arXiv subjects

M. A. Zubkov

Publications and source records attributed to M. A. Zubkov.

At least 73 records · Page 4Linked to original sources

arXiv2018

Wigner - Weyl formalism and the propagator of Wilson fermions in the presence of varying external electromagnetic field

We develop Wigner - Weyl formalism for the lattice models. For the definiteness we consider Wilson fermions in the presence of $U(1)$ gauge field. The given technique reduces calculation of the two point fermionic Green function to solution of the Groenewold equation. It relates Wigner transformation of the Green function with the Weyl symbol $Q_W$ of Wilson Dirac operator. We derive the simple expression for $Q_W$ in the presence of varying external $U(1)$ gauge field. Next, we solve the Groenewold equation to all orders in powers of the derivatives of $Q_W$. Thus the given technique allows to calculate the fermion propagator in the lattice model with Wilson fermions in the presence of arbitrary background electromagnetic field. The generalization of this method to the other lattice models is straightforward.

hep-lat↗

arXiv2018

The dimensionally reduced description of the high energy scattering and the effective action for the reggeized gluons

We discuss the high energy scattering of hadrons with the multi - Regge kinematics. The effective $2D$ model for the interaction between the produced hard gluons appears as a result of the dimensional reduction, which is similar to the dimensional reduction $3+1$ D $\to 3$ D of the high temperature gauge theory. It is demonstrated that being supplemented by the exchange by virtual $3+1$ D gluons this $2D$ model gives rise to the hermitian version of the effective action of Lipatov for the interaction between the ordinary and the reggeized gluons.

hep-ph↗

arXiv2018

The type II Weyl semimetals at low temperatures: chiral anomaly, elastic deformations, zero sound

We consider the properties of the type II Weyl semimetals at low temperatures basing on the particular tight - binding model. In the presence of electric field directed along the line connecting the Weyl points of opposite chirality the occupied states flow along this axis giving rise to the creation of electron - hole pairs. The electrons belong to a vicinity of one of the two type II Weyl points while the holes belong to the vicinity of the other. This process may be considered as the manifestation of the chiral anomaly that exists without any external magnetic field. It may be observed experimentally through the measurement of conductivity. Next, we consider the modification of the theory in the presence of elastic deformations. In the domain of the considered model, where it describes the type I Weyl semimetals the elastic deformations lead to the appearance of emergent gravity. In the domain of the type II Weyl semimetals the form of the Fermi surface is changed due to the elastic deformations, and its fluctuations represent the special modes of the zero sound. We find that there is one - to one correspondence between them and the sound waves of the elasticity theory. Next, we discuss the influence of the elastic deformations on the conductivity. The particularly interesting case is when our model describes the intermediate state between the type I and the type II Weyl semimetal. Then without the elastic deformations there are the Fermi lines instead of the Fermi points/Fermi surface, while the DC conductivity vanishes. However, even small elastic deformations may lead to the appearance of large conductivity.

cond-mat.mes-hall↗

arXiv2018

Anatomy of the chiral vortical effect

We consider the system of relativistic rotating fermions in the presence of rotation. The rotation is set up as an enhancement of the angular momentum. In this approach the angular velocity for the angular momentum plays the same role as the chemical potential for density. We calculate the axial current using the direct solutions of the Dirac equation with the MIT bag boundary conditions. Next, we consider the alternative way of the rotation description, in which the local velocity of the substance multiplied by the chemical potential serves as the effective gauge field. In this approach this is possible to relate the axial current of the chiral vortical effect for the massless fermions to the topological invariant in momentum space, which is robust to the introduction of interactions. We compare the results for the axial current obtained using the two above mentioned approaches.

hep-ph↗

arXiv2018

Momentum space topology of QCD

We discuss the possibility to consider quark matter as the topological material. We consider hadronic phase (HP), the quark - gluon plasma phase (QGP), and the hypothetical color - flavor locking (CFL) phase. In those phases we identify the relevant topological invariants in momentum space. The formalism is developed, which relates those invariants and massless fermions that reside on vortices and at the interphases. This formalism is illustrated by the example of vortices in the CFL phase.

