arXiv subjects

G. E. Volovik

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

At least 37 records · Page 2Linked to original sources

arXiv2024

Discrete $Z_4$ symmetry in quantum gravity

We consider the discrete $Z_4$ symmetry ${\hat {\bf i}}$, which takes place in the scenario of quantum gravity where the gravitational tetrads emerge as the order parameter. Under this symmetry operation $\hat {\bf i}$, the emerging tetrads are multiplied by the imaginary unit, $\hat {\bf i}\,e^a_μ= - i e^a_μ$. The existence of such symmetry and the spontaneous breaking of this symmetry are also supported by the consideration of the symmetry breaking scheme in the topological superfluid $^3$He-B. The order parameter $^3$He-B is the analogue of the tetrad field, but it has complex values. The $\hat {\bf i}$-symmetry operation changes the phase of the complex order parameter by $π/2$, which corresponds to the $Z_4$ discrete symmetry in quantum gravity. We also considered the alternative scenario of the breaking of this $Z_4$ symmetry, in which the $\hat {\bf i}$-operation changes sign of the scalar curvature, $\hat {\bf i} \,{\cal R} = - {\cal R}$, and thus the Einstein-Hilbert action violates the $\hat {\bf i}$-symmetry. In the alternative scenario of symmetry breaking, the gravitational coupling $K=1/16πG$ plays the role of the order parameter, which changes sign under $\hat {\bf i}$-transformation.

cond-mat.other↗

arXiv2024

Thermodynamics and decay of de Sitter vacuum

We discuss the consequences of unique symmetry of de Sitter spacetime, which is invariant under the modified translations, ${\bf r}\rightarrow {\bf r} -e^{Ht}{\bf a}$, where $H$ is the Hubble parameter. Due to this symmetry, all the comoving observers at any point of the de Sitter space perceive the de Sitter environment as the thermal bath with temperature $T=H/π$, which is twice larger than the Gibbons-Hawking temperature of the cosmological horizon. This leads to the heat exchange between gravity and matter, and to instability of de Sitter state towards the creation of matter, its further heating, and finally to the decay of the de Sitter state. The temperature $T=H/π$ determines different processes in the de Sitter environment, which are not possible in Minkowski vacuum, such as the process of ionization of an atom. This temperature also determines the local entropy of the de Sitter vacuum state, and this allows us to calculate the total entropy inside the cosmological horizon. The result reproduces the Gibbons-Hawking area law, which is related to the cosmological horizon, $S_{\rm hor}=4πKA$, where $K=1/(16πG)$. This supports the holographic properties of the cosmological event horizon. We extend the consideration of the local thermodynamics of the de Sitter state using the $f({\cal R})$ gravity. In this thermodynamics, the Ricci scalar curvature ${\cal R}$ and the effective gravitational coupling $K$ are thermodynamically conjugate variables. The holographic connection between the bulk entropy of the Hubble volume and the surface entropy of the cosmological horizon remains the same. Such connection takes place only in the $3+1$ spacetime, where there is the special symmetry due to which the variables $K$ and ${\cal R}$ have the same dimensionality. We also consider the lessons from the de Sitter symmetry for the thermodynamics of black and white holes.

gr-qc↗

arXiv2024

Spacetime geometry from Dirac spinor theory

The quintet of Dirac $4\times 4$ matrices suggests that the fundamental dimension of the internal (spin) space is $n=5$, instead of the conventional dimension $n=4$. Then extending the usual $4\times 4$ tetrads (vierbein), gravity is described in terms of the 5-bein (fünfbein or five legs). We discuss the properties of the spacetime geometry induced from this 5-leg Dirac spinor theory, where the spin connection contains $10\times 4=40$ elements instead of 24 elements in the tetrad formulation of the general relativity theory.

