Vacuum energy of one-dimensional supercritical Dirac–Coulomb system

The Casimir force between two short-range charge sources, embedded in a background of one dimensional massive Dirac fermions, is explored by means of the original ln [Wronskian] contour integration techniques. For identical sources with the same (positive) charge we find that in the non-perturbative region the Casimir interaction between them can reach sufficiently large negative values and simultaneously reveal the features of a long-range force in spite of nonzero fermion mass, that could significantly influence the properties of such quasi-one-dimensional QED systems. For large distances s between sources we recover that their mutual interaction is governed first of all by the structure of the discrete spectrum of a single source, in dependence on which it can be tuned to give an attractive, a repulsive, or an (almost) compensated Casimir force with various rates of the exponential fall-down, quite different from the standard exp(−2ms) law. By means of the same ln [Wronskian] techniques the case of two δ-sources is also considered in a self-consistent manner with similar results for variability of the Casimir force. A quite different behavior of the Casimir force is found for the antisymmetric source-anti-source system. In particular, in this case there is no possibility for a long-range interaction between sources. The asymptotics of the Casimir force follows the standard exp(−2ms) law. Moreover, for small separations between sources the Casimir force for symmetric and antisymmetric cases turns out to be of opposite sign.

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“…Applying further the same technique as in Refs. [2]- [4], [22]- [24] for the expression of the induced density in terms of TrG, one finds…”

Section: Casimir Forces In the Source-anti-source Systemmentioning

confidence: 99%

“…Since ρ vac (x) is odd from the very beginning, in contrast to symmetric case [30] and all the more to the one-dimensional QED systems with long-range external Coulomb sources considered in Refs. [2]- [4], the total induced charge vanishes now without any additional renormalization…”

Section: Casimir Forces In the Source-anti-source Systemmentioning

confidence: 99%

Casimir force variability in one-dimensional QED systems

2019

Self Cite

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“…WK contours in the complex energy plane, used for representation of the induced charge and current densities via contour integrals. The direction of contour integration is chosen in correspondence with (13).…”

Section: Evaluation Of the Induced Charge And Current Via Wk Techmentioning

confidence: 99%

“…The starting expression for the vacuum energy is quite analogous to the induced charge and current densities with the only principal difference that the energy should be further normalized on the free case [13,20,25]…”

Section: Casimir (Vacuum) Energy With Magnetic Polarization Effectsmentioning

confidence: 99%

“…For the planar DE there are known only single results, which concern either point-like Coulomb and string-like AB sources or a quite different background of vector and scalar Cornell potentials combined with an external magnetic field [8,12]. This circumstance makes impossible the evaluation of the Casimir (vacuum) energy via representing it as the sum of the integral of the total elastic scattering phase and the contribution of discrete spectrum, which is shown to be very powerful in purely Coulomb problems [3,[13][14][15]. However, elaborated recently in Refs.…”

Section: Introductionmentioning

confidence: 99%

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

Grashin

Sveshnikov

2019

Annalen der Physik

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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 * .

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