arXiv subjects

Nail Khusnutdinov

Publications and source records attributed to Nail Khusnutdinov.

18 recordsLinked to original sources

arXiv2026

Quest for particles production in the plane gravitational wave spacetime

Massless vector and scalar Green's functions are obtained in closed form for a plane gravitational wave spacetime using three independent methods: direct solution of the Green-function equation and construction via the DeWitt and Hadamard recursive schemes. The results coincide exactly with the DeWitt--Schwinger expansion, indicating no massless particles production in this background. Contrasting interpretations, based on Bogolyubov coefficient calculations predicting massless particle creation, are also addressed.

gr-qc↗

arXiv2024

The polarization tensor approach for Casimir effect

This paper gives a brief overview of the polarization tensor approach to the Casimir effect. The fundamental principles of this approach are discussed, along with its various applications to both three-dimensional and two-dimensional systems, with a focus on its implications for graphene.

cond-mat.mes-hall↗

arXiv2023

The Casimir effect for stack of graphenes

We consider a stack of parallel sheets composed of conducting planes with tensorial conductivities. Using the scattering matrix approach, we derive explicit formulas for the Casimir energy of two, three, and four planes, as well as a recurrence relation for arbitrary planes. Specifically, for a stack of graphene, we solve the recurrence relations and obtain formulas for the Casimir energy and force acting on the planes within the stack. Moreover, we calculate the binding energy in the graphene stack with graphite interplane separation, which amounts to $E_{ib} = 9.9$ meV/atom. Notably, the Casimir force on graphene sheets decreases rapidly for planes beyond the first one. In particular, for the second graphene layer in the stack, the force is $35$ times smaller than that experienced by the first layer.

cond-mat.mes-hall↗

arXiv2023

Casimir-Lifshitz force for moving graphene

We consider the system of two parallel sheets of graphene which are moving with relative parallel velocity $\vec{v}$ and calculate the Casimir energy by using the scattering approach. The energy has real and imaginary parts. The real part contains a velocity contribution to the force perpendicular to the sheets. The imaginary part is related to a friction force parallel to the graphene sheets. We prove that the friction appears if the relative velocity becomes greater than the velocity of Fermi and if the modulo of reflection coefficient is greater than the one which is significant for virtual photon production. We analyze in detail the real contribution to the Casimir energy for two systems -- graphene/graphene and ideal metal/graphene. In the non-relativistic case $v \ll v_F$, the relative correction to the Casimir energy $(\mathcal{E}_v - \mathcal{E}_0)/\mathcal{E}_0$ is proportional to the $(v/c)^2$ (the maximum value is $0.0033$ for the gapeless case and $v=v_F$) for the first system, and it is zero up to the Fermi velocity $v = v_F$ for system ideal metal/graphene.

cond-mat.mes-hall↗

arXiv2021

The low-temperature expansion of the Casimir-Polder free energy of an atom with graphene

We consider the low-temperature expansion of the Casimir-Polder free energy for an atom and graphene by using the Poisson representation of the free energy. We extend our previous analysis on the different relations between chemical potential $μ$ and mass gap parameter $m$. The key role plays the dependence of graphene conductivities on the $μ$ and $m$. For simplicity, we made the manifest calculations for zero values of the Fermi velocity. For $μ>m$ the thermal correction $\sim T^2$ and for $μ< m$ we confirm the recent result of Klimchitskaya and Mostepanenko, that the thermal correction $\sim T^5$. In the case of exact equality $μ=m$ the correction $\sim T$. This point is unstable and the system falls to the regime with $μ>m$ or $μ<m$. The analytical calculations are illustrated by numerical evaluations for the Hydrogen atom/graphene system.

cond-mat.mes-hall↗

arXiv2020

Self-action in Gravity

On a particle moving with variable acceleration in the flat space-time affects the self-force due to outgoing radiation. The gravitational fields bring an additional contribution to self-force due to scattering waves on the curved backgrounds. This force is not zero even for a particle at rest. A review of the self-interaction in the gravitational field is presented. We consider the self-force for the particle connected with the vector and scalar fields. Different backgrounds are considered -- black holes, stars, topological defects, and wormholes.

gr-qc↗

arXiv2020

Casimir-Polder force and torque for anisotropic molecules close to conducting planes and their effects on CO$_2$

