Nonperturbative vacuum polarization effects are explored for a supercritical Coulomb source with $Z>Z_{cr}$ in 1+1 D. Both the vacuum charge density $ρ_{vac}(x)$ and vacuum energy $E_{vac}$ are considered. It is shown that in the overcritical region the behavior of vacuum energy could be significantly different from perturbative quadratic growth up to decrease reaching large negative values.
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 $Z > Z_{cr,1}$ are explored. Both the vacuum charge density $ρ_{VP}(\vec{r})$ and vacuum energy $\mathcal{E}_{VP}$ are considered. The main result of the work is that in the overcritical region $\mathcal{E}_{VP}$ turns out to be a rapidly decreasing function $\sim - η_{eff}\, Z^3/R\, $ with $η_{eff}>0 $ and $R$ being the size of the external Coulomb so…
An expression for the density of a planar induced vacuum charge is obtained in a strong Coulomb potential in coordinate space. Treatment is based on a self-adjoint extension approach for constructing of the Green's function of a charged fermion in this potential. Induced vacuum charge density is calculated and analyzed at the subcritical and supercritical Coulomb potentials for massless and massive fermions. The behavior of the obtained vacuum charge density is investigated at long and short distances from the Coulomb center. The induced vacuum charge has a screening sign. Screening of a Coulo…
Non-perturbative vacuum polarization effects are explored for a supercritical Dirac-Coulomb system with $Z > Z_{cr,1}$ 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 $ρ_{VP}(\vec{r})$ and vacuum energy $\mathcal{E}_{VP}$ 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 $ρ_{VP}$, in the present part II the evaluation of the vacuum energy $\mathcal{E}_{…
We investigate wavepacket dynamics across supercritical barriers for the Klein-Gordon and Dirac equations. Our treatment is based on a multiple scattering expansion (MSE). For spin-0 particles, the MSE diverges, rendering invalid the use of the usual connection formulas for the scattering basis functions. In a time-dependent formulation, the divergent character of the MSE naturally accounts for charge creation at the barrier boundaries. In the Dirac case, the MSE converges and no charge is created. We show that this time-dependent charge behavior dynamics can adequately explain the Klein parad…
The Dirac equation for an electron in a finite dipole potential has been studied within the method of linear combination of atomic orbitals (LCAO). The Coulomb potential of the nuclei that compose a dipole is regularized, by considering the finite nuclear size. It is shown that if the dipole momentum reaches a certain critical value, the novel type of supercriticality occurs; namely, the wave function of the highest occupied electron bound state changes its localization from the negatively charged nucleus to the positively charged one. This phenomenon can be interpreted as a spontaneous creati…
Supercritical Coulomb center and excitonic instability in graphene
众所周知，石墨烯中的超临界库仑杂质存在具有复能量的共振态。我们发现，准粒子间隙的开放减少了虚部的能量，|ImE|，这些国家和稳定的系统。对于石墨烯中具有强库仑相互作用的无带隙准粒子，我们求解了电子-空穴束缚态的Bethe-Salpeter方程，并证明了当耦合足够强时，该方程具有快子解，α=e^2/κ \hbar v_F导致系统不稳定.在无规相位近似下，临界耦合系数α c =1.62，与库仑中心问题中的临界电荷相似。我们认为，激子不稳定性应解决通过形成一个激子凝聚和准粒子谱中的间隙产生。
The effective interaction of the electron magnetic moment anomaly with the Coulomb field of superheavy nuclei is investigated by taking into account its dynamical screening at small distances. The shift of the electronic levels, caused by this interaction, is considered for H-like atoms and for compact nuclear quasi-molecules, non-perturbatively both in $Zα$ and (partially) in $α/π$. It is shown that the levels shift reveals a non-monotonic behavior in the region $Zα>1$ and near the threshold of the lower continuum decreases both with the increasing the charge and with enlarging the size of th…
The Dirac equation with the Coulomb potential is studied. It is shown that there exists a new invariant in addition to the known Dirac and Johnson-Lippman ones. The solution of the Dirac equation, using the generalized invariant, and explicit expressions for the bispinors corresponding to the three sets of the invariants, their eigenvalues and quantum numbers are obtained. The general solution of the Dirac equation with the Coulomb potential is shown to contain free parameters, whose variation transforms one particular solution into any other and controls spatial electron probability amplitude…
The effect of supercritical charge impurities in graphene is very similar to the supercritical atomic collapses in QED for Z > 137, but with a much lower critical charge. In this sense graphene can be considered as a natural testing ground for the analysis of quantum field theory vacuum instabilities. We analyze the quantum transition from subcritical to supercritical charge regimes in gapped graphene in a common framework that preserves unitarity for any value of charge impurities. In the supercritical regime it is possible to introduce boundary conditions which control the singular behavior …
We study massless 1-dimensional Dirac-Coulomb Hamiltonians, that is, operators on the half-line of the form $D_{ω,λ}:=\begin{bmatrix}-\frac{λ+ω}{x}&-\partial_x \\ \partial_x & -\frac{λ-ω}{x}\end{bmatrix}$. We describe their closed realizations in the sense of the Hilbert space $L^2(\mathbb R_+,\mathbb C^2)$, allowing for complex values of the parameters $λ,ω$. In physical situations, $λ$ is proportional to the electric charge and $ω$ is related to the angular momentum. We focus on realizations of $D_{ω,λ}$ homogeneous of degree $-1$. They can be organized in a single holomorphic family of clos…
We explore the conditions for chiral symmetry breaking in reduced (or pseudo) quantum electrodynamics at finite temperature in connection with graphene and other 2D-materials with an underlying Dirac behavior of the charge carriers. By solving the corresponding Schwinger-Dyson equation in rainbow approximation, in a Landau-like gauge and neglecting wavefunction renormalization effects, we find the need of the coupling to exceed a critical value $α_c$ in order for chiral symmetry to be broken, in agreement with known results from other groups. In this supercritical regime, we add the effects of…
