arXiv subjects

M. Bordag

Publications and source records attributed to M. Bordag.

At least 19 recordsLinked to original sources

arXiv2025

Charged scalar bosons under rotation and acceleration

Creation of charged spinless bosons from vacuum in the rigidly rotating frame is studied in presence of the external static electromagnetic fields, being formed either in the resting, or in the general rotating or in the local-flat frames. It is shown that the description remains the same in the resting and the local-flat frames. More specifically, the case of a solenoid (magnetic flux tube) embedded into the rotating empty cylinder (rotation frame) is studied in presence or absence of a static square electric potential well $eA_0$. A supervortex of a spinless-boson field can be created from vacuum when the rotation frequency exceeds a critical value $\Omega_c$. It is shown that $\Omega_c$ is smaller provided the solenoid rests in the resting frame. Then the case is considered when the rotating frame additionally moves with acceleration $\vec{w}(\vec{r})\neq 0$. A specific case $w(r)=G/r$ for $G=const$ is treated explicitly. It is shown that for $G<0$ the charged spinless-boson vortex can be created in rapidly rotating system even in the limit when the magnetic and electric fields tend to zero.

hep-ph↗

arXiv2025

Generation of a scalar vortex in a rotational frame

We consider generation from the vacuum of a scalar charged field in a rigidly rotating frame. Adding an external magnetic field opens the way to Bose condensation of the field. This phenomenon has been studied for external uniform magnetic field occupying the whole volume of the uniformly rotating cylindrical system of finite radius $R$ with a Dirichlet boundary condition imposed on it. Besides continuing this study, we consider the field formed by a flux tube of small radius. We find numerical solutions of the Ginzburg-Pitaevskii equation for the charged scalar field, the critical rotation frequencies, the mean radii and the condensate energies, and compare them with those found in a linearization scheme and with approximate analytical solutions. We show that for the same input parameters the energy of the condensate in the case of the flux tube is lower than in the case of uniform magnetic field in the whole cylinder.

hep-ph↗

arXiv2025

Comment on "Electric conductivity of graphene: Kubo model versus a nonlocal quantum field theory model (arXiv:2403.02279v3)"

Recently, Rodriguez-Lopez, Wang, and Antezza [Phys. Rev. B v.111, 115428 (2025)] compared the theoretical descriptions of electric conductivity of graphene given by the Kubo model and quantum field theory in terms of the polarization tensor. According to this article, in the spatially nonlocal case, the quantum field theoretical description contains ``hard inconsistencies". By modifying the equality, which relates the conductivity and polarization expressions, the predictions of quantum field theory were revised and brought in agreement with those following from the nonrelativistic Kubo model. Here, it is shown that this modification violates the requirement of gauge invariance and, thus, is unacceptable. By comparing both theoretical approaches, we demonstrate that all the results obtained within quantum field theory are physically well justified whereas an application of the modified expression for the conductivity of graphene leads to the consequences of nonphysical character.

cond-mat.mes-hall↗

arXiv2025

Casimir effect for scalar field rotating on a disk

We compute the vacuum energy of a scalar field rotating with angular velocity $\Omega$ on a disk of radius $R$ and with Dirichlet boundary conditions. The rotation is introduced by a metric obtained by a Galilean transformation from a rest frame. The constraint $\Omega R<c$ must be obeyed to maintain causality. To compute the vacuum energy, we use an imaginary frequency representation and the well-known uniform asymptotic expansion of the Bessel function. We use the zeta-functional regularization and separate the divergent contributions, which we discuss in terms of the heat kernel coefficients. The divergences are found to be independent of rotation. The renormalized finite part of the vacuum energy is negative and becomes more negative for larger rotation frequencies.

hep-th↗

arXiv2025

Casimir effect with an unstable mode

We consider the Casimir effect in a (1+1)-dimensional model with a critical mode. Such a mode gives rise to a condensate described by the nonlinear Gross-Pitaevskii equation. In the condensate, there are two sources of the Casimir force; one is the conventional one resulting from the fluctuations, the other follows from the condensate. We consider three simple models that allow for condensate solutions in terms of elliptic Jacobi functions. We also investigate a method for obtaining approximate solutions and show its range of applicability. In all three examples we compute the condensate energy. In one example with a finite interval with Robin boundary conditions on one side and Dirichlet conditions on the other side, we calculate the vacuum energy and the Casimir force. There is a competition between the forces from the condensate and the fluctuations. We mention that the force from the condensate is always repulsive.

