Relativistic version of the imaginary-time formalism

A relativistic version of the quasiclassical imaginary-time formalism is developed. It permits calculation of the tunneling probability of relativistic particles through potential barriers, including barriers lacking spherical symmetry. Application of the imaginary-time formalism to concrete problems calls for finding subbarrier trajectories which are solutions of the classical equations of motion, but with an imaginary time (and thus cannot be realized in classical mechanics). The ionization probability of an s level, whose binding energy can be of the order of the rest energy, under the action of electric and magnetic fields of different configuration is calculated using the imaginary-time formalism. Besides the exponential factor, the Coulomb and pre-exponential factors in the ionization probability are calculated. The Hamiltonian approach to the tunneling of relativistic particles is described briefly. Scrutiny of the ionization of heavy atoms by an electric field provides an additional argument against the existence of the “Unruh effect.” Zh. éksp. Teor. Fiz. 114, 798–820 (September 1998)     

Ionization of a two-electron atom in a strong electromagnetic field

A one-dimensional model of a helium atom in an intense field of a femtosecond electromagnetic pulse has been constructed using the Hartree technique. “Exact” calculations have been compared to the approximations of “frozen” and “passive” electrons. A nonmonotonic dependence of the single-electron ionization probability on the radiation intensity has been detected. Minima in the ionization probability are due to multiphoton resonances between different atomic states due to the dynamic Stark effect. We suggest that the ionization suppression is due to the interference stabilization in this case. Zh. éksp. Teor. Fiz. 112, 470–482 (August 1997)     

On the geometry of relativistic magnetofluid flows

This paper deals with the construction of “magnetic vorticity” vector using Greenberg's theory of spacelike congruences for the trajectories of magnetic fields. A set of propagation equations is derived for the geometrical invariants associated with the congruences of magnetic field lines and fluid flow lines. Some applications of these propagation equations are made. A generalization of Ferraro's law of isorotation is obtained employing the propagation equation forω ² along the magnetic field lines.     

Imaginary-time method in quantum mechanics and field theory

An imaginary-time method was developed for calculating the probability of particle transmission through smooth barriers variable with time. Within the imaginary-time method, the tunneling process is described by using classical equations of motion written in terms of an imaginary time (t → it), while the probability of tunneling is determined by the imaginary part of the action functional, this imaginary part being calculated along the subbarrier particle trajectory. The fundamentals of the imaginary-time method are surveyed, and its applications in the theory of atomic-state ionization under the effect of constant electric and magnetic fields that have various configurations, in the field of intense monochromatic laser radiation and of an ultrashort electromagnetic pulse, in the process of Lorentz ionization of atoms and ions during their motion in a strong magnetic field, etc., are outlined. The applications of the imaginary-time method in relativistic cases—for example, in the theory of ionization of levels of multiply charged ions whose binding energy is commensurate with the electron rest energy—and in quantum field theory (Schwinger effect, which consists in the production of electron-positron pairs from a vacuum by a superstrong external field) are briefly described. Particular attention is given to methodological issues and details of the imaginary-time method that are of importance in solving specific physics problems, but which are usually skipped in original publications.     

Incommensurateness effects in a lattice Ginzburg-Landau model

This paper discusses the effect of magnetic translational symmetry on the vortex structure in superconducting crystals with a large basis in artificial Josephson media (regular lattices of superconducting clusters) prepared with opal as the base material. For external magnetic fields lower than the upper critical field, the lattice Ginzburg-Landau model reduces to the two-dimensional Frenkel’-Kontorova model which in some cases is exactly solvable, in which the crystal lattice plays the role of an “hard sublattice” while the deformable vortex lattice plays the role of a “soft sublattice.” It is shown that static shear waves in the vortex lattice are solutions to the two-dimensional sine-Gordon equation with an additional condition of incompressibility implied by flux quantization. The pinning energy is found as a function of the magnetic field, nearness to the transition line, and the crystal lattice constant. Fiz. Tverd. Tela (St. Petersburg) 39, 1158–1162 (July 1997)     

A “capacitor” model of the hysteresis of tunneling current in w -GaN/AlGaN(0001) structures

A “capacitor” model of the hysteresis is developed using the self-consistent calculation of the tunneling current in a w-GaN/AlGaN(0001) double-barrier structure. In the framework of this model, the current jumps and changes in the potential and the electric field in the structure upon transition from one branch of the current loop to the other branch are considered a result of the recharging of two joined capacitors with the plates located at the positions of the extrema of variations in the electron density in the regions of the emitter, the quantum well, and the collector. It is demonstrated that, when the external and internal fields in the quantum well compensate for each other, the tunneling current is sharply and irreducibly switched to the characteristics of the other resonance and forms a wide hysteresis loop so that, in the branches of this loop, the charge is redistributed between the quantum well and the collector. If the fields coincide with each other, there arises a narrow “singleresonance” hysteresis loop, which is accompanied by the transfer of the electron charge from the emitter to the collector. The developed model leads to agreement with the results of the self-consistent calculations and provides an illustrative interpretation of the complex electron tunneling processes. Original Russian Text ? A.N. Razzhuvalov, S.N. Grinyaev, 2009, published in Fizika Tverdogo Tela, 2009, Vol. 51, No. 1, pp. 168–177.     