hep-th↗

arXiv2018

Hall effect in the presence of rotation

The rotating relativistic fermion system is considered. The consideration is based on the Dirac equation written in the laboratory (non - rotating) reference frame. Rotation in this approach gives rise to the effective magnetic and electric fields that act in the same way both on positive and negative electric charges. In the presence of external electric field in the given system the electric current appears orthogonal to both the electric field and the axis of rotation. The possible applications to the physics of quark - gluon plasma are discussed.

hep-ph↗

arXiv2018

The black hole interior and the type II Weyl fermions

It was proposed recently that the black hole may undergo a transition to the state, where inside the horizon the Fermi surface is formed that reveals an analogy with the recently discovered type II Weyl semimetals. In this scenario the low energy effective theory outside of the horizon is the Standard Model, which describes excitations that reside near a certain point $P^{(0)}$ in momentum space of the hypothetical unified theory. Inside the horizon the low energy physics is due to the excitations that reside at the points in momentum space close to the Fermi surface. We argue that those points may be essentially distant from $P^{(0)}$ and, therefore, inside the black hole the quantum states are involved in the low energy dynamics that are not described by the Standard Model. We analyse the consequences of this observation for the physics of the black holes and present the model based on the direct analogy with the type II Weyl semimetals, which illustrates this pattern.

gr-qc↗

arXiv2017

Modified top quark condensation model with the extra heavy fermion, the $125$ GeV Pseudo - Goldstone boson, and the additional heavy scalar bosons

We discuss the modified top quark condensation model proposed in \cite{VZ2015}. This construction was inspired by the top - seesaw scenario, in which the extra heavy fermion $χ$ is added that may be paired with the top quark. Besides, this model incorporates the ideas of the Little Higgs scenario, in which the $125$ GeV scalar particle appears as a Pseudo - Goldstone boson. This model admits (in addition to the $125$ GeV scalar boson $H$) the heavier scalar excitation $H^\prime$. We consider the region of parameters, where its mass is $M_{H^\prime} \sim 1$ TeV, the width of $H^\prime$ is $Γ_{H^\prime} \sim 0.3 M_{H^\prime}$, while the mass of the heavy fermion is $m_χ\sim 1$ TeV. We find that in this model the value of the cross - section $σ_{pp \to H^\prime + X \to γ+γ+ X}$ for $\sqrt{s}=13$ TeV is essentially smaller than the present experimental upper bound. Besides, we find, that for the chosen values of parameters there should exist the CP - even scalar boson with mass $\approx 2 m_χ$ and very small width. In addition, the model predicts the existence of the extra neutral CP even scalar boson and the charged scalar boson with masses of the order of $1$ TeV.

hep-ph↗

arXiv2017

Scale Magnetic Effect in Quantum Electrodynamics and the Wigner-Weyl Formalism

The Scale Magnetic Effect (SME) is the generation of electric current due to conformal anomaly in external magnetic field in curved spacetime. The effect appears in a vacuum with electrically charged massless particles. Similarly to the Hall effect, the direction of the induced anomalous current is perpendicular to the direction of the external magnetic field $\bf B$ and to the gradient of the conformal factor $τ$, while the strength of the current is proportional to the beta function of the theory. In massive electrodynamics the SME remains valid, but the value of the induced current differs from the current generated in the system of massless fermions. In the present paper we use the Wigner--Weyl formalism to demonstrate that in accordance with the decoupling property of heavy fermions the corresponding anomalous conductivity vanishes in the large-mass limit with $m^2 \gg |e {\bf B}|$ and $m \gg |\nabla τ|$.

