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)     

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)     

The imaginary-time method for relativistic problems

A relativistic version of the imaginary-time method is presented. The method is used to calculate the probability w of ionization of a bound state by electric and magnetic fields of various configurations (including the case when the binding energy E _b is comparable to mc ₂). The formulas cover as limiting cases both the ionization of nonrelativistic bound systems (atoms and ions) and the case E _b =2mc ₂, when w equals the probability of electron-positron pair production from the vacuum in the presence of a strong field. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 4, 213–218 (25 August 1997)     

Effect of a magnetic field on the ionization of atoms

The ionization probability of an atomic s state under the action of static electric and magnetic fields is calculated taking into account the Coulomb interaction between the escaping electron and the atomic core. The structure of the perturbation series for the energy of the level is investigated and the asymptotic behavior of the higher orders of the perturbation theory is found. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 6, 398–402 (25 March 1996)     

Effect of a magnetic field on thermally stimulated ionization of impurity centers in semiconductors by submillimeter radiation

The probability of electron tunneling from a bound state into a free state in crossed ac electric and dc magnetic fields is calculated in the quasiclassical approximation. It is shown that a magnetic field decreases the electron tunneling probability. This decreases the probability of thermally activated ionization of deep impurity centers by submillimeter radiation. The logarithm of the ionization probability is a linear function of the squared amplitude of the electric field and increases rapidly with the frequency of the electric field.     

Lorentz ionization of atoms in a strong magnetic field

Lorentz ionization emerges due to the motion of atoms or ions in a strong magnetic field. We use the semiclassical approximation to calculate the probability w _L of Lorentz ionization. We also find the stabilization factor S, which takes into account the reduction by the magnetic field of the probability of ionization decay of the bound s state. We estimate the probabilities w _L in magnetic-cumulation experiments and in astrophysics. We also qualitatively examine the dynamics of the magnetic cumulation process with allowance for the conductivity of the shell. Finally, we discuss a paradox related to the use of the quasistationary solution at the shell expansion stage. Zh. éksp. Teor. Fiz. 115, 1642–1663 (May 1999)     

Ionization of atoms in electric and magnetic fields and the imaginary time method

A semiclassical theory is developed for the ionization of atoms and negative ions in constant, uniform electric and magnetic fields, including the Coulomb interaction between the electron and the atomic core during tunneling. The case of crossed fields (Lorentz ionization) is examined specially, as well as the limit of a strong magnetic field. Analytic equations are derived for arbitrary fields ℰ and ℋ that are weak compared to the characteristic intraatomic fields. The major results of this paper are obtained using the “imaginary time” method (ITM), in which tunneling is described using the classical equations of motion but with purely imaginary “time.” The possibility of generalizing the ITM to the relativistic case, as well as to states with nonzero angular momentum, is pointed out. Zh. éksp. Teor. Fiz. 113, 1579–1605 (May 1998)     

Ionization probability of the bound impurity states of two-dimensional electrons under strong magnetic and finite electric fields

The ionization probability of the bound impurity states in a semiconductor inversion layer under strong magnetic fields H is calculated as a function of temperature and electric field value E. The conditions for relatively large ionization probability are determined. The possibility of the bound state ionization must be taken into account for the interpretation of the inversion layer properties at the Shubnikov-De Haas conductivity minima.     

Contribution to the theory of Lorentzian ionization

The probability w _L of Lorentzian ionization, which arises when an atom or ion moves in a constant magnetic field, is calculated in the quasiclassical approximation. The nonrelativistic (v≲e ²/ℏ=1, v is the velocity of the atom) and ultrarelativistic (v→c=137) cases are examined and the stabilization factor S, which takes account of the effect of the magnetic field on tunneling of an electron, is found. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 5, 391–396 (10 March 1997)     

Tunneling ionization of Rydberg molecules

The theory of tunneling ionization of atoms is generalized to ionization of symmetric top molecules, either polar or nonpolar. Low-lying excited states of molecules, for which the ordinary Born-Oppenheimer approximation holds, and high-lying excited states, for which the inverse Born-Oppenheimer approximation holds, are discussed. Ionization in a constant external field is analyzed, as is ionization in an alternating field. It is shown that the orientation of the molecule’s axis along the field does not lead to any appreciable increase in the ionization probability as compared to other orientations. Zh. éksp. Teor. Fiz. 112, 115–127 (July 1997)     

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)     

Spectrum of indirect magnetoexcitons in coupled quantum wells

The indirect Mott exciton (spatially-separated electron and hole) in coupled quantum wells in crossed electric and magnetic fields is discussed. The exciton spectrum is calculated for the case where the distance between the quantum wells of the electron and hole is larger than the exciton Bohr radius. The magnetoexciton creation probability is calculated and its dependence on the electric field is found. The absorption of electromagnetic radiation between the indirect magnetoexciton levels in coupled quantum wells is discussed. Fiz. Tverd. Tela (St. Petersburg) 39, 2220–2223 (December 1997)     

Interference ionization of an impurity by an electric field in a system of quantum wells