quant-ph↗

arXiv2024

On the convergence of the polarization tensor in space-time of three dimensions

In this paper, we consider the convergence properties of the polarization tensor of graphene obtained in the framework of thermal quantum field theory in three-dimensional space-time. During the last years, this problem attracted much attention in connection with calculation of the Casimir force in graphene systems and investigation of the electrical conductivity and reflectance of graphene sheets. There are contradictory statements in the literature, especially on whether this tensor has an ultraviolet divergence in three dimensions. Here, we analyze this problem using the well known method of dimensional regularization. It is shown that the thermal correction to the polarization tensor is finite at any $D$, whereas its zero-temperature part behaves differently for $D=3$ and 4. For $D=3$, it is obtained by the analytic continuation with no subtracting infinitely large terms. As to the space-time of $D=4$, the finite result for the polarization tensor at zero temperature is found after subtracting the pole term. Our results are in agreement with previous calculations of the polarization tensor at both zero and nonzero temperature. This opens possibility for a wider application of the quantum field theoretical approach in investigations of graphene and other two-dimensional novel materials.

hep-th↗

arXiv2023

Tachyon condensation in a chromomagnetic center-vortex background

The chromomagnetic vacuum of SU(2) gluodynamics is considered in the background of a finite radius flux tube (center-vortex) with homogeneous field inside and zero field outside. In this background there are tachyonic modes. These modes cause an instability. It is assumed that the selfinteraction of these modes stops the creation of gluons and that a condensate will be formed. For constant condensates, the minimum of the effective potential is found on the tree level. In the background of these condensates, all tachyonic modes acquire nonzero, real masses which will result in a real effective potential of this system. Considering only the tachyonic modes and adding the energy of the background field, the total energy is found to have a minimum at some value of the background field, which depends on the coupling of the initial SU(2) model. For small coupling, this dependence is polynomial in distinction from the Savvidy vacuum where it is exponentially suppressed. The minimum of this energy will deepens with shrinking radius of the flux tube. It can be expected that this process can be stopped by adding quantum effects. Using the high temperature expansion of the effective potential, it can be expected that the symmetry, which is broken by the condensate, will be restored at sufficiently high temperature.

hep-th↗

arXiv2023

Tachyon condensation in a chromomagnetic background field and the groundstate of QCD

I consider the chromomagnetic vacuum in SU(2). The effective Lagrangian in one loop approximation is known to have a minimum below zero which results in a spontaneously generated magnetic field. However, this minimum is not stable; the effective action has an imaginary part. Over the past decades, there were many attempts to handle this situation which all were at some point unsatisfactory. I propose an idea for a new solution by assuming that the tachyonic mode, at low temperature, acquires a condensate and, as a result, undergoes a phase transition like in the Higgs model. I consider the approximation where all gluon modes are dropped except for the tachyonic one. For this mode, we have a O(2)-model with quartic self-interaction in two dimensions. I apply the CJT (2PI) formalism in the Hartree approximation. As a result, at zero and low temperatures, a minimum of the effective action at a certain value of the condensate and of the background fields is observed and there is no imaginary part. Raising the temperature, this minimum becomes shallower and at a critical temperature, the perturbative state becomes that with lower effective potential; the symmetry is restored. The physical interpretation says that the unstable mode creates tachyons until these come into equilibrium with their repulsive self-interaction and form a condensate. The relation to the Mermin-Wagner theorem is discussed. }

hep-th↗

arXiv2021

Effective potential of gluodynamics in background of Polyakov loop and colormagnetic field

In SU(N) gluodynamics, above the de-confinement temperature, the effective potential has minima at non-zero $A_0$-background fields in the two-loop approximation. Also, it has a minimum at non-zero chromomagnetic background field, known as 'Savvidy'-vacuum, which shows up on the one-loop level. In this paper, we join these two approaches. We formulate, at finite temperature, the effective action, or the free energy, in SU(2) gluodynamics on the two-loop level, with both, $A_0$ background and magnetic background present at the same time, which was not done so far. We provide the necessary representations for both, effective numerical calculation and high-temperature expansions. The results are represented as a 3D plot of the real part of the effective potential. Also, we reproduce for zero either, the $A_0$-background or the magnetic background, the known minima and compare them. The imaginary part is, on the two-loop level, still present. We mention that, as is known from literature for the case without $A_0$-background, the imaginary part is compensated by the ring ('daisy') diagrams. However, our results reveal an unnatural, singular behavior of the effective potential in the region, where the imaginary part sets in. Our conclusion is that one has to go beyond the two-loop approximation and its ring improved version, in order to investigate the minimum of the effective action as a function of $A_0$ and chromomagnetic field, and its stability, at least in the approximation of superdaisy diagrams, i.e., the Hartree approximation in the CJT formalism.

