Effect of quartic-phase aberrations on the focal switch of Hermite–Gaussian beams

The focal switch of Hermite–Gaussian beams diffracted at an aperture and subsequently focused by a spherically aberrated lens is studied. Our main attention is focused on the effect of quartic-phase aberrations on the behavior of the focal switch. It is shown that quartic-phase aberrations affect the relative focal shift Δz_f, turning position s_1,t, and relative transition height Δz_sw. Apart from a critical maximum truncation parameter α_c,max, there is a critical minimum truncation parameter α_c,min. Within the region α_c,min<α<α_c,max the focal switch can take place, but quartic-phase aberrations give rise to a decrease of α_c,max-α_c,min in comparison with the aberration-free case.     

Spectral changes of vector Gaussian Schell-model beams passing through an aperture lens

On the basis of the polarization matrix and propagation equation of the cross-spectral density matrix, the spectral changes in the focal plane of vector Gaussian Schell-model (GSM) beams focused by an aperture lens are studied, where the influence of correlation and polarizer on the behavior of the spectral switch is stressed. It is found that the critical position u_c, spectral minimum S_min, and transition height Δ of the spectral switch depend on the auto-correlation but do not depend on the cross-correlation of GSM beams if there is no polarizer. However, in the presence of the polarizer u_c, S_min and Δ depend on both auto- and cross-correlations. The polarizer affects the spectral switch of vector GSM beams, whereas it does not affect the spectral switch of scalar GSM beams.     

Influence of Thomson effect on the resultant local Seebeck coefficient in thermoelectric composite materials

The resultant local Seebeck coefficient α _R (=α _S−α _T) at the interface of a thermoelement has not yet been measured, although it is an important factor governing the thermoelectric efficiency, where α _S is the local Seebeck coefficient and α _T is the one caused by the Thomson effect. It is shown in this paper that α _S, α _T, and α _R of the p- and n-type Cu/Bi–Te/Cu composites are obtained analytically and experimentally on the assumption that the local temperature of the composite on which the temperature difference ΔT is imposed varies linearly with changes in position along the composite. They were indeed estimated as a function of position from the local experimental data of R,ΔI,ΔT, and V generated by applying an additional current of ±I to the composite, where R is the electrical resistance and ΔI is a current generated by the composite. As a result, it was found that the absolute values of α _S at the hot interface of the p- and n-type composites are approximately 1.5 and 1.4 times higher than their lowest values in the middle region of the composite, respectively, while those of α _T are less than 8% of α _S all over the composite and are so small that the relation α _R≈α _S can be held. We thus succeeded in measuring α _R at the interfaces of the composite.     

Quantum measurement and pure dephasing

The prerequisite of quantum measurement is a transformation of an initially off-diagonal density matrix _ρmα;nβ describing an interacting measured object and measuring device into a diagonal density matrix _{ρmα;mαδmnδαβ} . The latter density matrix describes a proper mixture of states having definitem-values. On the other hand, the irreversible relaxation (towards the thermodynamic equilibrium) is also characterized by transformation of an initially off-diagonal matrix into a diagonal one. It has been shown that the process of irreversible relaxation can be used to perform quantum measurement, provided the duration Δt of the measurement is much larger thanT ₂, the phase relaxation time, and much smaller thanT ₁, the population relaxation time:T ₂ ≪ Δt ≪T ₁. Agedanken experiment describing this kind of measurement is provided. Aπ/2-pulse transforms an initials _z = −1/2 state into superposition ofs _z = ±1/2 states. The irreversible relaxation leads to the proper mixture ofs _z = 1/2 ands _z = −1/2 state. Results of the measurements are verified by the second electromagnetic pulse.     

Focal shift and focal switch of partially polarized Gaussian Schell-model beams passing through a system with the aperture and spherically aberrated lens separated

Based on the beam coherent-polarization (BCP) matrix approach and propagation law of partially coherent beams, the focal shift and focal switch of partially polarized Gaussian Schell-model (PGSM) beams passing through a system with the aperture and spherically aberrated lens separated is studied in detail. Our main attention is focused on the effect of spherical aberration and partial coherence on the focal shift and focal switch of PGSM beams. It is shown that for polarizer-free case there is no focal switch of PGSM beams, the focal shift of PGSM beams is closely related with spherical aberration coefficient C₄, auto-coherence length σ_a, truncation parameter δ and relative position s/f between the aperture and lens in general, and is independent of the cross-coherence length σ_c. After inserting a polarizer the focal switch can take place. Numerical calculation results are given to illustrate how the spherical aberration and partial coherence affect the focal shift and focal switch of PGSM beams.     

