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D. Vassilevich

Publications and source records attributed to D. Vassilevich.

18 recordsLinked to original sources
arXiv2024

Impurities in graphene and their influence on the Casimir interaction

We study the influence of impurities in graphene described by a scattering rate $\Gamma$ on the Casimir interaction between graphene and an ideal conductor or between two identical sheets of graphene at zero temperature and chemical potential. To this end, we compute the polarization tensor of quasiparticles in graphene and corresponding conductivities for TE and TM channels. The Casimir energy density is evaluated with the help of the Lifshitz formula. We find that depending on the value of mass gap parameter the presence of $\Gamma$ may lead to a slight damping or to a considerable enhancement of the Casimir interaction.

cond-mat.mes-hall↗
arXiv2021

Bulk contributions to the Casimir interaction of Dirac materials

Exploiting methods of Quantum Field Theory we compute the bulk polarization tensor and bulk dielectric functions for Dirac materials in the presence of a mass gap, chemical potential, and finite temperature. Using these results (and neglecting eventual boundary effects), we study the Casimir interaction of Dirac materials. We describe in detail the characteristic features of the dielectric functions and their influence on the Casimir pressure.

cond-mat.mes-hall↗
arXiv2021

Quantum Dirac fermions in half space and their interaction with electromagnetic field

We study the polarization tensor of a Dirac field in $(3+1)$ dimensions confined to a half space -- a problem motivated by applications to the condensed matter physics, and to Topological Insulators in particular. Although the Pauli-Villars regularization scheme has a number of advantages, like explicit gauge invariance and decoupling of heavy modes, it is not applicable on manifolds with boundaries. Here, we modify this scheme by giving an axial mass to the regulators and to the physical field. We compute the renormalized polarization tensor in coordinate representation. We discuss then the induced Chern-Simons type action on the boundary and compare it to the effective action of a $(2+1)$ dimensional Dirac fermion.

hep-th↗
arXiv2019

Soliton Fermionic number from the heat kernel expansion

We consider different methods of calculating the (fractional) fermion number of solitons based on the heat kernel expansion. We derive a formula for the localized eta function a more systematic version of the derivative expansion for spectral assymmetry and that provides a more systematic version of the derivative expansion for spectral asymmetry and compute the fermion number in a multiflavour extension of the Goldstone-Wilczek model.We also propose an improved expansionof the heat kernelthat allows the tackling ofthe convergence issues and permits an automated computation of the coefficients

hep-th↗
arXiv2018

Nearly associative deformation quantization

We study several classes of non-associative algebras as possible candidates for deformation quantization in the direction of a Poisson bracket that does not satisfy Jacobi identities. We show that in fact alternative deformation quantization algebras require the Jacobi identities on the Poisson bracket and, under very general assumptions, are associative. At the same time, flexible deformation quantization algebras exist for any Poisson bracket.

math-ph↗
arXiv2018

Casimir interaction of strained graphene

We calculate the Casimir interaction of two freestanding graphene samples under uniaxial strain. Our approach fully takes retardation and dispersion into account and is based on quantum field theoretical expressions for conductivities in terms of the polarization operator. The force shows a rather weak dependence on the realistic values of strain, changing just by a few percent in its maximum as compared to the non-strained case.

cond-mat.mes-hall↗
arXiv2017

Parity anomaly in four dimensions

In an analogy to the odd-dimensional case we define the parity anomaly as the part of the one-loop effective action for fermions associated with spectral asymmetry of the Dirac operator. This quantity is computed directly on four-dimensional manifolds with boundary and related to the Chern-Simons current on the boundary. Despite a quite unusual Chern-Simons level obtained, the action is gauge invariant and passes all consistency checks.

hep-th↗
arXiv2017

Enhanced Casimir effect for doped graphene

We analyze the Casimir interaction of doped graphene. To this end we derive a simple expression for the finite temperature polarization tensor with a chemical potential. It is found that doping leads to a strong enhancement of the Casimir force reaching almost $60\%$ in quite realistic situations. This result should be important for planning and interpreting the Casimir measurements, especially taking into account that the Casimir interaction of undoped graphene is rather weak.

cond-mat.mes-hall↗
arXiv2012

Spectral action beyond the weak-field approximation

The spectral action for a non-compact commutative spectral triple is computed covariantly in a gauge perturbation up to order 2 in full generality. In the ultraviolet regime, $p\to\infty$, the action decays as $1/p^4$ in any even dimension.