Magnetoexciton light absorption in inhomogeneous quasi-two-dimensional systems

The problem of exciton light absorption in quasi-two-dimensional inhomogeneous systems in a strong transverse magnetic field H is analyzed. We assume that a random Gaussian field (“white noise”) acting separately on an electron and a hole is due to (1) fluctuations in the quantum well thickness or (2) fluctuations in the concentrations of the solid solution components. The problem of a magnetoexciton in a random Gaussian white noise field has been reduced to the problem of the motion in an H-dependent effective field of a single particle with the effective magnetic mass of the exciton, which is a function of the magnetic field and parameters of the quantum wells, in a field characterized by “colored noise,” whose correlation function is different from that of the white noise field. In this approximation, the problem of a magnetoexciton in isolated and coupled quantum dots is considered. In the coherent-potential approximation, the exciton absorption in random fields of the first and second type in single and coupled quantum wells has been calculated. The absorption decreases as H increases in the range of strong magnetic fields, which is in agreement with experimental data. Zh. éksp. Teor. Fiz. 114, 1451–1465 (October 1998)     

On Virtual Phonons,Photons, and Electrons

A macroscopic realization of the peculiar virtual particles is presented. The classical Helmholtz and the Schrödinger equations are differential equations of the same mathematical structure. The solutions with an imaginary wave number are called evanescent modes in the case of elastic and electromagnetic fields. In the case of non-relativistic quantum mechanical fields they are called tunneling solutions. The imaginary wave numbers point to strange consequences: The waves are non-local, they are not observable, and they are described as virtual particles. During the last two decades QED calculations of the solutions with an imaginary wave number have been experimentally confirmed for phonons, photons, and electrons. The experimental proofs of the predictions of non-relativistic quantum mechanics and the Wigner phase time approach for the elastic, electromagnetic and Schrödinger fields will be presented in this article. The results are zero time in the barrier and an interaction time (i.e. a phase shift) at the barrier interfaces. The measured tunneling time scales approximately inversely with the particle energy. Actually, the tunneling time is given only by the barrier boundary interaction time, as zero time is spent inside a barrier.     

Deep impurity-center ionization by far-infrared radiation

An analysis is made of the ionization of deep impurity centers by high-intensity far-infrared and submillimeter-wavelength radiation, with photon energies tens of times lower than the impurity ionization energy. Within a broad range of intensities and wavelengths, terahertz electric fields of the exciting radiation act as a dc field. Under these conditions, deep-center ionization can be described as multiphonon-assisted tunneling, in which carrier emission is accompanied by defect tunneling in configuration space and electron tunneling in the electric field. The field dependence of the ionization probability permits one to determine the defect tunneling times and the character of the defect adiabatic potentials. The ionization probability deviates from the field dependence e(E) ∝ exp(E ²/E _c ² ) (where E is the wave field, and E _c is a characteristic field) corresponding to multiphonon-assisted tunneling ionization in relatively low fields, where the defects are ionized through the Poole-Frenkel effect, and in very strong fields, where the ionization is produced by direct tunneling without thermal activation. The effects resulting from the high radiation frequency are considered and it is shown that, at low temperatures, they become dominant. Fiz. Tverd. Tela (St. Petersburg) 39, 1905–1932 (November 1997)     

Electrodynamics of Balanced Charges

We introduce here a new “neoclassical” electromagnetic (EM) theory in which elementary charges are represented by wave functions and individual EM fields to account for their EM interactions. We call so defined charges balanced or “b-charges”. We construct the EM theory of b-charges (BEM) based on a relativistic field Lagrangian and show that: (i) the elementary EM fields satisfy the Maxwell equations; (ii) the Newton equations with the Lorentz forces hold approximately when b-charges are well separated and move with non-relativistic velocities. When the BEM theory is applied to atomic scales it yields a hydrogen atom model with a frequency spectrum matching the Schrodinger model with desired accuracy. An important feature of the theory is a mechanism of elementary EM energy absorption established for retarded potentials.     