We derive the Casimir-Polder force and Casimir torque expressions for an anisotropic molecule close to a conducting plane with a tensorial conductivity. We apply our general expressions to the case of a carbon dioxide CO$_2$ molecule close to a plane with pure Hall conductivity and to graphene. We show that the equilibrium position of this linear molecule is with its main axis perpendicular to the surface. We hence conjecture a possible way to exploit the Casimir torque to mechanically improve the performance of CO$_2$ separation membranes useful for an efficient atmospheric CO$_2$ reduction.

cond-mat.mes-hall↗

arXiv2020

Self-force and the Huygens principle

We consider a relation between the Huygens Principle (HP) in gravity and the self-interaction force. We show that the self-force for an electric particle in the plane gravitational wave space-time has no tail term even the vector Green function does not obey the HP. The reason for this observation is that even vector potential does not obey the HP, the electromagnetic field does obey.

gr-qc↗

arXiv2019

Signatures of Complex Optical Response in Casimir Interactions of Type I and II Weyl Semimetals

The Casimir interaction is induced by electromagnetic fluctuations between objects and it is strongly dependent upon the electronic and optical properties of the materials making up the objects. Here we investigate this ubiquitous interaction between Weyl semimetals, a class of 3D systems with low energy linear dispersion and nontrivial topology due to symmetry conditions and stemming from separated energy cones. A comprehensive examination of all components of the bulk conductivity tensor as well as the surface conductivity due to the Fermi arc states in real and imaginary frequency domains is presented using the Kubo formalism for Weyl semimetals with different degree of tilting of their linear energy cones. The Casimir energy is calculated using a generalized Lifhsitz approach, for which electromagnetic boundary conditions for anisotropic materials were derived and used. We find that the Casimir interaction between Weyl semimetals is metallic-like and its magnitude and characteristic distance dependence can be modified by the degree of tilting and chemical potential. The nontrivial topology plays a secondary role in the Casimir interaction of these 3D materials and thermal fluctuations are expected to have similar effects as in metallic systems.

cond-mat.mtrl-sci↗

arXiv2018

The low temperature behavior the Casimir-Polder energy for conductive plane

The low temperature expansion of the free energy of atom/plane system is considered for general symmetric form of tensor conductivity of the plane. It is shown that the first correction is proportional to second order of the temperature $\sim T^2$ and comes from TM mode. The agreement of the expansion and exact expressions for different models of conductivity is numerically demonstrated.

cond-mat.mes-hall↗

arXiv2018

The quest for Casimir repulsion between Chern-Simons surfaces

In this paper we critically reconsider the Casimir repulsion between surfaces that carry the Chern-Simons interaction (corresponding to the Hall type conductivity). We present a derivation of the Lifshitz formula valid for arbitrary planar geometries and discuss its properties. This analysis allows us to resolve some contradictions in the previous literature. We compute the Casimir energy for two surfaces that have constant longitudinal and Hall conductivities. The repulsion is possible only if both surfaces have Hall conductivities of the same sign. However, there is a critical value of the longitudinal conductivity above which the repulsion disappears. We also consider a model where both parity odd and parity even terms in the conductivity are produced by the polarization tensor of surface modes. In contrast to the previous publications L. Chen and S.-L. Wan, Phys. Rev. B84, 075149 (2011); B85, 115102 (2012), we include the parity anomaly term. This term ensures that the conductivities vanish for infinitely massive surface modes. We find that at least for a single mode regardless of the sign and value of its mass, there is no Casimir repulsion.

cond-mat.mes-hall↗

arXiv2018

Thermal Casimir and Casimir-Polder interactions in $N$ parallel 2D Dirac materials

The Casimir and Casimir-Polder interactions are investigated in a stack of equally spaced graphene layers. The optical response of the individual graphene is taken into account using gauge invariant components of the polarization tensor extended to the whole complex frequency plane. The planar symmetry for the electromagnetic boundary conditions is further used to obtain explicit forms for the Casimir energy stored in the stack and the Casimir-Polder energy between an atom above the stack. Our calculations show that these fluctuation induced interactions experience strong thermal effects due to the graphene Dirac-like energy spectrum. The spatial dispersion and temperature dependence in the optical response are also found to be important for enhancing the interactions especially at smaller separations. Analytical expressions for low and high temperature limits and their comparison with corresponding expressions for an infinitely conducting planar stack are further used to expand our understanding of Casimir and Casimir-Polder energies in Dirac materials. Our results may be useful to experimentalists as new ways to probe thermal effects at the nanoscale in such universal interactions.

