Stationary states of crystal growth in three dimensions

A new Markov process describing crystal growth in three dimensions is introduced. States of the process are configurations of the crystal surface, which has a terrace-edge-kink structure. The states are continuous along edges but discrete across edges, in accordance with the very different rates for the two types of captures of particles. Stationary distributions, describing steady crystal growth, are found in general. To our knowledge, these are the first examples of stationary distributions for layered crystal growth in three dimensions. The steady growth rate and other quantities are obtained explicitly for two interacting edges. For many interacting edges, growth behavior is determined (a) in various asymptotic regimes including thermodynamic limits, (b) via simulations, and (c) using series (cluster) expansions in the slope of the surface, the first three coefficients being computed. The theoretical growth rates show a marked dependence on surface dimensions. This may contribute to the size dependence and dispersion in the observed growth rate of small crystals.     

Electric field of an isolated charged impurity in an ionic crystal

The character of the behavior of the electric field created by a charged impurity in an ionic crystal is studied on the basis of both cluster and analytical approaches. In the cluster approach about 30 000 ions surrounding the impurity are taken into account. These ions are described in a model of polarizable sites. A direct calculation shows that the asymptote of the electric field of a charged impurity at lattice points can differ strongly from the one given by the Coulomb equation written for a homogeneous polarizable medium. The behavior of the electric field at intermediate distances, where the asymptotic behavior cannot yet be used, is studied in detail. It is found that the electric field is increased significantly in comparison to the Coulomb field in the region near the defect. The size of this (strongly polarized) region increases as the dielectric constant increases. These data are in qualitative agreement with the results obtained by Vikhnin et al. and account for the results of recent experiments designed to investigate polarization in reduced virtual ferroelectrics. Fiz. Tverd. Tela (St. Petersburg) 40, 662–667 (April 1998)     

Quantum electron levels in the field of a charged black hole

Stationary solutions of the Dirac equation in the metric of the charged Reissner–Nordstrom black hole are found. In the case of an extremal black hole, the normalization integral of the wave functions is finite, and the regular stationary solution is physically self-consistent. The presence of quantum electron levels under the Cauchy horizon can have an impact on the final stage of the Hawking evaporation of the black hole, as well as on the particle scattering in the field of the black hole.     

Stationary solutions of the Dirac equation in the gravitational field of a charged black hole

A stationary solution of the Dirac equation in the metric of a Reissner-Nordström black hole has been found. Only one stationary regular state outside the black hole event horizon and only one stationary regular state below the Cauchy horizon are shown to exist. The normalization integral of the wave functions diverges on both horizons if the black hole is non-extremal. This means that the solution found can be only the asymptotic limit of a nonstationary solution. In contrast, in the case of an extremal black hole, the normalization integral is finite and the stationary regular solution is physically self-consistent. The existence of quantum levels below the Cauchy horizon can affect the final stage of Hawking black hole evaporation and opens up the fundamental possibility of investigating the internal structure of black holes using quantum tunneling between external and internal states.     

Unstable electron states in the field of a superheavy nucleus

The problem of bound states in supercritical fields is considered. The shape of the energy distribution for the |1s> electron bound state embedded in the lower continuum is obtained within the generalized quantum dynamics formalism.     

Theoretical resistance of an ionic crystal to destruction by an electric field

We describe an electrostriction mechanism for destruction of an ionic crystal by an electric field. We present a simple theory that transforms into the well-known Rogowskii theory when there is no electrostatic breakdown. We show that electrostatic breakdown of the crystal lattice is due to separation of nearestneighbor ions with different charges to the point where the electric field exceeds the interionic attractive forces. The theoretical tensile strength of a crystal lattice undergoing electrostriction by an electric field is 15 MV/cm.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 47–50, March, 1989.     

Controlled hole burning in the photon-number distribution of field states in a cavity

A feasible experimental scheme to generate states of a field mode in a high-Q cavity possessing holes in their photon-number distributions at controlled positions is proposed. Such kind of states may be of interest to optical data storage and communications with a possible readout system consisting of an atomic deflection setup.     

Bound states of spin-half particles in a static gravitational field close to the black hole field

We consider the bound-state energy levels of a spin-1/2 fermion in the gravitational field of a near-black hole object. In the limit that the metric of the body becomes singular, all binding energies tend to the rest-mass energy (i.e. total energy approaches zero). We present calculations of the ground state energy for three specific interior metrics (Florides, Soffel and Schwarzschild) for which the spectrum collapses and becomes quasi-continuous in the singular metric limit. The lack of zero or negative energy states prior to this limit being reached prevents particle pair production occurring. Therefore, in contrast to the Coulomb case, no pairs are produced in the non-singular static metric. For the Florides and Soffel metrics the singularity occurs in the black hole limit, while for the Schwarzschild interior metric it corresponds to infinite pressure at the centre. The behaviour of the energy level spectrum is discussed in the context of the semi-classical approximation and using general properties of the metric.     

Charge distributions of crystal field states

A formalism is presented, by which the charge density of anyd- orf-crystal field state can be calculated, if the corresponding crystal field wavefunction in the angular representation is known. Based on this formalism three dimensional plots of the spatial crystal field charge distributions of selected 4f-ions are shown.     

Dynamics of a pair of electron and hole in semiconductor superlattice under an intense electric field

This paper investigates the behavior of a pair of electron and hole in semiconductor superlattice under an external electric field with the consideration of Coulomb interaction. By numerically calculating the corresponding probability in the nearest neighbor tight binding approximation, we find that the single electron (or the hole) can not be dynamically localized due to the Coulomb interaction, while the dynamic localization of exciton (the pair of the electron and hole) still exists. Moreover we find that with the increase of the intensity of electric field, the exciton can be dynamically localized more completely.     

Melting of a Wigner crystal in an ionic dielectric

The melting of a Wigner Crystal of electrons placed into a host polar material is examined as a function of the density and the temperature. When the coupling to the longitudinal optical modes of the host medium is turned on, the WC is progressively transformed into a polaronic Wigner crystal. We estimate the critical density for crystal melting at zero temperature using the Lindeman criterion. We show that above a certain critical value of the Fr?hlich electron-phonon coupling, the melting towards a quantum liquid of polarons is not possible, and the insulator-to-metal transition is driven by the ionization of the polarons (polaron dissociation). The phase diagram at finite temperature is obtained by making use of the same Lindeman criterion. Results are also provided in the case of an anisotropic electron band mass, showing that the scenario of polaron dissociation can be relevant in anisotropic compounds such as the superconducting cuprates at rather moderate e-ph couplings. Received 13 August 1999     

Positronium atom in an ionic crystal

The Sommerfeld-Welker model of a hydrogen atom in a spherical, impenetrable force cavity is used to calculate the basic properties of positronium in an ionic crystal. The basic properties of positronium (the lifetime against 2- and 3-annihilation, the count rate of 3 coincidences, and the magnetic-quenching parameter) are found as functions of the radius of the spherical force cavity.Translated from Izvestiya VUZ. Fizika, No. 7, pp. 71–75, July, 1970.