hep-th↗

arXiv2017

Fermi points and the Nambu sum rule in the polar phase of $^3$He

We discuss the polar phase of $^3$He, which is realized in the anisotropic aerogel. We consider it in the framework of the BCS model. In the absence of the spin - orbit interaction this model predicts the appearance of the Fermi line. However, it is topologically unstable. We demonstrate, that the spin - orbit interaction gives rise to the appearance of the two Fermi points instead of the Fermi line. In addition to the gapless Nambu - Goldstone bosons in this system the collective gapped bosonic states exist. Their gaps are calculated, and the corresponding Nambu sum rule is established.

cond-mat.mes-hall↗

arXiv2016

Schwinger pair creation in Dirac semimetals in the presence of external magnetic and electric fields

We discuss the Schwinger pair creation process for the system of massless Dirac fermions in the presence of constant external magnetic and electric fields. The pair production rate remains finite unlike the vacuum decay rate. In the recently discovered Dirac semimetals, where the massless Dirac fermions emerge, this pair production may be observed experimentally through the transport properties. We estimate its contribution to the ordinary conductivity of the semimetals.

cond-mat.mes-hall↗

arXiv2016

Standard Model as the topological material

Study of the Weyl and Dirac topological materials (topological semimetals, insulators, superfluids and superconductors) opens the route for the investigation of the topological quantum vacua of relativistic fields. The symmetric phase of the Standard Model (SM), where both electroweak and chiral symmetry are not broken, represents the topological semimetal. The vacua of the SM (and its extensions) in the phases with broken Electroweak symmetry represent the topological insulators of different types. We discuss in details the topological invariants in both symmetric and broken phases and establish their relation to the stability of vacuum.

hep-ph↗

arXiv2016

Landau Levels in graphene in the presence of emergent gravity

We consider graphene in the presence of external magnetic field and elastic deformations that cause emergent magnetic field. The total magnetic field results in the appearance of Landau levels in the spectrum of quasiparticles. In addition, the quasiparticles in graphene experience the emergent gravity. We consider the particular choice of elastic deformation, which gives constant emergent magnetic field and vanishing torsion. Emergent gravity may be considered as perturbation. We demonstrate that the corresponding first order approximation affects the energies of the Landau levels only through the constant renormalization of Fermi velocity. The degeneracy of each Landau level receives correction, which depends essentially on the geometry of the sample. There is the limiting case of the considered elastic deformation, that corresponds to the uniformly stretched graphene. In this case in the presence of the external magnetic field the degeneracies of the Landau levels remain unchanged.

cond-mat.mes-hall↗

arXiv2015

Emergent gravity in the cubic tight-binding model of Weyl semimetal in the presence of elastic deformations

We consider the tight-binding model with cubic symmetry that may be relevant for the description of a certain class of Weyl semimetals. We take into account elastic deformations of the semimetal through the modification of hopping parameters. This modification results in the appearance of emergent gauge field and the coordinate dependent anisotropic Fermi velocity. The latter may be interpreted as emergent gravitational field.

cond-mat.mes-hall↗

arXiv2015

Scalar excitation with Leggett frequency in $^3$ He-B and the $125$ GeV Higgs particle in top quark condensation models as Pseudo - Goldstone bosons

We consider the scenario, in which the light Higgs scalar boson appears as the Pseudo - Goldstone boson. We discuss examples both in condensed matter and in relativistic field theory. In $^3$He-B the symmetry breaking gives rise to 4 Nambu-Goldstone modes and 14 Higgs modes. At lower energy one of the four NG modes becomes the Higgs boson with small mass. This is the mode measured in experiments with the longitudinal NMR, and the Higgs mass corresponds to the Leggett frequency $M_{\rm H}=\hbar Ω_L$. The formation of the Higgs mass is the result of the violation of the hidden spin-orbit symmetry at low energy. In this scenario the symmetry breaking energy scale $Δ$ (the gap in the fermionic spectrum) and the Higgs mass scale $M_{\rm H}$ are highly separated: $M_{\rm H}\ll Δ$. On the particle physics side we consider the model inspired by the models of \cite{dobrescu,Yamawaki}. At high energies the $SU(3)$ symmetry is assumed that relates the left - handed top and bottom quarks to the additional fermion $χ_L$. This symmetry is softly broken at low energies. As a result the only CP - even Goldstone boson acquires a mass and may be considered as the candidate for the role of the $125$ GeV scalar boson. We consider the condensation pattern different from the one typical for the top - seesaw models, where the condensate $< \bar{t}_Lχ_R >$ is off - diagonal. In our case the condensates are mostly diagonal. Unlike \cite{dobrescu,Yamawaki} the explicit mass terms are absent and the soft breaking of $SU(3)$ symmetry is given solely by the four - fermion terms. This reveals the complete analogy with $^3$He, where there is no explicit mass term and the spin - orbit interaction has the form of the four - fermion interaction.