cond-mat.mes-hall↗

arXiv2016

The Casimir-Polder effect for a stack of conductive planes

The Casimir-Polder interaction between an atom and a multilayered system composed of infinitely thin planes is considered using the zeta-function regularization approach with summation of the zero-point energies. As a prototype material, each plane is represented by a graphene sheet whose optical response is described by a constant conductivity or Drude-Lorentz model conductivity. Asymptotic expressions for various separations are derived and compared to numerical calculations. We distinguish between large atom/plane limit, where retardation effects are prominent, and small atom/plane limit, where the typical van der Waals coefficient is found to be dependent on the number of graphenes and characteristic distances. The calculated energies for different atoms and graphene conductivity models brings forward the basic science of the Casimir-Polder effect and suggests ways to manipulate this interaction experimentally.

cond-mat.mes-hall↗

arXiv2015

The Casimir effect for a stack of conductive planes

The Casimir interaction in a stack of equally spaced infinitely thin layers is investigated within the zero-frequency mode summation method. The response properties are considered to be described by a constant conductivity or by a Drude-Lorentz model with a finite set of oscillators consistent with the optical characteristics for graphite. It is found that the asymptotic distance dependence is affected significantly by the specific response. While the energy is $\sim 1/d^3$ for the constant conductivity model, the energy exhibits fractional dependence $\sim 1/d^{5/2}$ for the Drude-Lorentz description. The Casimir force on a plane is also strongly dependent upon the particular plane location in the stack. Furthermore, the calculated Casimir energy within the Drude-Lorentz model yields results in good agreement with measured cohesion energy in graphite.

cond-mat.mes-hall↗

arXiv2014

Casimir energy for surfaces with constant conductivity

We consider the vacuum energy of the electromagnetic field in systems characterized by a constant conductivity using the zeta-regularization approach. The interaction in two cases is investigated: two infinitely thin parallel sheets and an infinitely thin spherical shell. We found that the Casimir energy for the planar system is always attractive and it has the same characteristic distance dependence as the interaction for two perfect semi-infinite metals. The Casimir energy for the spherical shell depends on the inverse radius of the sphere, but it maybe negative or positive depending on the value of the conductivity. If the conductivity is less than a certain critical value, the interaction is attractive, otherwise the Casimir force is repulsive regardless of the spherical shell radius.

quant-ph↗

arXiv2014

The Casimir-Polder interaction an atom with spherical shell

The Casimir-Polder and van der Waals interaction energy of an atom with infinitely thin sphere with finite conductivity is investigated in the framework of the hydrodynamic approach. We put the sphere into spherical cavity inside the infinite dielectric media, then calculate the energy of vacuum fluctuations in the context of the zeta-function approach. The energy for a single atom is obtained by rarefying media. The Casimir-Polder expression for an atom and plate is recovered in the limit of the infinite radius of the sphere. Assuming a finite radius of the sphere, the interaction energy of an atom falls down monotonic as third power of distance between atom and sphere for short distance and as seventh power for large distance from the sphere.

quant-ph↗

arXiv2014

Self-interaction for particles in the wormhole space-times

The self-energy and self-force for particles with electric and scalar charges at rest in the space-time of massless and massive wormholes are considered. The particle with electric charge is always attracted to wormhole throat for arbitrary profile of the throat. The self-force for scalar particle shows different behavior depending on the non-minimal coupling. The self-force for massive scalar field is localized close to the throat of the wormhole.

gr-qc↗

arXiv2014

Bremstrahlung in wormhole spacetime with infinitely short throat

We consider the total energy loss and spectral density of uniformly moving electrically charged particles in the spacetime of a wormhole with an infinitely short throat. We show that the total energy loss $\mathcal{E} \sim e^2vγa^2/b^3$, where $γ$ is relativistic factor, $a$ is the radius of the wormhole's throat and $b$ is the impact factor. The spectrum of the energy for particles radially moving through the wormhole's throat $\mathcal{E} \sim e^2vγ/a$. The spectral density of the total energy has a maximum at frequency $ω_m \sim vγ/b$ and at $ω_m \sim vγ/a$ for radial motion.

gr-qc↗