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M. Bordag

Publications and source records attributed to M. Bordag.

At least 55 records · Page 3Linked to original sources
arXiv2012

Comment on "Casimir Force and In Situ Surface Potential Measurements on Nanomembranes"

Recently D. Garcia-Sanches, K. Y. Fong, H. Bhaskaran, S. Lamoreaux, and H. X. Tang [Phys. Rev. Lett. v.109, 027202 (2012)] claimed that the frequency shift of an oscillator under the influence of the residual electric and Casimir forces is best described by the Drude model approach to the Casimir force and excludes the plasma model approach. We demonstrate that calculations in support of this claim are performed incorrectly and that the measured data are in strong disagreement with both theoretical approaches to the Casimir force, thus, suggesting the presence of an unaccounted systematic error in the data.

quant-ph↗
arXiv2012

Thermal Casimir effect in the interaction of graphene with dielectrics and metals

We investigate the thermal Casimir interaction of a suspended graphene described by the Dirac model with a plate made of dielectric or metallic materials. The reflection coefficients on graphene expressed in terms of a temperature-dependent polarization tensor are used. We demonstrate that for a graphene with nonzero mass gap parameter the Casimir free energy remains nearly constant (and the thermal correction negligibly small) over some temperature interval. For the interaction of graphene with metallic plate, the free energy is nearly the same, irrespective of whether the metal is nonmagnetic or magnetic and whether it is described using the Drude- or plasma-model approaches. The free energy computed using the Dirac model was compared with that computed using the hydrodynamic model of graphene and big differences accessible for experimental observation have been found. For dielectric and nonmagnetic metallic plates described by the Drude model these differences vanish with increasing temperature (separation). However, for nonmagnetic metals described by the plasma model and for magnetic metals, a severe dependence on the chosen theoretical description of graphene remains even at high temperature. In all cases the analytic asymptotic expressions for the free energy at high temperature are obtained and found in a very good agreement with the results of numerical computations.

cond-mat.mtrl-sci↗
arXiv2012

The type of the phase transition and coupling values in λϕ^4 model

The temperature induced phase transition is investigated in the one-component scalar field ϕ^4 model on the lattice. Using the GPU cluster a huge amount of Monte Carlo simulation data is collected for a wide interval of coupling values. This gives a possibility to determine the low bound on the coupling constant λ_0 when the transition happens and investigate its type. We found that for the values of λclose to this bound a weak-first-order phase transition takes place. It converts into a second order one with the increase of λ. A comparison with the results obtained in analytic and numeric calculations by other authors is given.

hep-lat↗
arXiv2012

Comparison between experiment and theory for the thermal Casimir force

We analyze recent experiments on measuring the thermal Casimir force with account of possible background effects. Special attention is paid to the validity of the proximity force approximation (PFA) used in the comparison between the experimental data and computational results in experiments employing a sphere-plate geometry. The PFA results are compared with the exact results where they are available. The possibility to use fitting procedures in theory-experiment comparison is discussed. On this basis we reconsider experiments exploiting spherical lenses of centimeter-size radii.

quant-ph↗
arXiv2012

Groundstate projection of the charged SU(2) polarization tensor in a chromomagnetic background field

We consider the polarization tensor of a color charged gluon field in SU(2) in the background of a homogeneous color magnetic field and calculate its projection onto the lower (tachyonic) state. We obtain a quite simple representation of the polarization tensor in terms of double parametric integral. We provide examples for the numerical evaluation of the polarization tensor in this case. Also, we consider the corresponding expressions at high temperature and calculate the charged gluon magnetic mass in this limit. We conclude that radiation corrections stabilize the ground state. Applications of the results obtained are discussed.

hep-th↗
arXiv2011

Quantum vacuum interaction between two sine-Gordon kinks

We calculate the quantum vacuum interaction energy between two kinks of the sine-Gordon equation. Using the $TGTG$--formula, the problem is reduced to the known formulas for quantum fluctuations in the background of a single kink. This interaction induces an attractive force between the kinks in parallel to the Casimir force between conducting mirrors.

hep-th↗
arXiv2011

On the corrections beyond proximity force approximation (PFA)

We recalculate the first analytic correction beyond PFA for a sphere in front of a plane for a scalar field and for the electromagnetic field. We use the method of Bordag and Nikolaev [J.Phys.A, {\bf 41} (2008) p.164002]. We confirm their result for Dirichlet boundary conditions whereas we find a different one for Robin, Neumann and conductor boundary conditions. The difference can be traced back to a sign error. As a result, the corrections depend on the Robin parameter. Agreement is found with a very recent method of derivative expansion.

hep-th↗
arXiv2011

Drude model and Lifshitz formula

Since nearly 10 years, it is known that inserting the permittivity of the Drude model into the Lifshitz formula for free energy causes a violation of the third law of thermodynamics. In this paper we show that the standard Matsubara formulation for free energy contains a contribution that is non-perturbative in the relaxation parameter. We argue that the correct formula must have a perturbative expansion and conclude that the standard Matsubara formulation with the permittivity of the Drude model inserted is not correct. We trace the non-perturbative contribution in the complex frequency plane, where it shows up as a self-intersection or a bifurcation of the integration path.