Determination of imaginary components of anomalous scattering of some elements from experimental data

Using the Bijvoet difference data reported in the literature for four compounds,viz./it, zinc sulphide, L-α-glyceryl phosphoryl ethanolamine monohydrate, 1-β-arabinofurinosyl cytosine hydrochloride and lithium aluminium oxide, the anomalous dispersion components Δf″ of the stronger anomalous scatterer in each case is calculated accepting the theoretical values for the lighter anomalous scatterers. For MoKα radiation the values turn out to be Δf″ z _n=1.470 (85), and for CuKα Δf″ _P=0.430 (25) Δf″ _C1=0.715 (18) and Δf″ _A1=0.264 (21). Contribution No. 421 from the Department of Crystallography and Biophysics, University of Madras, Guindy Campus, Madras 600025.     

The relative motion of membranes

The relative classical motion of membranes is governed by the equation (w _{β c} ^{α c} r ^βa ) _a = R _δγβ ^α r ^gb x ^δa p _a ^γ , where w is the hessian. This is a generalization of the geodesic deviation equation and can be derived from the lagrangian p · ṙ. Quantum mechanically the picture is less clear. Some quantizations of the classical equations are attempted so that the question as to whether the Universe started with a quantum fluctuation can be addressed.     

Spectroscopy of quasiparticle excitations of superconducting bismuth cuprate at high pressures

We study the energy spectrum of Bi2223 (Bi_1.6Pb_0.4Sr_1.8Ca_2.2Cu₃O_x) at high hydrostatic pressures by Andreev-and tunneling-spectroscopy methods. We determine the gap anisotropy in the basal ab plane and find the following values for the parameters Δ(ϕ): Δ_max=42 mV, and Δ_min=19.5 mV (T _c =110 K and dT _c /dP=0.16 K/kbar). We detect an increase in the ratio R=2Δ_max/kT _c with pressure P; for Bi2223 cuprate, dR/dP≈0.017 kbar⁻¹. In the phonon-frequency region we detect a “softening,” due to pressure, of the high-frequency part of the phonon spectrum corresponding to “breathing” modes of oxygen, as well as other optical modes of Cu-O. The characteristic frequencies of the spectrum for ℏΩ>60 mV are found to decrease, with increasing pressure, at a rate d ln(ℏΩ)/dP≈−6.5±0.5×10⁻³ kbar⁻¹. This result explains the observed increase in the ratio 2Δ/kT _c (P) in the model of strong electron-phonon interaction. Zh. éksp. Teor. Fiz. 113, 1397–1410 (April 1998)     

Third-order elastic moduli of single-layer graphene

In the framework of the Keating model with allowance made for the anharmonic constant of the central interaction between the nearest neighbors μ, analytical expressions have been obtained for three third-order independent elastic constants c _ijk (μ, ζ) of single-layer graphene, where ζ = (2α − β)/(4α + β) is the Kleinman internal displacement parameter and α and β are the harmonic constants of the central interaction between the nearest neighbors and the noncentral interaction between the next-nearest neighbors, respectively. The dependences of the second-order elastic constants on the pressure p have been determined. It has been shown that the moduli c ₁₁ and c ₂₂ differently respond to the pressure. Therefore, graphene is isotropic in the harmonic approximation, whereas the inclusion of anharmonicity leads to the appearance of the anisotropy.     

On bound state computations in three- and four-electron atomic systems

A variational approach is developed for bound state calculations in three- and four-electron atomic systems. This approach can be applied to determine, in principle, an arbitrary bound state in three- and four-electron ions and atoms. Our variational wave functions are constructed from four- and five-body Gaussoids that respectively depend on six (r ₁₂, r ₁₃, r ₁₄, r ₂₃, r ₂₄, r ₃₄) and ten (r ₁₂, r ₁₃, r ₁₄, r ₁₅, r ₂₃, r ₂₄, r ₂₅, r ₃₄, r ₃₅ and r ₄₅) relative coordinates. The approach allows operating with the more than one electron spin functions. In particular, the trial wave functions for the ¹ S states in four-electron atomic systems include the two independent spin functions χ₁ = αβαβ + βαβα − βααβ − αββα and χ₂ = 2ααββ + 2ββαα − βααβ − αββα − βαβα − αβαβ. We also discuss the construction of variational wave functions for the excited 2³ S states in four- electron atomic systems.     

On the mechanism of phase transformation in Ag2Se

A differential thermal analysis ΔT _y (T) in vacuum has been performed, and the temperature gradient ΔT _x (T) along the Ag₂Se sample during the transition α → β has been studied. It has been shown that the transitions α → α′ and β′ → β are displacive transitions and that the transition α′ → β′ is a reconstructive transition. It has been found that the temperature gradient along the sample during the transition α′ → β′ passes through a deep minimum due to a strong increase in the specific heat capacity.     