hep-th↗

arXiv2021

A0--condensation in quark-gluon plasma with finite baryon density

In the present paper, we return to the problem on a spontaneous generation of the $A_0$-background field in QCD at finite temperature and include in addition a quark chemical potential, $μ$. We reproduce the known expressions in terms of Bernoulli's polynomials for the gluons and quarks using the same formalism. Then we calculate the $μ$-dependence, both for small $μ$ as expansion, and numerically for finite $μ$. One result is that the chemical potential only weakly changes the values of the condensed field, but quite strongly deepens the minima of the effective potential. The gauge dependence of the condensation is discussed in terms of Nielsen's identity. It also is expressed in terms of Polyakov's loop. Both these representations guarantee gauge invariance of the condensation phenomenon. Also, we discuss the dependence of the Polyakov loop in the minimum of the effective potential on the chemical potential.

hep-th↗

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

Vacuum energy for a scalar field with self-interaction in (1+1) dimensions

We calculate the vacuum (Casimir) energy for a scalar field with $ϕ^4$ self-interaction in (1+1) dimensions non perturbatively, i.e., in all orders of the self-interaction. We consider massive and massless fields in a finite box with Dirichlet boundary conditions and on the whole axis as well. For strong coupling, the vacuum energy is negative indicating some instability.

hep-th↗

arXiv2020

The closed piecewise uniform string revisited

We reconsider the composite string model introduced {30 years ago} to study the vacuum energy. The model consists of a scalar field, describing the transversal vibrations of a string consisting of piecewise constant sections with different tensions and mass densities, keeping the speed of light constant across the junctions. We consider the spectrum using transfer matrices and Chebyshev polynomials to get a closed formula for the eigenfrequencies. We calculate vacuum and free energy as well as the entropy of this system in two approaches, one using contour integration and another one using a Hurwitz zeta function. The latter results in a representation in terms of finite sums over polynomials. Several limiting cases are considered as well, for instance, the high-temperature expansion, which is expressed in terms of the heat kernel coefficients. The vacuum energy has no ultraviolet divergences, and the corresponding heat kernel coefficient $a_1$ is zero due to the constancy of the speed of light. This is in parallel to a similar situation in macroscopic electrodynamics with isorefractive boundary conditions.

hep-th↗

arXiv2020

Free energy and entropy for finite temperature quantum field theory under the influence of periodic backgrounds

The basic thermodynamic quantities for a non-interacting scalar field in a periodic potential composed of either a one-dimensional chain of Dirac $δ$-$δ^\prime$ functions or a specific potential with extended compact support are calculated. First, we consider the representation in terms of real frequencies (or one-particle energies). Then we turn the axis of frequency integration towards the imaginary axis by a finite angle, which allows for easy numerical evaluation, and finally turn completely to the imaginary frequencies and derive the corresponding Matsubara representation, which this way appears also for systems with band structure. In the limit case $T \to 0$ we confirm earlier results on the vacuum energy. We calculate for the mentioned examples the free energy and the entropy and generalize earlier results on negative entropy.

math-ph↗

arXiv2019

Revisiting the Casimir Energy with General Boundary Conditions, and applications in 1D Crystals

We obtain new expressions for the Casimir energy between plates that are mimicked by the most general possible boundary conditions allowed by the principles of quantum field theory. This result enables to provide the quantum vacuum energy for scalar fields propagating under the influence of a one-dimensional crystal represented by a periodic potential formed by an infinite array of identical potentials with compact support.

math-ph↗

arXiv2018

Photon dispersion relations in $A_0$-background

We calculate the photon dispersion relations generated by the quark loop in a quark-gluon plasma with the color $A_0$ background condensate $A_0^c = A_0^{c3} + A_0^{c8}$ = const. It is found that both transversal and longitudinal modes are exited. They have a gap at low momenta and are stable in high temperature approximation. The background fields act as imaginary chemical potentials and decrease the photon frequencies compared to the case of zero background. The comparison with QED plasma with chemical potential is discussed.

hep-ph↗

arXiv2018

On the entropy of a spherical plasma shell

Negative entropy was repeatedly observed in the Casimir effect caused by dissipation or geometry. However, it was restricted to subsystems. Recently the question about the entropy for a complete Casimir effect like configuration was raised. In the present paper we consider a spherical plasma shell which can be considered as a (crude) model for a giant carbon molecule (e.g., $C_{60}$). The entropy is free of ultraviolet divergences and its calculation does not need any regularization. We calculate the entropy numerically and demonstrate unambiguously the existence of a region where it takes negative values. This region is at small values of temperature and plasma frequency (in units of the radius).

quant-ph↗

arXiv2018

Entropy in some simple one-dimensional configurations

Continuing the discussion on negative entropy in Casimir-effect like configurations, we consider two simple one-dimensional examples. One is the s-wave contribution to a plasma sphere and the other a single delta function potential. Some information on generic background potential is gained applying Levinson's theorem. For the first example we find negative entropy. The one-dimensional examples are especially interesting as these do not require the subtraction of contributions growing with temperature faster than the classical limit.

quant-ph↗