hep-th↗
arXiv2010

Graviton 1-loop partition function for 3-dimensional massive gravity

The graviton 1-loop partition function in Euclidean topologically massive gravity (TMG) is calculated using heat kernel techniques. The partition function does not factorize holomorphically, and at the chiral point it has the structure expected from a logarithmic conformal field theory. This gives strong evidence for the proposal that the dual conformal field theory to TMG at the chiral point is indeed logarithmic. We also generalize our results to new massive gravity.

hep-th↗
arXiv2002

Heat kernels and zeta-function regularization for the mass of the supersymmetric kink

We apply zeta-function regularization to the kink and susy kink and compute its quantum mass. We fix ambiguities by the renormalization condition that the quantum mass vanishes as one lets the mass gap tend to infinity while keeping scattering data fixed. As an alternative we write the regulated sum over zero point energies in terms of the heat kernel and apply standard heat kernel subtractions. Finally we discuss to what extent these procedures are equivalent to the usual renormalization conditions that tadpoles vanish.

hep-th↗
arXiv2002

Non-existence of a dilaton gravity action for the exact string black hole

We prove that no local diffeomorphism invariant two-dimensional theory of the metric and the dilaton without higher derivatives can describe the exact string black hole solution found a decade ago by Dijkgraaf, Verlinde and Verlinde. One of the key points in this proof is the concept of dilaton-shift invariance. We present and solve (classically) all dilaton-shift invariant theories of two-dimensional dilaton gravity. Two such models, resembling the exact string black hole and generalizing the CGHS model, are discussed explicitly.

hep-th↗
arXiv2002

Duality symmetry of the p-form effective action and super trace of the twisted de Rham complex

We consider quantum p-form fields interacting with a background dilaton. We calculate the variation with respect to the dilaton of a difference of the effective actions in the models related by a duality transformation. We show that this variation is defined essentially by the supertrace of the twisted de Rham complex. The supertrace is then evaluated on a manifold of an arbitrary dimension, with or without boundary.

hep-th↗
arXiv2001

Area spectrum in Lorentz covariant loop gravity

We use the manifestly Lorentz covariant canonical formalism to evaluate eigenvalues of the area operator acting on Wilson lines. To this end we modify the standard definition of the loop states to make it applicable to the present case of non-commutative connections. The area operator is diagonalized by using the usual shift ambiguity in definition of the connection. The eigenvalues are then expressed through quadratic Casimir operators. No dependence on the Immirzi parameter appears.

gr-qc↗
arXiv2001

Multiple reflection expansion and heat kernel coefficients

We propose the multiple reflection expansion as a tool for the calculation of heat kernel coefficients. As an example, we give the coefficients for a sphere as a finite sum over reflections, obtaining as a byproduct a relation between the coefficients for Dirichlet and Neumann boundary conditions. Further, we calculate the heat kernel coefficients for the most general matching conditions on the surface of a sphere, including those cases corresponding to the presence of delta and delta prime background potentials. In the latter case, the multiple reflection expansion is shown to be non-convergent.

hep-th↗
arXiv1999

Extended chiral Group and Scalar Diquarks

We introduce extended chiral transformation, which depends both on pseudoscalar and diquark fields as parameters and determine its group structure. Assuming soft symmetry breaking in diquark sector, bosonisation of a quasi-Goldstone $ud$-diquark is performed. In the chiral limit the $ud$-diquark mass is defined by the gluon condensate, $m_{ud}\approx 300 MeV$. The diquark charge radius is $ ^{1/2}\approx 0.5 fm$. We consider also the flavour triplet of scalar diquarks $(ud)$, $(us)$ and $(ds)$ together with pseudoscalar mesons and calculate diquark masses and decay constants in terms of meson parameters and the gluon condensate.

hep-ph↗
arXiv1998

On the ground state energy for a penetrable sphere and for a dielectric ball

We analyse the ultraviolet divergencies in the ground state energy for a penetrable sphere and a dielectric ball. We argue that for massless fields subtraction of the ``empty space'' or the ``unbounded medium'' contribution is not enough to make the ground state energy finite whenever the heat kernel coefficient $a_2$ is not zero. It turns out that $a_2\ne 0$ for a penetrable sphere, a general dielectric background and the dielectric ball. To our surprise, for more singular configurations, as in the presence of sharp boundaries, the heat kernel coefficients behave to some extend better than in the corresponding smooth cases, making, for instance, the dilute dielectric ball a well defined problem.

hep-th↗