arXiv subjects

K. Sveshnikov

Publications and source records attributed to K. Sveshnikov.

18 recordsLinked to original sources

arXiv2023

Spontaneous emission in the supercritical QED: what is wrong and what is possible

Spontaneous positron emission, caused by the supercritical Coulomb source with charge $Z$ and size $R$, is explored in essentially non-perturbative approach with emphasis on the VP-energy $\cal E_{VP}$, considered as a function of the Coulomb source parameters $Z$ and $R$. The specific contribution to $\cal E_{VP}$, which appears in the supercritical case due to direct Coulomb interaction between VP-charge densities $\varrho_{VP}(\vec{r})$, is outlined and studied in detail. It is shown that after first levels diving into the lower continuum this contribution, being properly renormalized, turns out to be negative in contrast to the classical electrostatics and so could play an important role in spontaneous emission, especially for $Z$ just above the first $Z_{cr,1}$. The additional problems of spontaneous emission, caused by the lepton number conservation, are also discussed.

hep-ph↗

arXiv2022

Estimating the realistic start-up of spontaneous emission in the supercritical QED

The scenario of spontaneous positron emission, caused by the supercritical Coulomb source with charge $Z$ and size $R$, is explored in essentially non-perturbative approach with emphasis on the vacuum energy $\mathcal{E}_{VP}$\footnote{Throughout the paper the abbreviation "VP"\, stands for "vacuum polarization"\,.}, considered as a function of $R$ with fixed $Z>Z_{cr,1}\simeq 170$. It is shown that in the supercritical region the behavior of $\mathcal{E}_{VP}(R)$ turns out to be quite different in dependence on the value of the Coulomb charge $Z$. In particular, spontaneous emission becomes a visible effect starting only from $Z \sim 300$. With further growth of $Z$ its intensity increases very rapidly, which opens up the possibility for unambiguous detection. For such $Z$ the appearing picture of spontaneous emission turns out to be well-established and quite transparent in terms of the resonance decay combined with vacuum shells formation. The intimate, but crucial role of $\mathcal{E}_{VP}(R)$ in the total energy balance in the system is outlined. The additional problems of spontaneous emission, caused by the lepton number conservation, are also discussed.

hep-ph↗

arXiv2022

Super-critical QED-effects via VP-energy

The properties of the QED-vacuum energy $\hbox{$\cal E $}_{VP}$ under Coulomb super-criticality condition $Z>Z_{cr,1}$ are explored in essentially non-perturbative approach. It is shown that in the supercritical region $\hbox{$\cal E $}_{VP}$ is the decreasing function of the Coulomb source parameters, resulting in decay into the negative range as $\sim - Z^4/R$. The conditions, under which the emission of vacuum positrons can be unambiguously detected on the nuclear conversion pairs background, are also discussed. In particular, for a super-critical dummy nucleus with charge $Z$ and $R(Z) \simeq 1.2 \ (2.5\, Z)^{1/3}$ fm the lowest $1s$-level dives into the lower continuum at $Z_{cr,1} \simeq 170$ (the model of uniformly charged ball) or $Z_{cr,1} \simeq 173$ (the spherical shell model), whereupon there appears the vacuum shell with the induced charge (-$2|e|$) and the QED-vacuum becomes charged, but in both cases the actual threshold for reliable spontaneous positrons detection is not less than $Z^\ast \simeq 210$.

physics.atom-ph↗

arXiv2022

Lepton Number vs Coulomb Super-Criticality

The non-perturbative effects of QED-vacuum reconstruction under influence of a supercritical EM-source ($Z>Z_{cr,1}$) are considered in view of lepton number conservation. The question is here that if the vacuum shells formation and spontaneous positron emission, associated with discrete levels diving into the lower continuum, exist in reality, then it by no means should be a signal of new physics. The reason is that the emitted positrons carry away the lepton number equal to $(-1)\times$their total number, and so the corresponding amount of positive lepton number should be shared by VP-density, concentrated in vacuum shells. In this case instead of integer lepton number of real particles there should appear the lepton number VP-density. Otherwise either the lepton number conservation in such processes must be broken, or the spontaneous positron emission prohibited. The conditions, under which the emission of vacuum positrons can be unambiguously detected on the nuclear conversion pairs background, are also discussed.

physics.atom-ph↗

arXiv2019

Casimir force variability in one-dimensional QED systems

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 $\ln\text{[Wronskian]}$ 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 $\exp (-2 m s)$ law. By means of the same $\ln\text{[Wronskian]}$ techniques, the case of two $δ$-sources is also considered in a self-consistent manner with similar results for the 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 $\exp (-2 m s)$ law. Moreover, for small separations between sources, the Casimir force for symmetric and antisymmetric cases turns out to be of opposite sign.