A radical change in the ionization energy of the donor impurity Si in a GaAs/AlGaAs double-well heterostructure is observed experimentally when the electronic wave function is relocated in an electric field. The ionization energy of the impurity decreases from 15.5 meV to 0 when the voltage across the structure changes by less than 1 V. The Stark effect would give a change in the ionization energy of not more than 3 meV. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 3, 194–199 (10 February 1999)     

Characteristic features of the photoconductivity and spin conversion of electron-hole pairs in doped amorphous molecular semiconductors in the dye absorption region

The photoconductivity of doped poly-N-epoxypropylcarbazole films in the absorption region of a cationic polymethine dye is observed to increase when the BF ₄ ⁻ ion is replaced by Cl⁻ and I⁻. The effect of a magnetic field on the photoluminescence is investigated at room temperature. The photoconductivity is studied as a function of the electric field intensity and wavelength of light. The dependence of the photoconductivity on the nature of the anion can be explained by a change in the probability of intercombination conversion in ionic and electron-hole pairs. Fiz. Tverd. Tela (St. Petersburg) 41, 44–48 (January 1999)     

Ohm’s law in a chiral plasma

The motion of plasma electrons in a stochastic electromagnetic field is studied in the low-conductivity limit. It is shown that under very general conditions, in the presence of a nonzero average chirality of the small-scale electromagnetic field, the effective current depends on the curl of the applied electric field, j=§ E+§_κcurl E, just as for similar dependences for the electric displacement and magnetic induction vectors in optically active and artificial chiral media. Under certain conditions such an Ohm’s law leads to growth of the magnetic field, the structure of the growth being dependent on the conductivity of the medium. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 4, 268–273 (25 August 1999)     

The Poole–Frenkel effect in a dielectric under nanosecond irradiation by an electron beam with moderate or high current density

Processes of electron trapping and detrapping determine in many respects intense processes arising in dielectric and delayed by 1–100 ns from the irradiation pulse of a high-power electron beam, such as electron emission, electric discharge in the bulk of the dielectric, flashover, and electric breakdown. A model of charged donor center ionization in a dielectric exposed to a strong electric field is constructed. The model takes into account 1) the energy spectrum of the charged donor center in the dielectric, 2) the semiclassical state density in the donor center, 3) spontaneous emission of phonons by the electron localized in the donor center, 4) increase in the kinetic energy of the electron (heating) in the external electric field, 5) electron tunneling through a potential barrier and its reflection from the barrier depending on the external field intensity, and 6) thermal fluctuations of energy of the electron localized in the donor center. The probability of charged donor center ionization in the dielectric per unit time is calculated. In weak fields, the field dependence of the ionization probability almost coincides with that for the Poole–Frenkel theory. In strong fields, the contribution of electron heating to the external electric field is the deciding factor. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 10–16, December, 2008.     

Distribution of the electric field and current in a turbulent conducting fluid for small magnetic Reynolds numbers

Various aspects of the influence of an external magnetic field on turbulent flow of a conducting fluid are investigated. The distributions of electric variables are determined for weak magnetic fields (both the electric field and the current have nonzero values in this case). For very strong magnetic fields it is shown that turbulent motion acquires a two-dimensional character. The emergence of an electric current component perpendicular to the flow and to the magnetic field is described in the case of a temperature-stratified medium in the presence of turbulent heat flux. Zh. éksp. Teor. Fiz. 111, 528–535 (February 1997)     

Development of ionization in nonequilibrium inert-gas plasmas in magnetogasdynamic channels

Effects accompanying the interaction of a flow of preionized inert gas with a magnetic field are studied: selective electron heating, the development of nonequilibrium ionization, and the onset of the ionization instability. Local and average densities and temperatures of the electrons are measured and the average ionization rate is determined. It is found that the average electron density increases as the magnetic induction is raised, in both stable and ionization unstable plasmas. The difference in the rates at which ionization develops in these two states is revealed. The mechanism for the coupling between the average ionization rate in an ionization unstable plasma and the spatial-temporal characteristics of the plasma inhomogeneities is established. Zh. Tekh. Fiz. 69, 56–61 (November 1999)     

Magnetoelectric response of the spin-Peierls compound CuGeO3

The effect of an electric field on the magnetic susceptibility in a pure CuGeO₃ single crystal at microwave frequencies is investigated. A quadratic effect of the electric field on the magnetic susceptibility, which increases with decreasing temperature, is observed in the spin-Peierls state at temperatures below 5 K. The observed effect is tentatively attributed to residual magnetism, due to distortions of the regular dimerized structure at domain walls with different values of the dimerization phase, and to the effect of the electric field on the interchain exchange interaction. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 9, 646–651 (10 November 1996)     

On the unified nature of the longitudinal and transverse acoustoelectric effects in type-II superconductors

A longitudinal ultrasonic wave should drag the vortex structure of superconductors at an acute angle with respect to the direction of wave propagation. This motion engenders longitudinal and transverse electric fields in the superconductor and, moreover, effects of the “optical rectification” type contribute to the observed longitudinal and transverse electric fields. The effect should be observed in all type-II superconductors above the irreversibility line. Both fields have extrema with respect to temperature and magnetic field. In contrast to the acoustoelectric effect in the normal state, the sign of the induced electric field depends on the external magnetic field. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 3, 222–227 (10 February 1998)