Correlation between the electric-field effect and weak-link type in YBa2Cu3−x Oy and YBa2Cu3−x Oy /Agx high-T c superconducting ceramics

An experimental study is reported of the effect of an electric field E⩽120 MV/m and of temperature T on the critical current I _c and I-V characteristics of yttrium-based high-T _c superconducting ceramics. The materials studied were copper-deficient ceramics, YBa₂Cu_3−x O_y (D samples), and YBa₂Cu_3−x O_y/Ag_x ceramics [S samples with silver present in amounts equal to the copper deficiency (0⩽x⩽0.4)]. It has been established that in D samples at 77 K, the electric field increases I _c and reduces substantially R for I>I _c, whereas in S samples no field effect is observed. Measurements of the I _c(T) dependence near the critical temperature showed that they can be described for all samples by a relation of the type I _c =const(1−T/T _c )^α, where α≈1 for the D samples, and α≈2 for the S samples. The results obtained suggest that the electric-field effect correlates with the existence in the ceramic of SIS-type weak links at grain boundaries. Fiz. Tverd. Tela (St. Petersburg) 40, 1195–1198 (July 1998)     

Weak chaos and metastability in a symplectic system of many long-range-coupled standard maps

We introduce, and numerically study, a system of N symplectically and globally coupled standard maps localized in a d=1 lattice array. The global coupling is modulated through a factor r^-α, being r the distance between maps. Thus, interactions are long-range (nonintegrable) when 0≤α≤1, and short-range (integrable) when α>1. We verify that the largest Lyapunov exponent λ_M scales as λ_M ∝ N^-κ(α), where κ(α) is positive when interactions are long-range, yielding weak chaos in the thermodynamic limit N↦∞ (hence λ_M→0). In the short-range case, κ(α) appears to vanish, and the behaviour corresponds to strong chaos. We show that, for certain values of the control parameters of the system, long-lasting metastable states can be present. Their duration t_c scales as t_c ∝N^β(α), where β(α) appears to be numerically in agreement with the following behavior: β>0 for 0 ≤α< 1, and zero for α≥1. These results are consistent with features typically found in nonextensive statistical mechanics. Moreover, they exhibit strong similarity between the present discrete-time system, and the α-XY Hamiltonian ferromagnetic model.     

Quark momentum-space charge distribution in deuteron and neutron/proton structure functions ratio

The electromagnetic polarizabilities of the nucleon are shown to be essentially composed of the nonresonant α _p(E ₀₊) = + 3.2, α _n(E ₀₊) = + 4.1, the t-channel α ^t _{p, n} = - β ^t _{p, n} = + 7.6 and the resonant β _{p, n}(P ₃₃(1232)) = + 8.3 contributions (in units of 10^-4fm^3). The remaining deviations from the experimental data Δα _p = 1.2±0.6, Δβ _p = 1.2±0.6, Δα _n = 0.8±1.7 and Δβ _n = 2.0±1.8 are contributed by a larger number of resonant and nonresonant processes with cancellations between the contributions. This result confirms that dominant contributions to the electric and magnetic polarizabilities may be represented in terms of two-photon coupling to the σ-meson having the predicted mass m _σ = 666MeV and two-photon width Γ _γγ = 2.6keV.     

Josephson and single-particle currents between partially dielectricized superconductors with charge-density waves

The amplitudes of the nonstationary Josephson current I ¹, the interference current I ², and the quasiparticle current J through symmetric and asymmetric tunnel junctions, including superconductors with charge density waves, are calculated. In the symmetric (s) case the dependence of the Josephson current I _s ¹ on the voltage V on the junction has a logarithmic singularity at |eV|=2Δ, Δ+D, and 2D, where , Δ and Σ are the superconducting and dielectric order parameters, and e is the unit charge. At temperatures T≠0 jumps appear in the current-voltage characteristics I _s ¹ (V) at |eV|=D−Δ. Jumps and singularities are observed in the currents I _s ² and J _s at the same voltages at which singularities and jumps appear in I _s ¹ , respectively. In the nonsymmetric (ns) junctions which include an ordinary superconductor, singularities and jumps occur at |eV|=D+Δ_BCS, Δ+Δ_BCS, and (for T≠0) |D−Δ_BCS| and |Δ−Δ_BCS|, where Δ_BCS is the order parameter of an ordinary superconductor. The quasiparticle current J _ns is an asymmetric function of the voltage V and does not depend on the sign of Σ. The results are compared with experiment. Fiz. Tverd. Tela (St. Petersburg) 39, 991–999 (June 1997)     

Spectral shifts and spectral switches of spatially and spectrally partially coherent pulsed beams in Young’s interference experiment

