odd dependence of the zero-temperature density of the normal component on the rotation velocity in 3He-A.

hep-ph↗
arXiv1999

Monopoles and fractional vortices in chiral superconductors

We discuss two exotic objects, which must be experimentally identified in chiral superfluids and superconductors. These are (i) the vortex with fractional quantum number (N=1/2 in chiral superfluids, and N=1/2 and N=1/4 in chiral superconductors), which plays the part ofthe Alice string in relativistic theories; and (ii) the hedgehog in the l-field, which is the counterpart of the Dirac magnetic monopole. These objects of different dimensions are topologically connected. They form the combined object which is called nexus in relativistic theories. In chiral superconductors the nexus has magnetic charge emanating radially from the hedgehog, while the half-quantum vortices play the part of the Dirac string. Each of them supplies the fractional magnetic flux to the hedgehog, representing 1/4 of the "conventional" Dirac string. We discuss the topological interaction of the superconductor's nexus with the `t Hooft-Polyakov magnetic monopole, which can exist in GUT. The `t Hooft-Polyakov magnetic monopole and the hedgehog with the same magnetic charge are topologically confined by a piece of the Abrikosov vortex. Other properties of half-quantum vortices and monopoles are discussed as well, including fermion zero modes.

cond-mat↗
arXiv1999

Monopole, half-quantum vortices and nexus in chiral superfluids and superconductors

Two exotic objects are still not identified experimentally in chiral superfluids and superconductors. These are the half-quantum vortex, which plays the part of the Alice string in relativistic theories, and the hedgehog in the l-field, which is the counterpart of the Dirac magnetic monopole. These two objects of different dimensionality are topologically connected. They form the combined object which is called nexus in relativistic theories (hep-th/9911125). Such combination will allow us to observe half-quantum vortices and monopoles in several realistic geometries.

cond-mat↗
arXiv1999

Vierbein walls in condensed matter

The effective field, which plays the part of the vierbein in general relativity, can have topologically stable surfaces, vierbein domain walls, where the effective contravariant metric is degenerate. We consider vierbein walls separating domains with the flat space-time which are not causally connected at the classical level. Possibility of the quantum mechanical connection between the domains is discussed.

gr-qc↗