quant-ph↗
arXiv2011

Observation of the Thermal Casimir Force is Open to Question

We discuss theoretical predictions for the thermal Casimir force and compare them with available experimental data. Special attention is paid to the recent claim of the observation of that effect, as predicted by the Drude model approach. We show that this claim is in contradiction with a number of experiments reported so far. We suggest that the experimental errors, as reported in support of the observation of the thermal Casimir force, are significantly underestimated. Furthermore, the experimental data at separations above $3\,μ$m are shown to be in agreement not with the Drude model approach, as is claimed, but with the plasma model. The seeming agreement of the data with the Drude model at separations below $3\,μ$m is explained by the use of an inadequate formulation of the proximity force approximation.

quant-ph↗
arXiv2011

On the type of the temperature phase transition in phi-4 model

The temperature induced phase transition is investigated in the one-component scalar field ϕ^4 model on a lattice by using Monte Carlo simulations. Using the GPGPU technology a huge amount of data is collected that gives a possibility to determine the Linde-Weinberg low bound on the coupling constant λ_0 and investigate the type of the phase transition for a wide interval of coupling values. It is found that for the values of λclose to this bound a weak-first-order phase transition happens. It converts into a second order phase transition with the increase of λ. A comparison with analytic calculations in continuum field theory and lattice simulations obtained by other authors is given.

hep-lat↗
arXiv2011

Quantum Fields bounded by one dimensional crystal plates

We get deeper understanding of the role played by boundary conditions in quantum field theory, by studying the structure of a scalar massless quantum field theory bounded by two one dimensional planar crystal plates. The system can also be understood as a massless scalar confined to propagate in the surface of a finite cylinder. We classify the most general type of regular behaved boundary conditions that the quantum field can satisfy, in accordance with the unitarity principle of quantum field theory. Also, we characterize the frequency spectrum for each quantum field theory, by computing the holomorphic spectral function. The spectral function is the starting point to compute the Casimir energy as a global function over the space of allowed boundary conditions for the quantum field theory.

math-ph↗
arXiv2010

On the Casimir entropy for a ball in front of a plane

The violation of the third law of thermodynamics for metals described by the Drude model and for dielectrics with finite \DC conductivity is one of the most interesting problems in the field of the Casimir effect. It manifests itself as a non-vanishing of the entropy for vanishing temperature. We review the relevant calculations for plane surfaces and calculate the corresponding contributions for a ball in front of a plane. In this geometry, these appear in much the same way as for parallel planes. We conclude that the violation of the 3rd law is not related to the infinite size of the planes.

quant-ph↗
arXiv2010

Vacuum energy between a sphere and a plane at finite temperature

We consider the Casimir effect for a sphere in front of a plane at finite temperature for scalar and electromagnetic fields and calculate the limiting cases. For small separation we compare the exact results with the corresponding ones obtained in proximity force approximation. For the scalar field with Dirichlet boundary conditions, the low temperature correction is of order $T^2$ like for parallel planes. For the electromagnetic field it is of order $T^4$. For high temperature we observe the usual picture that the leading order is given by the zeroth Matsubara frequency. The non-zero frequencies are exponentially suppressed except for the case of close separation.

quant-ph↗
arXiv2010

Polarization rotation and Casimir effect in suspended graphene films

The low-energy quasi-excitations in graphene are known to be described as Dirac fermions in 2+1 dimensions. Adopting field-theoretical approach we investigate the interaction of these quasi-particles with 3+1 dimensional electromagnetic field focusing on the optical properties of suspended graphene layers and their Casimir interaction with ideal conductor. The magnitude of predicted effects (the rotation of polarization of light and the Casimir force) appears to be well within modern experimental capabilities.

cond-mat.mes-hall↗
arXiv2009

On the definition of dielectric permittivity for media with temporal dispersion in the presence of free charge carriers

We show that in the presence of free charge carriers the definition of the frequency-dependent dielectric permittivity requires additional regularization. As an example, the dielectric permittivity of the Drude model is considered and its time-dependent counterpart is derived and analyzed. The respective electric displacement cannot be represented in terms of the standard Fourier integral. The regularization procedure allowing to circumvent these difficulties is suggested. For purpose of comparison it is shown that the frequency-dependent dielectric permittivity of insulators satisfies all rigorous mathematical criteria. This permits us to conclude that in the presence of free charge carriers the concept of dielectric permittivity is not as well defined as for insulators and we make a link to widely discussed puzzles in the theory of thermal Casimir force which might be caused by the use of such kind permittivities.

quant-ph↗
arXiv2009

Casimir interaction between a perfect conductor and graphene described by the Dirac model

We adopt the Dirac model for graphene and calculate the Casimir interaction energy between a plane suspended graphene sample and a parallel plane perfect conductor. This is done in two ways. First, we use the Quantum Field Theory (QFT) approach and evaluate the leading order diagram in a theory with 2+1 dimensional fermions interacting with 3+1 dimensional photons. Next, we consider an effective theory for the electromagnetic field with matching conditions induced by quantum quasi-particles in graphene. The first approach turns out to be the leading order in the coupling constant of the second one. The Casimir interaction for this system appears to be rather weak. It exhibits a strong dependence on the mass of the quasi-particles in graphene.

hep-th↗
arXiv2009

First analytic correction beyond PFA for the electromagnetic field in sphere-plane geometry

We consider the vacuum energy for a configuration of a sphere in front of a plane, both obeying conductor boundary condition, at small separation. For the separation becoming small we derive the first next-to-leading order of the asymptotic expansion in the separation-to-radius ratio $\ep$. This correction is of order $\ep$. In opposite to the scalar cases it contains also contributions proportional to logarithms in first and second order, $\ep \ln \ep$ and $\ep (\ln \ep)^2$. We compare this result with the available findings of numerical and experimental approaches.

hep-th↗