hep-ph↗

arXiv2015

Emergent gravity and chiral anomaly in Dirac semimetals in the presence of dislocations

We consider the recently discovered Dirac semimetals with two Dirac points $\pm{\bf K}$. In the presence of elastic deformations each fermion propagates in a curved space, whose metric is defined by the expansion of the effective Hamiltonian near the Dirac point. Besides, there is the emergent electromagnetic field that is defined by the shift of the Dirac point. We consider the case, when the deformations are caused by the dislocations. The dislocation carries singular torsion and the quantized flux of emergent magnetic field. Both torsion singularity and emergent magnetic flux may be observed in the scattering of quasiparticles on the dislocation due to Stodolsky and Aharonov - Bohm effects. We discuss quantum anomalies in the quasiparticle currents in the presence of emergent gauge and gravitational fields and the external electromagnetic field. In particular, it is demonstrated, that in the presence of external electric field the quasiparticles/holes are pumped from vacuum along the dislocation. The appeared chiral imbalance along the dislocation drives the analogue of chiral magnetic effect, that is the appearance of electric current along the dislocation.

cond-mat.mes-hall↗

arXiv2015

Emergent geometry experienced by fermions in graphene in the presence of dislocations

In graphene in the presence of strain the elasticity theory metric naturally appears. However, this is not the one experienced by fermionic quasiparticles. Fermions propagate in curved space, whose metric is defined by expansion of the effective Hamiltonian near the topologically protected Fermi point. We discuss relation between both types of metric for different parametrizations of graphene surface. Next, we extend our consideration to the case, when the dislocations are present. We consider the situation, when the deformation is described by elasticity theory and calculate both torsion and emergent magnetic field carried by the dislocation. The dislocation carries singular torsion in addition to the quantized flux of emergent magnetic field. Both may be observed in the scattering of quasiparticles on the dislocation. Emergent magnetic field flux manifests itself in the Aharonov - Bohm effect while the torsion singularity results in Stodolsky effect.

cond-mat.mes-hall↗

arXiv2015

Schwinger - Dyson equation and NJL approximation in massive gauge theory with fermions

We consider massive $SU(N)$ gauge theory with fermions. Gauge bosons become massive due to the interaction with the scalar field, whose vacuum average provides the spontaneous breakdown of gauge symmetry. We investigate Dyson - Schwinger equation for the fermion propagator written in ladder approximation and in Landau gauge. Our analysis demonstrates that the chiral symmetry breaking in the considered theory is the strong coupling phenomenon. There are the indications that there appears the second order phase transition between chirally broken and symmetric phases of the theory at the value of coupling constant $α_c = (1+γ)\times \fracπ{3}\times \frac{1}{2 C_2(F)}$, where $0<γ<1$, and $γ$ depends on the scale, at which the fluctuations of the scalar field destroy the gauge boson mass. In the broken phase near the critical value of $α$ the Dyson - Schwinger equation is approximated well by the gap equation of the effective Nambu - Joina - Lasinio model with the value of cutoff around gauge boson mass $M$ and the effective four - fermion coupling constant $\frac{4 πα}{M^2}\times \frac{2C_2(F)}{N}$. The dynamical fermion mass $m$ may be essentially smaller than $M$.

hep-ph↗