General magnetized Weyl solutions: disks and motion of charged particles

We construct three families of general magnetostatic axisymmetric exact solutions of Einstein-Maxwell equations in spherical coordinates, prolate, and oblates. The solutions obtained are then presented in the system of generalized spheroidal coordinates which is a generalization of the previous systems. The method used to build such solutions is the well-known complex potential formalism proposed by Ernst, using as seed solutions vacuum solutions of the Einstein field equations. We show explicitly some particular solutions among them a magnetized Erez-Rosen solution and a magnetized Morgan-Morgan solution, which we interpret as the exterior gravitational field of a finite dislike source immersed in a magnetic field. From them we also construct using the well known “displace, cut and reflect” method exact solutions representing relativistic thin disks of infinite extension. We then analyze the motion of electrically charged test particles around these fields for equatorial circular orbits and we discuss their stability against radial perturbations. For magnetized Morgan-Morgan fields we find that inside of disk the presence of magnetic field provides the possibility of to find relativist charged particles moving in both prograde and retrograde direction.     

Selected Problems of Relativistic Quantum Mechanics and Atomic Physics

The paper presents a brief review of the scientific work performed by the authors in the field of quantum mechanics and atomic, laser, and mathematical physics. The following problems are considered: the semiclassical theory of tunneling and multiphoton ionization of atoms and ions in a strong electromagnetic field; generalization of the Keldysh ionization theory to the relativistic case; calculation of the Coulomb corrections to the ionization rate of atoms for arbitrary values of the adiabaticity parameter γ: from γ ≪ 1 (the adiabatic region) to γ ≫ 1, when the laser field changes its direction and magnitude many times during the time of flight of the electron through the barrier; the Lorentz ionization of atoms moving in a constant magnetic field; the WKB approximation and the imaginary time method for describing electron tunneling through a time-varying barrier; the Stark effect in a strong field; the energy spectrum of a hydrogen atom in a strong and superstrong magnetic field; quantization with account of the barrier transparency; creation of electron-positron pairs from vacuum in a constant electric or intense pulsed (laser) field and the dependence of the number of pairs on the intensity and frequency of the laser field; the Feynman method of disentanglement of noncommuting operators and its applications: transitions between atomic states in an alternating magnetic field (the Majorana problem); a quantum oscillator with time-dependent frequency; and a singular oscillator. The mathematical problems of quantum mechanics are considered: the fall of a particle to the center; modification of the Bohr-Sommerfeld quantization condition for potentials with a barrier and the Kramers matching conditions; divergence of perturbation series and their summation; eigenvalues of the Casimir operators for irreducible representations of Lie groups, including the SU(2), SU(3), and SU(6) groups, which are widely used in physics.     

Effect of asymmetry of CuO2 layers in copper oxides on the anomalous neutron scattering near T c

Reasons for critical magnetic scattering of neutrons near T _c in copper oxides with CuO₂ layers whose nearest environment has no “up-down” symmetry are discussed. The intracrystalline electric field, which threads the CuO₂ planes on account of the asymmetry, induces coupling between the spin and momentum of the current carriers. This coupling is shown to result in a manifestation of virtual Cooper pairs in the imaginary part of the spin susceptibility. Thus spin density fluctuations as well as current fluctuations should participate in the scattering. A way of experimentally distinguishing between the two mechanisms is pointed out. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 5, 363–368 (10 March 1999) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Ionization of atoms in weak fields and the asymptotic behavior of higher-order perturbation theory

Using the imaginary time method, we study the structure of the perturbation series for the hydrogen atom in electric ℰ and magnetic ℋ fields. It is shown that there is a “critical” value of the ratio γ=ℋ|ℰ at which the perturbation series for the ground state changes from having a fixed sign (for γ<γ _c ) to having a variable sign (for γ>γ _c ). This conclusion is confirmed by direct higher-order perturbation calculations. The change in the asymptotic regime is explained by competition among the contributions of the various complex trajectories that describe the subbarrier motion of the electrons. Here the parameter γ _c depends on the angle θ between the electric and magnetic fields. Zh. éksp. Teor. Fiz. 113, 2047–2055 (June 1998)     

Non-Fermi-liquid effects in tunneling

Non-Fermi-liquid tunneling mechanisms in a quantum structure with its own two-dimensional continuum doped with transition metal impurities are considered. New physical realizations of the two-channel Kondo orbital model with mechanisms different from those previously described in literature occur in such quantum structures. The tunneling transparency is anomalously high owing to new channels generated by multiparticle Fermi-liquid resonances near the edge of the two-dimensional energy band in the process of tunneling. The widths of new edge resonances can be much smaller than the width of the “bare” non-Fermi-liquid resonance at the Fermi level in the banks. The additional scattering due to tunneling induces a transition from the non-Fermi-liquid to the Fermi-liquid state as the separation between the Fermi level in the banks and the two-dimensional band edge in the quantum well varies. Zh. éksp. Teor. Fiz. 114, 1466–1486 (October 1998)     