gr-qc↗

arXiv2023

Fermionic quartet and vestigial gravity

We discuss the two-step transitions in superconductors, where the intermediate state between the Cooper pair state and the normal metal is the 4-fermion condensate, which is called the intertwined vestigial order. We discuss different types of the vestigial order, which are possible in the spin-triplet superfluid $^3$He, and the topological objects in the vestigial phases. Since in $^3$He the order parameter $A_{αi}$ represents the analog of gravitational tetrads, we suggest that the vestigial states are possible in quantum gravity. As in superconductors, the fermionic vacuum can experience two consequent phase transitions. At first transition the metric appears as the bilinear combination of tetrads $g_{μν} =η_{ab}< \hat E^a_μ\hat E^b_ν>$, while the tetrad order parameter is still absent, $e_μ^a=< \hat E^a_μ> =0$. This corresponds to the bosonic Einstein general relativity, which emerges in the fermionic vacuum. The nonzero tetrads $e_μ^a=< \hat E^a_μ> \neq 0$ appear at the second transition, where a kind of the Einstein-Cartan-Sciama-Kibble tetrad gravity is formed. This suggests that on the levels of particles, gravity acts with different strength on fermions and bosons.

cond-mat.other↗

arXiv2023

Andreev hidden spinor coordinates: Standard Model, gravity and $^3$He

This paper is prepared for a special memorial issue of J. Low Temp. Phys. dedicated to memory of Alexander Andreev. I discuss his ideas devoted to the fundamental problem in modern physics -- the origin and validity of the superselection rule, which forbids the superposition of a fermion and a boson state. Andreev suggested extra spin degrees of freedom, due to which the $2π$ rotation does not change the sign of the fermionic wave function, and as a result the fermion-boson transmutations becomes possible. Although his approach looks somewhat contradictory from the point of view of the present physics, in principle his ideas can be realized on the more fundamental trans-Planckian level leading to new physics. Different scenarios of the extension of the internal spinor space are considered.

cond-mat.other↗

arXiv2023

Gravity through the prism of condensed matter physics

In the paper "Life, the Universe, and everything--42 fundamental questions", Roland Allen and Suzy Lidström presented personal selection of the fundamental questions. Here, based on the condensed matter experience, we suggest the answers to some questions concerning the vacuum energy, black hole entropy and the origin of gravity. In condensed matter we know both the many-body phenomena emerging on the macroscopic level and the microscopic (atomic) physics, which generates this emergence. It appears that the same macroscopic phenomenon may be generated by essentially different microscopic backgrounds. This points to various possible directions in study of the deep quantum vacuum of our Universe.

cond-mat.other↗

arXiv2023

Topological nodal line in superfluid $^3$He and the Anderson theorem

Superconductivity and superfluidity with anisotropic pairing -- such as $d$-wave in cuprates and $p$-wave in superfluid $^3$He -- are strongly suppressed by impurities. Meanwhile, for applications, the robustness of Cooper pairs to disorder is highly desired. Recently, it has been suggested that unconventional systems become robust if the impurity scattering mixes quasiparticle states only within individual subsystems obeying the Anderson theorem that protects conventional superconductivity. Here, we experimentally verify this conjecture by measuring the temperature dependence of the energy gap in the polar phase of superfluid $^3$He. We show that oriented columnar non-magnetic defects do not essentially modify the energy spectrum, which has a Dirac nodal line. Although the scattering is strong, it preserves the momentum along the length of the columns and forms robust subsystems according to the conjecture. This finding may stimulate future experiments on the protection of topological superconductivity against disorder and on the nature of topological fermionic flat bands.

cond-mat.other↗

arXiv2023

Analog Sommerfeld law in quantum vacuum

The activation temperature $T$ in the de Sitter environment is twice larger than the Gibbons-Hawking temperature, related to the cosmological horizon. We consider the activation temperature as the local temperature of the de Sitter vacuum, and construct the local thermodynamics of the de Sitter state. This thermodynamics includes also the gravitational coupling $K$ and the scalar Riemann curvature ${\cal R}$ as the thermodynamically conjugate variables. These variables modify the thermodynamics of the Gibbs-Duhem relation in the de Sitter state. The free energy density is proportional to $-T^2$, which is similar to that in the non-relativistic Fermi liquids and in relativistic matter with equation of state $w=1$. The local entropy is proportional to the local temperature, while the total entropy inside the cosmological horizon is $A/4G$, where $A$ is the area of the horizon. This entropy is usually interpreted as the entropy of the cosmological horizon. We also consider the possible application of the de Sitter thermodynamics to the Schwarzschild-de Sitter black hole and to black and white holes with the de Sitter cores.

