Nonperturbative effects of vacuum polarization for a quasi-one-dimensional Dirac–Coulomb system with Z &gt; Z cr

Voronina

2018

Int. J. Mod. Phys. A

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Non-perturbative vacuum polarization effects are explored for a supercritical Dirac-Coulomb system with Z > Zcr,1 in 2+1 D, based on the original combination of analytical methods, computer algebra and numerical calculations, proposed recently in Refs.[1]- [3]. Both the vacuum charge density ρV P ( r) and vacuum energy EV P are considered. Due to a lot of details of calculation the whole work is divided into two parts I and II. Taking account of results, obtained in the part I [4] for ρV P , in the present part II the evaluation of the vacuum energy EV P is investigated with emphasis on the renormalization and convergence of the partial expansion for EV P . It is shown that the renormalization via fermionic loop turns out to be the universal tool, which removes the divergence of the theory both in the purely perturbative and essentially non-perturbative regimes of the vacuum polarization. The main result of calculation is that for a wide range of the system parameters in the overcritical region EV P turns out to be a rapidly decreasing function ∼ −η ef f Z 3 /R with η ef f > 0 and R being the size of the external Coulomb source. To the end the similarity in calculations of EV P in 2+1 and 3+1 D is discussed, and qualitative arguments are presented in favor of the possibility for complete screening of the classical electrostatic energy of the Coulomb source by the vacuum polarization effects for Z Zcr,1 in 3+1 D.

Section: Resultsmentioning

confidence: 99%

Section: Vacuum Polarization Energy For Z > Zcr1: General Propertiesmentioning

confidence: 96%

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Nonperturbative vacuum polarization effects in two-dimensional supercritical Dirac–Coulomb system II. Vacuum energy

Davydov

Voronina

2018

Int. J. Mod. Phys. A

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“…However, it should be noted that this approach contains a number of approximations too, and so the expression (41) is exact only in the vicinity of the corresponding Z cr , what is quite explicitly shown in Refs. [1]- [3]. The substantial difference between vacuum polarization effects in 2+1 and 3+1 D and those from the onedimensional case shows up also in that the renormalized density (40) is represented now as a infinite partial series in m j .…”

Section: The Divergencies and Renormalization Of The Vacuum Density Imentioning

confidence: 98%

“…Recently, in Refs. [1]- [3] an original combination of analytical methods, computer algebra tools and numerical calculations has shown that for a wide range of the system parameters in the one-dimensional Dirac-Coulomb problem the nonlinear effects could lead in the supercritical region to the behavior of the vacuum energy, substantially different from the perturbative quadratic growth, up to (almost) quadratic decrease into the negative region ∼ −|η|Z 2 . In the present paper, which is divided into two parts I and II, these methods are applied to the study of analogous vacuum polarization effects for a 2+1 Dirac-Coulomb system in the overcritical region.…”

Section: Introductionmentioning

confidence: 99%

Nonperturbative vacuum polarization effects in two-dimensional supercritical Dirac–Coulomb system I. Vacuum charge density

Davydov

Voronina

2018

Int. J. Mod. Phys. A

Self Cite

Based on the original combination of analytical methods, computer algebra tools and numerical calculations, proposed recently in Refs.[1]-[3], the non-perturbative vacuum polarization effects in the 2+1 D supercritical Dirac-Coulomb system with Z > Zcr,1 are explored. Both the vacuum charge density ρV P ( r) and vacuum energy EV P are considered. The main result of the work is that in the overcritical region EV P turns out to be a rapidly decreasing function ∼ −η ef f Z 3 /R with η ef f > 0 and R being the size of the external Coulomb source. Due to a lot of details of calculation the whole work is divided into two parts I and II. In the present part I we consider the evaluation and behavior of the vacuum density ρV P , which further is used in the part II for evaluation of the vacuum energy, with emphasis on the renormalization, convergence of the partial expansion for ρV P and behavior of the integral induced charge QV P in the overcritical region.

Ferromagnetic Phase in Graphene‐Based Planar Heterostructures Induced by Charged Impurity

Grashin

2019

Annalen der Physik

The spontaneous self-consistent generation of axial current and corresponding dipole-like magnetic field in a planar electron-positron system similar to graphene and related hetero-structures doped by charged impurity with charge Z is explored. It is shown that this effect takes place for Z ≥ Z * with Z * being a peculiar analogue of the Curie point in ferromagnetics. The properties of induced ferromagnetic state are studied in detail. It is shown also that the arising this way magnetic dipole leads to a significant decrease of the total Casimir (vacuum) energy of the system, which in turn provides its spontaneous generation above the "Curie point" Z ≥ Z * .