Role of electron “lakes” in the negative magnetoresistance effect in the region of Mott hopping conductivity

It is shown for doped and compensated germanium that the appearance of negative magnetoresistance under the conditions of Mott hopping conductivity may be due to the presence of a nonuniform spatial distribution of the electron density, the temperature at which the effect appears apparently being determined by the temperature at which the electron gas condenses into electron “lakes.” A “dead zone” effect was also observed in weak magnetic fields, the threshold field increasing with the nonuniformity of the electron distribution. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 3, 187–191 (10 February 1996)     

Symmetric hyperbolic systems for a large class of fields in arbitrary dimension

Symmetric hyperbolic systems of equations are explicitly constructed for a general class of tensor fields by considering their structure as r-fold forms. The hyperbolizations depend on 2r−1 arbitrary timelike vectors. The importance of the so-called “superenergy” tensors, which provide the necessary symmetric positive matrices, is emphasized and made explicit. Thereby, a unified treatment of many physical systems is achieved, as well as of the sometimes called “higher order” systems. The characteristics of these symmetric hyperbolic systems are always physical, and directly related to the null directions of the superenergy tensor, which are in particular principal null directions of the tensor field solutions. Generic energy estimates and inequalities are presented too. Examples are included, in particular a mixed gravitational-scalar field system at the level of the Bianchi equations.     

Magnetic properties and magneto-birefringence of magnetic fluids

Static magnetic properties of a large variety of magnetic fluids with magnetite particles is studied. A qualitative study of magnetization curves was performed to establish the influence of interactions or the presence of agglomerations in each sample. Improved equations for magneto-granulometric analysis, for ideal ferrofluids, were proposed. Better results for the mean magnetic diameter than in the case of using the known equations were obtained. A quantitative study using several models for ideal and interacting particles was performed to select the best method and dimensional distribution function for magneto-granulometric analysis as well as for accurately determining macroscopic quantities of samples (initial susceptibility, saturation magnetization, particle number density or magnetic volume fraction) and properties of nanoparticles (mean magnetic diameter, thickness of the nonmagnetic layer and particle distribution). A new model for magneto-birefringence was proposed and discussed as well as applied for diluted and concentrated ferrofluids. The Langevin behaviour of samples was investigated and compared with the investigation based on magnetic properties. Nanoparticles parameters like mean “magneto-optical” diameter, effective anisotropy constant, Shliomis diameter and the real part of the electrical permittivity of particles were accurately determined. Received 18 July 1999 and Received in final form 13 January 2000     

Goldstone mode relaxation in a quantum hall ferromagnet due to hyperfine interaction with nuclei

Spin relaxation in quantum Hall ferromagnet regimes is studied. As the initial non-equilibrium state, a coherent deviation of the spin system from the B direction is considered and the breakdown of this Goldstone-mode state due to hyperfine coupling to nuclei is analyzed. The relaxation occurring non-exponentially with time is studied in terms of annihilation processes in the “Goldstone condensate” formed by “zero spin excitons”. The relaxation rate is calculated analytically even if the initial deviation is not small. This relaxation channel competes with the relaxation mechanisms due to spin-orbit coupling, and at strong magnetic fields it becomes dominating.     

Effect of the state of a quantized electromagnetic field on the interaction with an atom with allowance for the continuum

This paper studies the effect of a transition into the continuous spectrum on the “collapse” and “revival” of population oscillations in an atom. It is shown that at large values of the mean number of photons in a radiation field and in conditions of weak ionization the phenomena of collapse and revival can still be observed, but the amplitude of population oscillations decreases exponentially because of the damping of the level. The interaction of a quantized electromagnetic field with a Λ system of an atom when one state is continuous is examined. Expressions are derived for the probability of “survival” of the atom when the quantized field was initially in a state with a given number of photons and when it was in a coherent state. An approximate calculation of the sum in averaging over the photon number distribution in the case of a coherent field leads to expressions for the probabilities of survival of the atom that transform into expressions, as the mean number of photons tends to infinity, corresponding to the case of a field in the representation of a fixed number of photons. The possibility of a stable state existing in a coherent quantized field is examined. It is found that for a Λ system the condition for the existence of a stable state remains valid in the case of a coherent state of the field when the photon number is large. Zh. éksp. Teor. Fiz. 113, 1193–1205 (April 1998)