gr-qc↗

arXiv2023

On the global temperature of the Schwarzschild-de Sitter spacetime

It is shown that the Schwarzschild-de Sitter (SdS) spacetime has the fundamental temperature. This temperature describes the thermal processes of decay of the composite particles and the other processes, which are energetically forbidden in the Minkowski spacetime, but are allowed in the de Sitter and in SdS backgrounds. In particular, this temperature describes the probability of ionization of the atom in the SdS, which is observed by the stationary observer at the point where the shift function (velocity) in the Arnowitt-Deser-Misner formalism changes sign. This activation temperature does not depend on the black hole mass and is fully determined by the Hubble parameter, $T_{\rm SdS}=\sqrt{3}H/π$. This temperature is twice the Bousso-Hawking temperature $T_{\rm BH}$, which characterizes the limit of degenerate Lorentzian Schwarzschild-de Sitter universe, when the cosmological and black hole horizons are close to each other, $T_{\rm SdS}=2T_{\rm BH}$. The similar doubling of the temperature of Hawking radiation is known in the pure de Sitter spacetime, where the corresponding local temperature describing the ionization of atoms is twice the Gibbons-Hawking temperature, $T_{\rm dS}=2T_{\rm GH}=H/π$. We suggest that the activation temperature $T_{\rm dS}$ can be considered as the thermodynamic temperature of the de Sitter state, which determines the local entropy in this state, $s=3H/4G$.

gr-qc↗

arXiv2023

Planck constants in the symmetry breaking quantum gravity

The theory of quantum gravity, in which tetrads emerge as the bilinear combinations of the fermionic field, suggests that in general relativity the interval $ds$ is dimensionless. Several other approaches to quantum gravity, including the model of superplastic vacuum and $BF$-theories of gravity support this suggestion. The important consequence of such metric dimension is that all the diffeomorphism invariant quantities are dimensionless for any dimension of spacetime. These include the action $S$, cosmological constant $Λ$, scalar curvature $R$, scalar field $Φ$, wave function $ψ$, etc. The composite fermion approach to quantum gravity suggests that the Planck constant $\hbar$ can be the parameter of the Minkowski metric. Here we extend this suggestion by introducing two Planck constants, bar h and slash h, which are the parameters of the correspondingly time component and space component of the Minkowski metric. The parameters bar h and slash h are invariant only under $SO(3)$ transformations, and thus they are not diffeomorphism invariant. As a result they have nonzero dimensions -- the dimension of time for bar h and dimension of length for slash h. Then according to the Weinberg criterion these parameters are not fundamental, and may vary. They also change sign at the topological domain walls resulting from the symmetry breaking.

