Self-focusing of electromagnetic waves in a magnetoplasma

The steady state self-focusing of a Gaussian electromagnetic beam in a magneto-plasma has been studied. On a short time scale, a non-linearity in the dielectric constant of a plasma appears due to the ponderomotive force. This force in the case of the extraordinary mode has opposite signs forω>ω _c andω<ω _c, whereω _c is the electron cyclotron frequency. The self-focusing due to this effect is predicted at frequencies except forω _c /2<ω<ω _c . The focusing of the ordinary mode is adversely affected by the magnetic field. On a larger time scale, the non-uniform heating of electrons by the beam and the resulting redistribution of the electron density is a source of non-linearity. This non-local non-linearity is several orders of magnitude higher than the ponderomotive non-linearity. We predict self-focusing of the extraordinary mode only above the gyroresonance (ω>ω _c ), while the ordinary mode can be focused at all frequencies.     

Stability of bipolarons in the presence of a magnetic field

The stability of large Fröhlich bipolarons in the presence of a static magnetic field is investigated with the path integral formalism. We find that the application of a magnetic field (characterized by the cyclotron frequence ω _c) favors bipolaron formation: (i) the critical electronphonon coupling parameter α _c (above which the bipolaron is stable) decreases with increasing ω _c and (ii) the critical Coulomb repulsion strength U _c (below which the bipolaron is stable) increases with increasing ω _c. The binding energy and the corresponding variational parameters are calculated as a function of α, U and ω _c. Analytical results are obtained in various limiting cases. In the limit of strong electron-phonon coupling (α ? 1) we obtain for ω _c ? 1 that E _estim ? E _estim(ω _c = 0) + c(u)ω _c/α ⁴ with c(u) an explicitly calculated constant, dependent on the ratio u = U/α where U is the strength of the Coulomb repulsion. This relation applies both in 2D and in 3D, but with a different expression for c(u). For ω _c ? α ²? 1 we find in 3D E _estim ? ω _c - α ² A(u) ln²(ω _c/α ²), (also with an explicit analytical expression for A(u)) whereas in 2D E _estim ^2D ? ω _c - α√ω _cπ(u-2-√2)/2. The validity region of the Feynman-Jensen inequality for the present problem, bipolarons in a magnetic field, remains to be examined.     

Critical changes in vibrational modes in a magnetic debye crystal with a magnon-phonon coupling

Using the Green function technique we calculate the mean square of the vibrational amplitude of an ion (or equivalently the Debye Waller factor W, or the Mössbauer recoil free fraction ?) in a magnetic Debye crystal near the magnetic phase transition temperature T_c. We find that the magnon-phonon coupling which leads to the phonon spectrum broadening and frequency shift leads to sharp changes in W near T_c. The frequency shift leads to an increase in W, the broadening leads to a decrease in W. These results can explain the anisotropic critical changes in W near T_c observed recently in the magnetostrictive materials RFe₂ and RCo₂ (R = rare earth). In addition we calculate the expected changes in the second order Doppler shift near T_c. We find that when T approaches T_c from above a positive discontinuity and decrease in absolute value of slope of the thermal shift should occur.     

Free carrier absorption in quantizing magnetic fields: Nonpolar optical phonon scattering

A quantum theory of free carrier absorption in nondegenerate semiconductors and in strong magnetic fields which was previously developed to treat the case when acoustic phonon scattering dominates the free carrier absorption process [1] is extended to treat the case when nonpolar optical scattering is important. When the electromagnetic radiation field is polarized parallel to the direction of the applied magnetic field, results are obtained which are similar to those when acoustic phonon scattering is dominant. The free carrier absorption is an oscillatory function of the magnetic field which on the average increases in magnitude with the magnetic field. However, more structure in the free carrier absorption occurs when nonpolar optical phonon scattering dominates. This is due to the fact that there are two periods in the oscillatory magnetic field dependence associated with the emission or the absorption of optical phonons during the intraband transitions. When the cyclotron frequency exceeds the sum of the photon and optical phonon frequencies, i.e. ω_c > θ + ω_o, the free carrier absorption is predicted to increase linearly with magnetic field when ?ω_c? k_BT. The magnetic field dependence of the free carrier absorption can be explained in terms of phonon-assisted transitions between the various Landau levels in a band involving the emission and absorption of optical phonons.     