Taking the Gaussian Schell-model pulsed (GSMP) beam as a typical example of spatially and spectrally partially coherent pulsed beams, an analytical expression for the far-field spectrum of diffracted GSMP beams in Young’s interference experiment is derived, and used to study the spectral shifts and spectral switches of GSMP beams in the far field. Numerical calculation results are given to illustrate the dependence of spectral shifts and spectral switches on the obscuration ratio ε, temporal coherent length T_c, spatial correlation parameter β and diffraction angle α. It is shown that the critical angle α_c of the first- and second-order spectral switches moves away from the z axis with increasing T_c, but α_c of the third-order spectral switch moves towards the z axis with increasing T_c. The spectral transition height Δ decreases and spectral minimum S_min increases as T_c increases. α_c decreases, Δ increases and S_min decreases as β increases. The potential application of spectral switches of spatially and spectrally partially coherent pulsed beams in information encoding and transmission is proposed.     

A Class of Well Behaved Charged Analogues of Schwarzchild’s Interior Solution

A class of well behaved charged analogues of Schwarzchild’s interior solution has been obtained using a particular electric intensity. The solutions of this class are utilized to depict a superdense star model with surface density 2×10¹⁴ g cm⁻³. The solution obtained is new and the pressure (p), density (c ² ρ), velocity of sound and (p/(c ² ρ)) are monotonically decreasing towards the pressure free interface. Moreover the adiabatic constant is found to be more than (4/3) which is necessary for stability under radial perturbation. Also the electric intensity increases monotonically towards the surface. The well behaved model has the maximum mass M=1.740793M _Θ , Radius 12.130308 km. The redshift at the center and on the surface is given by z ₀=0.384261 and z _a =0.292489. Out of the models of superdense star obtained couple of models represent Vela Pulsar for (i) α ²=1.03, b=0.33, , Radius=10.8566 km, M=1.18331M _Θ , I=0.642601×10⁴⁵, (ii) α ²=1.1, b=0.3, , Radius=11.197533 km, M=1.311438M _Θ , I=0.774508×10⁴⁵. All the solutions mentioned above are reducible to Schwarzchild interior solution in the absence of charge.     

X-ray diffraction investigations of the crystallographic parameters and thermal expansion of β-BaB2O4 crystals

The lattice parameters a and c of β-BaB₂O₄ crystals have been measured in the temperature range 80–300 K by the x-ray diffraction method. The thermal expansion coefficients α are calculated from the measured values of the parameters. A substantial anisotropy of the thermal expansion is found. It is shown that the thermal expansion coefficient α _c along the c axis is an order of magnitude greater than the thermal expansion coefficient α _a in a plane perpendicular to this axis. It is established that α _a becomes negative in the temperature range 80–190 K. Fiz. Tverd. Tela (St. Petersburg) 39, 1038–1040 (June 1997)     

Modeling a dimer state in CuGeO3 in the two-dimensional anisotropic Heisenberg model with alternated exchange interaction

The two-dimensional Heisenberg spin-1/2 model with alternated exchange interaction along the c axis and an anisotropic distribution of the exchange interaction in the lattice, J _b/J _c=0.1, is examined. A quantum Monte Carlo method is used to calculate the phase diagrams of the antiferromagnet, the dimer state in a plane, the value of the alternation δ of the exchange interaction, and the anisotropy Δ=1−J ^xy/J ^z of the exchange interaction, Δ∼δ ^0.58(6). The following characteristics are calculated for Δ=0.25: the dependence of the temperature of the dimer-state-paramagnet transition on the alternation of the exchange interaction, T _c(δ)=0.55(4)(δ−0.082(6))^0.50(3), the singlet-triplet energy gap, and the dependence of the magnetization on the external field for some values of δ. The value of the exchange interaction, J _c=127 K, the alternation of the exchange interaction, δ=0.11J _c, and the correlation radius along the c axis, ξ _c≈28c, are determined. Finally, it is found that the temperature dependence of the susceptibility and the specific heat are in good agreement with the experimental data. Zh. éksp. Teor. Fiz. 112, 2184–2197 (December 1997)     

Focal shift and focal switch of Bessel–Gaussian beams passing through a lens system with or without aperture

The focal shift and focal switch of Bessel–Gaussian (B–G) beams passing through a lens system with or without aperture is studied in detail. For the unapertured case, the necessary condition for the focal switch and the expression for the amplitude of the focal switch are derived. It is shown that if the truncation parameter δδ_c or beam parameter ββ_c (δ_c, β_c are the corresponding critical values), there exits only one axial intensity maximum, and the focusing without focal shift can be achieved for u/f=1 (u is the separation between the aperture and lens, f is the focal length of the lens); if δ>δ_c and β>β_c, there exist two axial intensity maxima, and the focal switch can take place at the turning point u/f=1 for both apertured and unapertured cases. The dependence of the amplitude of focal switch and normalized axial intensity minimum on the truncation parameter, beam parameter and Fresnel number is also studied.