hep-th↗

arXiv2019

Atomic H over plane: effective potential and level reconstruction

The behavior of atomic H in a semi-bounded space $z \geq 0$ with the condition of "not going through" the boundary (the surface $z=0$) for the electronic wavefunction (WF) is considered. It is shown that in a wide range of "not going through" condition parameters the effective atomic potential, treated as a function of the distance $h$ from H to the boundary plane, reveals a well pronounced minimum at certain finite but non-zero $h$, which describes the mode of "soaring" of the atom above the plane. In particular cases of Dirichlet and Neumann conditions the analysis of the soaring effect is based on the exact analytical solutions of the problem in terms of generalized spheroidal Coulomb functions. For $h$ varying between the regions $h \gg a_B$ and $h \ll a_B$ both the deformation of the electronic WF and the atomic state are studied in detail. In particular, for the Dirichlet condition the lowest $1s$ atomic state transforms into $2p$-level with quantum numbers $210$, the first excited ones $2s$ --- into $3p$ with numbers $310$, $2p$ with $m=0$ --- into $4f$ with numbers $430$, etc. At the same time, for Neumann condition the whole picture of the levels transmutation changes drastically. For a more general case of Robin (third type) condition the variational estimates, based on special type trial functions, as well as the direct numerical tools, realized by pertinent modification of the finite element method, are used. By means of the latter it is also shown that in the case of a sufficiently large positive affinity of the atom to the boundary plane a significant reconstruction of the lowest levels takes place, including the change of both the asymptotics and the general dependence on $h$.

physics.atom-ph↗

arXiv2018

Casimir (vacuum) energy in planar QED with strong coupling

The essentially non-perturbative vacuum polarization effects, caused by an extended external supercritical Coulomb source, are explored for a planar Dirac-Coulomb (DC) system with strong coupling (similar to graphene and graphene-based heterostructures). Taking account of results, obtained in \cite{partI2018} for the induced charge density $ρ_{VP}(\vec{r})$, in the present paper the evaluation of the Casimir (vacuum) energy $\mathcal{E}_{VP}$ is presented. The main result is that for a wide range of the system parameters in the overcritical region $\mathcal{E}_{VP}$ turns out to be a rapidly decreasing negative function $\sim - Z^3/R_0\, $ with $Z\, , R_0$ being the charge and the size of the external source. By an explicit calculation the possibility for complete screening of the electrostatic reflection self-energy of the external source by such polarization effects for $Z \gg Z_{cr,1}$ is demonstrated. The dependence of the Casimir energy on the screening of the Coulomb asymptotics of the external source at some $R_1>R_0$ is also explored in detail, and some peculiar effects in the partial channels with the lowest rotational numbers $m_j=\pm 1/2\, , \pm3/2$ in the screened case are also discussed.

cond-mat.mes-hall↗

arXiv2018

Essentially non-perturbative and peculiar polarization effects in planar QED with strong coupling

The essentially non-perturbative polarization effects are considered for a planar supercritical Dirac-Coulomb system with strong coupling (similar to graphene and graphene-based heterostructures) in terms of induced charge density $ρ_{VP}(\vec{r})$. The main attention is paid to the renormalization, convergence of the partial expansion and the behavior of $ρ_{VP}(\vec{r})$ and the integral induced charge $Q_{VP}$ in the overcritical region. The dependence of the induced density on the screening of the Coulomb asymptotics of the external source is also explored in detail. Some peculiar effects in the discrete spectrum with the lowest rotational numbers $m_j=\pm 1/2\, , \pm3/2$ in the screened case are detected and their possible role in the transition through corresponding $Z_{cr}$ is also discussed.

cond-mat.mes-hall↗

arXiv2016

Spontaneous spherical symmetry breaking in atomic confinement

The effect of spontaneous breaking of initial SO(3) symmetry is shown to be possible for an H-like atom in the ground state, when it is confined in a spherical box under general boundary conditions of "not going out" through the box surface (i.e. third kind or Robin's ones), for a wide range of physically reasonable values of system parameters. The reason is that such boundary conditions could yield a large magnitude of electronic wavefunction in some sector of the box boundary, what in turn promotes atomic displacement from the box center towards this part of the boundary, and so the underlying SO(3) symmetry spontaneously breaks. The emerging Goldstone modes, coinciding with rotations around the box center, restore the symmetry by spreading the atom over a spherical shell localized at some distances from the box center. Atomic confinement inside the cavity proceeds dynamically -- due to the boundary condition the deformation of electronic wavefunction near the boundary works as a spring, that returns the atomic nuclei back into the box volume.

physics.atom-ph↗

arXiv2013

Quantum confinement under Neumann condition: atomic H filled in a lattice of cavities