The sensitivity of the transition temperature to changes in α2 F(ω)

The transition temperature of a superconductor depends on α² F(ω), the spectral function of the effective interaction due to phonon exchange. We discuss how strongly the transition temperature is influenced by different frequency parts of α² F(ω). For this purpose the functional derivative δT _c /δα² F(ω) is calculated. It is shown that all frequency regions of α² F(ω) yield a positive contribution toT _c and that the most effective range covers frequencies, slightly above 2πT _c . The functional derivative is calculated numerically for several superconductors from their measured α² F(ω)-spectra. Finally, we discuss the change in transition temperature due to the softening of α² F(ω) which has been observed in amorphous superconductors.     

Phase transition in anyon superconductivity at finite temperature

The magnetic response of the charged anyon fluid at temperatures higher than the fermion energy gap (T ⪢ ω_c) is investigated in the self-consistent field approximation. In this temperature region a new phase, characterized by an inhomogeneous magnetic penetration, is found. The inhomogeneity is linked to the existence of an imaginary magnetic mass which increases with the temperature. It is explicitly proved that the electromagnetic field magnetic masses and rest-energies are different in the (T ⪢ ω_c)-phase.     

Anomalous behavior of the surface tension at the interface of the metallic and insulating phases in the vicinity of the metal-insulator phase transition in a magnetic field

Mean-field equations describing the metal-insulator (MI) transition are formulated. They involve two coupled order parameters characterizing this transition: (i) a scalar order parameter describing the density change accompanying the transition from the insulating state to the metallic one and (ii) an order parameter (a two-component vector) describing the electron density in the metallic or semimetallic phase affected by the applied magnetic field. Two components of this vector correspond to different possible spin states of electrons in the applied magnetic field. The transition in the density of metallic and insulating phases being a first order phase transition is treated in terms of the Cahn-Hilliard-type gradient expansion. The transition in the electron density is a second order phase described by the Ginzburg-Landau-type functional. The coupling of these two parameters is described by the term linearly dependent on the electron density n in the metal with the proportionality factor being a function of the density of the metallic phase. The derived equations are solved in the case of the MI interface in the presence of both parallel and perpendicular uniform magnetic fields. The calculated surface tension Σ_mi between the metallic and insulating phases has a singular behavior. In the limit of zero electron density n ? 0, Σ_mi ～ n ^3/2. Near the MI transition point T _c(h) in the applied magnetic field, Σ_mi ～ [T - T _c(h)]^3/2. The singular behavior of the surface tension at the MI interface results in the clearly pronounced hysteresis accompanying the transition from the insulating to metallic state and vice versa.     

Low wavenumber wall pressure measurements using a rectangular membrane as a spatial filter

The response of a rectangular membrane to a convecting random pressure field is interpreted to reveal the inherent wavenumber filtering characteristics of the device. After experimental determination of its resonant response characteristics, one such membrane is used to measure the low wavenumber components of the wall pressure fluctuations beneath a plane turbulent boundary layer. The measurements were made at wavenumbers far below the convective region (k₁ = ω/U_c) but above the acoustic region (k₁ ? ω/c_o). Possible contamination by acoustic and convective ridge effects is considered. The low wavenumber measurements are also compared with values of the wavenumber-frequency pressure spectral density $\text{Φ}{}_{\mathrm{p}}\text{(}\text{k}\text{,ω)}$ obtained by Fourier transforming cross-spectral density data obtained by Blake in the same wind tunnel. From this comparison it is seen that this transformation of Blake's data (based on a Corcos model) grossly overestimates the magnitude of $\text{Φ}{}_{\mathrm{p}}\text{(}\text{k}\text{,ω)}$ in the low-wavenumber region. The measured values of $\text{Φ}{}_{\mathrm{p}}\text{(}\text{k}\text{, c}{}_{\mathrm{o}}\text{)}$ are about 36 dB down from convective ridge levels at the same frequency. The data are also compared with earlier results obtained by Jameson. In a similar frequency range the current data levels are approximately 10 dB higher than those of Jameson.     