cond-mat.other↗

arXiv2023

Acoustic metric and Planck constants

Based on Akama-Diakonov (AK) theory of emergent tetrads, it was suggested\cite{Volovik2023b} that one can introduce two Planck constants, which are the parameters of the corresponding components of Minkowski metric. In the AK theory, the interval $ds$ is dimensionless, as a result the metric elements and thus the Planck constants have nonzero dimensions. The Planck constant $\hbar$ has dimension of time, and the second Planck constant $\hslash$ has dimension of length. It is natural to compare $\hslash$ with the Planck length $l_{\rm P}$, which is related to the Newton constant as $l_{\rm P}^2= \hslash G$. However, this connection remains an open question, because the microscopic (trans-Planckian) physics of the quantum vacuum is not known. Here we study this question using the effective gravity emerging for sound wave quanta (phonons) in superfluid Bose liquid, such as $^4$He, where the microscopic physics is known: it is atomic physics. The elements of the effective acoustic metric are determined by the parameters of this Bose liquid, and as in the AK theory, the interval $ds$ is dimensionless. One may introduce the effective "acoustic Planck constants" as elements of acoustic metric, $g^{μν}_{\rm ac}= {\rm diag}(-\hbar_{\rm ac}^2,\hslash_{\rm ac}^2,\hslash_{\rm ac}^2,\hslash_{\rm ac}^2)$. Then one obtains that the acoustic Planck constant $\hslash_{\rm ac}$ has dimension of length, and in liquid helium it is on the order of the interatomic distance in this liquid, $\hslash_{\rm ac} \sim a$. This supports the scenario in which the Planck constant in the relativistic quantum vacuum is on the order of the Planck length, $\hslash\sim l_{\rm P} \sim G$. We also use the acoustic metric for consideration of the possible dependence of the Planck constant on the Hubble parameter in expanding Universe.

cond-mat.other↗

arXiv2022

Dimensionless physics: Planck constant as an element of Minkowski metric

Diakonov theory of quantum gravity, in which tetrads emerge as the bilinear combinations of the fermionis fields,\cite{Diakonov2011} suggests that in general relativity the metric may have dimension 2, i.e. $[g_{μν}]=1/[L]^2$. Several other approaches to quantum gravity, including the model of superplastic vacuum and $BF$-theories of gravity support this suggesuion. The important consequence of such metric dimension is that all the diffeomorphism invariant quantities are dimensionless for any dimension of spacetime. These include the action $S$, interval $s$, cosmological constant $Λ$, scalar curvature $R$, scalar field $Φ$, etc. Here we are trying to further exploit the Diakonov idea, and consider the dimension of the Planck constant. The application of the Diakonov theory suggests that the Planck constant $\hbar$ is the parameter of the Minkowski metric. The Minkowski parameter $\hbar$ is invariant only under Lorentz transformations, and is not diffeomorphism invariant. As a result the Planck constant $\hbar$ has nonzero dimension -- the dimension of length [L]. Whether this Planck constant length is related to the Planck length scale, is an open question. In principle there can be different Minkowski vacua with their own values of the parameter $\hbar$. Then in the thermal contact between the two vacua their temperatures obey the analog of the Tolman law: $\hbar_1/T_1= \hbar_2/T_2$.

gr-qc↗

arXiv2022

Painleve-Gullstrand coordinates for Schwarzschild-de Sitter spacetime

The Painleve-Gullstrand coordinates are extended to describe the black hole in the cosmological environment: the Schwarzschild-de-Sitter black hole, which has two horizons. The extension is made using the Arnowitt-Deser-Misner formalism. In this extension, which describes the metric in the whole range of radial coordinates $0 r_0$ are free falling towards the cosmological horizon. The existence of the stationary observer allows to determine the temperature of Hawking radiation, which is in agreement with R. Bousso and S.W. Hawking, Phys. Rev. D 54, 6312 (1996). It is the red-shifted modification of the conventional Hawking temperature determined by the gravity at the horizon. We also consider the Painlevé-Gullstrand coordinates and their extension for such configurations as Schwarzschild-de-Sitter white hole, where the sign of the shift function is everywhere positive; the black hole in the environment of the contracting de Sitter spacetime, where the sign of the shift function is everywhere negative; and the white hole in the contracting de Sitter spacetime, where the shift velocity changes sign at $r=r_0$.