Energy spectrums of a nonrelativistic particle and an H-like atom in a spherical box of size R with general conditions of "not going out" through the box surface are explored. The lowest energy levels reconstruction is described from the point of view of their asymptotical behavior for large R. The role of von Neumann-Wigner level reflection/avoided crossing effect in this spectrum reconstruction is emphasized. The properties of atomic H ground state in a cell, formed by a spherical cavity with an outer potential shell and Neumann condition on the outward boundary, are studied in detail. Some of them turn out to be quite new. The relevance of such a cell to a cubic lattice of cavities, occupied by H, is discussed be means of first principles and assumptions of the Wigner-Seitz model.

physics.atom-ph↗

arXiv2005

On the numerical method of Casimir energy renormalization in the presence of logarithmical divergencies

A non-subtractive recipe of Casimir energy renormalization efficient in the presence of logarithmically divergent terms is proposed. It is demonstrated that it can be applied even then, when energy levels can be obtained only numerically and neither their asymptotical behavior, nor the analytic form of spectral equation is known. The results of calculations performed with this method are compared to those obtained by means of explicit subtraction of divergent terms from energy.

hep-th↗

arXiv2005

On the numerical technique of Casimir energy calculation

A non-subtractive recipe of Casimir energy renormalization efficient in the presence of logarithmically divergent terms is proposed. It is demonstrated that it can be applied even in such cases, when energy levels can be obtained only numerically whereas neither their asymptotical behavior, nor the analytical form of the corresponding spectral equation can be studied. The results of numerical calculations performed with this method are compared to those obtained by means of explicit subtraction of divergent terms from energy.

hep-th↗

arXiv2002

Topological and non-topological solutions in the 3-phase model of hybrid chiral bag

The 3-phase version of the hybrid chiral bag model, containing the phase of asymptotic freedom, the hadronization phase as well as the intermediate phase of constituent quarks, is proposed. For this model the self-consistent solutions, which take into account the fermion vacuum polarization effects, are found in 1+1 D. The renormalized total energy of the bag is studied as a function of its geometry and topological (baryon) number. It is shown that in the case of non-zero topological charge there exists a set of configurations being the local minima of the total energy of the bag and containing all the three phases, while in the non-topological case the minimum of the total energy of the bag corresponds to vanishing size of the phase of asymptotic freedom.

hep-ph↗

arXiv1999

Chiral Hybrid Bag Model with the Boson Field inside the Bag

The three-phase version of the hybrid chiral bag model, containing the phase of asymptotic freedom, the hadronization phase as well as the intermediate phase of constituent quarks, is proposed. For this model the self-consistent solution, which takes into account the fermion vacuum polarization effects, is found in (1+1) D. Within this solution the total energy of the bag, including the one-loop contribution from the Dirac's sea, is studied as the function of the bag geometry under condition of nonvanishing boson condensate density in the interior region. The existence and uniqueness of the ground state bag configuration, which minimizes the total energy and contains all the three phases, are shown.

hep-th↗

arXiv1997

UV-regularization of field discontinuities

A nonperturbative regularization of UV-divergencies, caused by finite discontinuities in the field configuration, is discussed in the context of 1+1-dimensional kink models. The relationship between this procedure and the appearance of "quantum copies" of classical kink solutions is studied in detail and confirmed by conventional methods of soliton quantization.

hep-th↗

arXiv1994

Quantum deflation of classical extended objects

It is shown, that extended particle-like objects should infinitely long collapse into some discontinuous configurations of the same topology, but vanishing mass. Analytic results concerning the general properties and asymptotic rates of such a process are given for 1+1-dimensional soliton models.

hep-th↗

arXiv1994

Decoupling of Translational and Rotational Modes for a Quantum Soliton

A set of integral relations for rotational and translational zero modes in the vicinity of the soliton solution are derived from the particle-like properties of the latter and verified for a number of models (solitons in 1+1-dimensions, skyrmeons in 2+1- and 3+1-dimensions, non-abelian monopoles). It is shown, that by consistent quantization within the framework of collective coordinates these relations ensure the correct diagonal expressions for the kinetic and centrifugal terms in the Hamiltonian in the lowest orders of the perturbation expansion. The connection between these properties and virial relations is also determined.

hep-th↗

arXiv1994

Spin Content of the Quantum Soliton

The classical soliton solution, quantized by means of suitable translational and rotational collective coordinates, is embedded into the one-particle irreductible representation of the Poincare group corresponding to a definite spin. It is shown, that within the conventional quasiclassical expansion such embedding leads to a set of nontrivial consistency conditions imposed on the classical solution. The validity of these relations is considered for a number of soliton models in 2+1- and 3+1-dimensions.

hep-th↗