Anderson transition in a magnetic field — Weak field conductivity and hall effect —

The influence of a weak magnetic field on the Anderson transition is investigated by extending Götze's recent zero field theory. Whereas the diagonal components of the conductivity tensor are not essentially effected and the Hall conductivity tends to zero linearly when the Fermi energyε _F approaches the mobility edgeε _c from above, the Hall coefficient goes to zero discontinuously whenε _F=ε _c at zero temperature. At finite temperatures, however, no such discontinuity appears.     

Spin glass behavior and critical analysis across the magnetic phase transition in Gd2CoMnO6: dc magnetization and ac susceptibility study

We report here on critical analysis across magnetic phase transition and spin dynamics in Gd₂CoMnO₆. We found that this material behaves differently below and above the applied magnetic field of 20 kOe. The magnetic phase transition switches from nearly mean-field type to unusual class and T_c shifts towards the high temperature above 20 kOe field. The nature of the magnetic phase transition is explored by carrying out critical analysis at low as well as at high magnetic field. The critical exponents obtained at low field using Kouvel-Fisher method are β = 0.65 (2) γ = 0.90 (2), δ = 2.43 and T_c = 120 K. Apparently, these values of critical exponents appear close to mean-field model. For high field the critical exponents are β = 1.24 (2) γ = 0.64 (5), δ = 1.51 (3) and T_c = 128 K. The critical exponents show significant deviation from any universal class. This switchover in the nature of the magnetic phase transition is unique and not seen in many compounds. The formation of non-Griffiths-like clusters in this compound can be a reason for such unique behavior. Further, ac susceptibility has been measured to understand the spin dynamics in detail. The dispersion of frequency-dependent χ_ac below T_c confirms a spin glass state in this material. The observed value of τ_o and T_o indicate the slow dynamic spin which is caused by co-existence of Co/Mn spin magnetic moments. The magneto-caloric effect is also presented for Gd₂CoMnO₆ in this study. The magnetic study and critical analysis across the phase transition reveal a switchover in the nature of phase transition in this material. A non-Griffiths like cluster formation above T_c is found and dynamic susceptibility study reveals a spin glass state below T_c in Gd₂CoMnO₆.     

Ionic polarization effects on a shallow exciton at a finite temperature

The effective Hamiltonian for the interaction of a shallow exciton with longitudinal optical (LO) phonons at a finite temperature is derived to first order in the electron-phonon coupling α and E_B/?ω.     

CDW instability of electron gas in a strong magnetic field

It is shown that within the Hartree-Fock approximation the electron gas in the quantum limit of a strong magnetic field has an instability as the temperature is lowered toward the charge density wave state with an wave-vector which has finite components in the directions not only parallel but also perpendicular to the field. The critical temperature, T_c, is estimated under the assumption of T_c??_F?ω_c, where ?_F and ω_c are the Fermi energy of the non-interacting system and the cyclotron frequency respectively.     

Microwave photoresistance of a double quantum well at high filling factors

The effect of millimeter wave radiation on the electronic transport in a GaAs double quantum well at a temperature of 4.2 K in a magnetic field of up to 2 T has been studied. Resistance (conductance) oscillations have been shown to appear in the two-dimensional electronic system under investigation at high filling factors. The magnetic field positions of the oscillation maxima are determined by the condition Δ_SAS/? = lω_c, where Δ_SAS = (E ₂ ? E ₁) is the size quantization sublevel splitting in the quantum well, ω_c is the cyclotron frequency, and l is a positive integer. It has been found that the microwave field substantially modifies the oscillations in the double quantum well, which results in alternating two-frequency oscillations of photoresistance with the inverse magnetic field.     

Propagation regimes of intense circularly polarized laser beam in magnetoactive plasma

This paper presents an analytical and numerical investigation of an intense circularly polarized wave propagating along the static magnetic field parallel to oscillating magnetic field in magnetoactive plasma. In the relativistic regime such a magnetic field is created by pulse itself. The authors have studied different regimes of propagation with relativistic electron mass effect for magnetized plasma. An appropriate expression for dielectric tensor in relativistic magnetoactive plasma has been evaluated under paraxial theory. Two modes of propagation as extraordinary and ordinary exist; because of the relativistic effect, ultra-strong magnetic fields are generated which significantly influence the propagation of laser beam in plasma. The nature of propagation is characterized through the critical-divider curves in the normalized beam width with power plane For given values of normalized density (ω_p/ω) and magnetic field (ω_c/ω) the regions are namely steady divergence (SD), oscillatory divergence (OD) and self-focusing (SF). Numerical computations are performed for typical parameters of relativistic laser-plasma interaction: magnetic field B = 10-100 MG; intensity I = 10¹⁶ to 10²⁰ W/cm²; laser frequency ω = 1.1 × 10¹⁵ s⁻¹; cyclotron frequency ω_c = 1.7 × 10¹³ s⁻¹; electron density n_e = 2.18 × 10²⁰ cm⁻³. From the calculations, we confirm that a circularly polarized wave can propagate in different regimes for both the modes, and explicitly indicating enhancement in wave propagation, beam focusing/self-guiding and penetration of E-mode in presence of magnetic field.     