gr-qc↗

arXiv2022

Double Hawking temperature: from black hole to de Sitter

The double Hawking temperature $T=2T_H$ appears in some approaches to the Hawking radiation, when the radiation is considered in terms of the quantum tunneling. We consider the origin of such temperature for the black hole horizon and also for the cosmological horizon in de Sitter spacetime. In case the black hole horizon, there are two contributions to the tunneling process of radiation, each being governed by the temperature $T=2T_H$. These processes are coherently combined to produce the radiation with the Hawking temperature $T_H$. This can be traditionally interpreted as the pair creation of two entangled particles, of which one goes towards the centre of the black hole, while the other one escapes from the black hole. In case of the cosmological horizon, the temperature $T=2T_H$ is physical. While the creation of the entangled pair is described by the Hawking temperature, the de Sitter spacetime allows for the another process, in which only single (non-entangled) particle inside the cosmological horizon is created. This process is characterized by the local temperature $T=2T_H$. Such single particle process takes place also outside the black hole horizon, but it is exponentially suppressed.

gr-qc↗

arXiv2022

Particle creation: Schwinger + Unruh + Hawking

We discuss the interconnection between the Schwinger pair creation in electric field, Hawking radiation and particle creation in the Unruh effect. All three processes can be described in terms of the entropy and temperature. These thermodynamic like processes can be combined. We consider the combined process of creation of charged and electrically neutral particles in the electric field, which combine the Schwinger and Unruh effects. We also consider the creation of the charged black and white holes in electric field, which combines the Schwinger effect and the black hole entropy. The combined processes obey the sum rules for the entropy and for the inverse temperature. Some contributions to the entropy and to the temperature are negative, which reflects the quantum entanglement between the created objects.

gr-qc↗

arXiv2022

Dimensionless physics: continuation

Several approaches to quantum gravity (including the model of superplastic vacuum; Diakonov tetrads emerging as the bilinear combinations of the fermionis fields; $BF$-theories of gravity; and effective acoustic metric) suggest that in general relativity the metric must have dimension 2, i.e. $[g_{μν}]=1/[L]^2$, irrespective of the dimension of spacetime. This leads to the "dimensionless physics" discussed in the review paper G.E. Volovik, Dimensionless physics, JETP 132, 727 (2021). Here we continue to exploit this unusual dimension of the metric.

gr-qc↗

arXiv2022

From elasticity tetrads to rectangular vielbein

The paper is devoted to the memory of Igor E. Dzyaloshinsky. In our common paper I.E. Dzyaloshinskii and G.E. Volovick, Poisson brackets in condensed matter, Ann. Phys. {\bf 125} 67--97 (1980), we discussed the elasticity theory described in terms of the gravitational field variables -- the elasticity vielbein $E_μ^a$. They come from the phase fields, which describe the deformations of crystal. The important property of the elasticity vielbein $E^a_μ$ is that in general they are not the square mstrices. While the spacetime index $μ$ takes the values $μ=(0,1,2,3)$, in crystals the index $a=(1,2,3)$, in vortex lattices $a=(1,2)$, and in smectic liquid crystals there is only one phase field, $a=1$. These phase fields can be considered as the spin gauge fields, which are similar to the gauge fields in Standard Model (SM) or in Grand Unification (GUT). On the other hand, the rectangular vielbein $e^μ_a$ may emerge in the vicinity of Dirac points in Dirac materials. In particular, in the planar phase of the spin-triplet superfluid $^3$He the spacetime index $μ=(0,1,2,3)$, while the spin index $a$ takes values $a=(0,1,2,3,4)$. Although these $(4 \times 5)$ vielbein describing the Dirac fermions are rectangular, the effective metric $g^{μν}$of Dirac quasiparticles remains (3+1)-dimensional. All this suggests the possible extension of the Einstein-Cartan gravity by introducing the rectangular vielbein, where the spin fields belong to the higher groups, which may include SM or even GUT groups.

physics.class-ph↗

arXiv2022

Fundamental scalar field with zero dimension from anomaly cancelations

In this article a novel mechanism for dynamical electroweak symmetry breaking and the ensuing appearance of fermion mass terms in the action is proposed. The action contains massless fermions of the SM coupled to gravity through a new type of non-minimal coupling to the vielbein field. The corresponding coupling constants in our approach become zero-dimension scalar fields. Such scalar fields provide the cancellation of the Weyl anomaly \cite{Boyle:2021jaz}.

hep-th↗