Magnetic superconductors of HoMo6S8 type: The effect of magnetic field and supercurrent

We study the magnetic superconductors for which the second order phase transition to the ferro-magnetic state would take place at the temperature θ_c ? T_c1 if the superconductivity was absent. In this case the inhomogeneous magnetic structure of domain-like type (DS phase) appears in superconductors below T_M ≈ θ_c. The effect of the magnetic field H on DS phase is analysed and the region of DS phade existence in the plane (H, T) is found. The new peaks 2nQ (n is integer) should appear in the neutron scattering in the presence of the magnetic field. The wavevector Q of magnetic structure decreases with the growth of magnetic field or supercurrent.     

General Schrödinger equation for whistler waves propagating along a magnetic field

The general Schrödinger equation (GSE) for whistler waves with their group velocity directed along an external magnetic field is derived. The “mean” wave vector of the wave beam may be parallel to or have an angle Θ = arccos(2ω/ω_c) with the magnetic field. Applications of GSE to the whistler propagation in density ducts are considered. The results are important for the problem of the self-focusing of whistler waves.     

Relation between the critical magnetic field and energy gap of a superconductor

A dynamical model is used to derive a relationship between the slope of the reduced critical magnetic field for T = T_c and the energy gap Δ_o of a superconductor. Good agreement with the relation |dh/dt|_t=1 = Δ_o/ k T_c proposed by Toxen is found up to Δ_o/k T_c = 4.     

Superconductivity in the graphite-potassium intercalation compound C8K

Superconducting properties of pseudo-single crystals of C₈K were investigated by low frequency a.c. magnetic susceptibility and electrical resistivity measurements. The measured values of T_c were between 128 and 198 mK for 13 samples. Measurements of the superconducting transition in a magnetic field revealed a remarkable anisotropy, such that if θ is defined as the angle between the applied magnetic field and the layer plane, type II superconductivity was observed for 0° ≦ ∣ θ ∣ ? 25° and type I superconductivity for 25° ? ∣ θ ∣≦ 90°. The angular dependences of H_c2 and H_c3 were fairly well-explained by the effective mass model.     

Oxygen content and oxide barrier thickness in granular aluminum films

Granular aluminium films were prepared by evaporation in an oxygen atmosphere. The oxygen content C_o of the films was determined by Rutherford backscattering. The superconducting transition temperature T_c is measured as a function of the oxygen concentration. From the results the thickness of the oxide barriers is derived by applying a model of spherical granula. This model is confirmed by the observed linear dependence T_c α C_o.     

Dynamics of a dissipative two level system. II

The problem of quantum coherence in a symmetric double well potential with a dimensionless damping coefficient α for classical motion is studied within a spin 1/2-boson model. The experimentally measured probabilityp(t) of refinding a definite initial state after timet is approximately expressed by the transverse spin relaxation function ?(t), which is determined from a three-pole approximation, that incorporates both the correct long and short time behaviour. For a bare tunnelsplitting δ small compared to the heat bath cutoffω _c we find, that the oscillating component of ?(t) is negligible compared to the relaxational one unless α is of orderΔ/ω _c . Thusp(t)?(1+exp(?νt))/2 with a mean tunneling rateν proportional to \(\tilde \Delta = \Delta (\Delta /\omega _c )^{\frac{\alpha }{{2 - \alpha }}} \) for α < 2 andT ? \(\tilde \Delta \) and proportional toΔ ²/ω _c ·(T/ω _c ) ^α?1 otherwise. The results apply directly to recent measurements of the dynamics of flux states in a SQUID.