Dielectric relaxation and ac conductivity of sodium tungsten phosphate glasses

Studies of dielectric relaxation and ac conductivity have been made on three samples of sodium tungsten phosphate glasses over a temperature range of 77–420 K. Complex relative permitivity data have been analyzed using dielectric modulus approach. Conductivity relaxation frequency increases with the increase of temperature. Activation energy for conductivity relaxation has also been evaluated. Measured ac conductivity (σ_m(ω)) has been found to be higher than σ_dc at low temperatures whereas at high temperature σ_m(ω) becomes equal to σ_dc at all frequencies. The ac conductivity obeys the relation σ_ac(ω)=Aω ^S over a considerable range of low temperatures. Values of exponent S are nearly equal to unity at about 78 K and the values decrease non-linearly with the increase of temperature. Values of the number density of states at Fermi level (N(E _F)) have been evaluated at 80 K assuming values of electron wave function decay constant α to be 0.5 (Å)^?1. Values of N(E _F) have the order 10²⁰ which are well within the range suggested for localized states. Present values of N(E _F) are smaller than those for tungsten phosphate glasses.     

Temperature and purity dependence of the nuclear-spin relaxation rate in the gapless region of type-II superconductors

The volume average of the nuclear-spin relaxation rate in type-II superconductors,R _s, is calculated for magnetic fields slightly below the upper critical field and all mean free paths,l, and temperatures. It is found to be expressible solely in terms of the volume average of the density of states,\(\bar N(\omega )\), where the latter quantity has been determined recently byNeumann for alll. The derivation is based onHelfand andWerthamer's eigen-value equation for the order parameter,Δ. The deviation of\(\bar R_s \) from the relaxation rate in the normal state,R _n, is proportional to the quantity\([|\overline {\Delta |^2 } /\Delta _{BCS}^2 (T)]R_n \) (the bar denotes the spatial average). The proportionality factor is found to decrease monotonously as the temperature decreases and/orl increases. This behavior is closely related to the fact that\(\bar N(\omega )\) shows no gap for the excitation energiesω and decreases asl increases, in particular at energiesω close to zero (ω=0 corresponds to the Fermi energy).     

Diamagnetism and the dispersion of the magnetic permeability

It is well known that the usual Kramers–Kronig relations for the relative permeability function μ(ω) are not compatible with diamagnetism (μ(0) < 1) and a positive imaginary part (Im μ(ω) > 0 for ω > 0). We demonstrate that a certain physical meaning can be attributed to μ for all frequencies, and that in the presence of spatial dispersion, μ does not necessarily tend to 1 for high frequencies ω and fixed wavenumber k. Taking the asymptotic behavior into account, diamagnetism can be compatible with Kramers–Kronig relations even if the imaginary part of the permeability is positive. We provide several examples of diamagnetic media and metamaterials for which μ(ω, k) ?  1 as ω →∞.     

Controlling depinning and propagation of single domain-walls in magnetic microwires

The magnetization reversal in magnetostrictive amorphous microwires takes place by depinning and propagation of a single domain wall. This is a consequence of the particular domain structure determined by the strong uniaxial anisotropy from the reinforcement of magnetoelastic and shape contributions. In the present study, after an overview on the current state-of-the art on the topic, we introduce the general behaviour of single walls in 30 to 40 cm long Fe-base microwires propagating under homogeneous field. Depending on the way the walls are generated, we distinguish among three different walls namely, standard wall, DW _st , depinned and propagating from the wire’s end under homogeneous field which motion is the first one to switch on; reverse wall, DW _rev , propagating from the opposite end under non-homogeneous field, and defect wall, DW _def , nucleated around local defect. Both, DW _rev and DW _def are observed only under large enough applied field. In the subsequent section, we study the propagation of a wall under applied field smaller than the switching field. There, we conclude that a minimum field, H _dep,0, is needed to depin the DW _st , as well as that a minimum field, H _prop,0, is required for the wall to propagate long distances. In the last section, we analyse the shape of induced signals in the pickup coils upon the crossing of the walls and its correlation to the domain walls shape. We conclude that length and shape of the wall are significantly distorted by the fact that the wall is typically as long as the measuring coils.     

Investigation of zero-frequency solutions to the pion dispersion equation

The instability of nuclear matter is considered for the case where it is generated by the vanishing of the frequencies of collective excitations belonging to specific types (specifically, excitations that have the pion quantum numbers J ^π = 0^?). The behavior of zero-frequency solutions to the pion dispersion equation is analyzed versus the strength G′ of spin—isospin particle—hole interaction. It is shown that there exists a strength value G′_tr (|G′_tr| ? 1) such that, for G′ < G′_tr, zero-frequency solutions are excitations of the ω _P type, while, for G′ ≥ G′_tr, such solutions are excitations of the ω _c type. Excitations of the ω _P type for G′ < ?1 describe the instability of nuclear matter against small density fluctuations (Pomeranchuk’s instability), while excitations of the ω _c type are responsible for the instability associated with pion condensation at G′ ≈ 2. For stable nuclear matter, the solutions ω _P(κ) and ω _c (κ) lie on unphysical sheets of the complex plane of frequency.     

Long-time relaxation phenomena in Pb<Subscript>0.94</Subscript>Ba<Subscript>0.06</Subscript>Sc<Subscript>0.5</Subscript>Nb<Subscript>0.5</Subscript>O<Subscript>3</Subscript> (PBSN-6) single crystals

Long-time polarization relaxation in the temperature range where PBSN-6 single crystals reside in the relaxor state was studied. An analysis of the time dependence of the permittivity ε′(t) performed at measuring frequencies from 1 Hz to 1 kHz in weak electric fields E₀ showed that the relaxation (or freezing) times derived by extrapolating relations of the type ε′(t) ～ log(t/t₀) and ε′(t) ～ exp{?[ln(t/t₀)]_β} range from 10⁸ to 10¹¹ min and depend substantially on the bias voltage applied to the sample. A study of the pattern of the dielectric response in moderate and strong infralow-frequency fields revealed that, after a sample was maintained under a bias lower than the coercive force, it no longer exhibited the additional anomalies in the amplitude dependences of the effective loss tangent tan_eff(E₀) than were observed in a thermally recuperated sample.     

The structure of a vortex line and the lower critical field in superconducting alloys

The structure of an isolated vortex line, and the lower critical fieldH _c 1, is calculated by means of the generalized Ginzburg-Landau (GL) theory for arbitrary values of the GL-parameterk(≧1/√2) and the mean free pathl at temperaturesT in the vicinity ofT _c . The free energy functional including the corrections of order [1?(T/T _c )] to the GL-functional is derived exactly. The corresponding Euler-Lagrange equations determining the zero-order (GL) contributions and the corrections of order [1?(T/T _c )] to the order parameter,f(r), and the superfluid velocity,v(r), have been solved numerically. The shapes of the first-order corrections off(r), v(r), and the magnetic field,h(r) are found to depend markedly, for a given value ofκ, on a second parameter,α=0.882(ξ ₀ /l) (whereξ ₀ is theBCS-coherence-distance). The deviations from the GL-solutions become largest forh(r) at parameter valuesk≈ 1 andα ≈ 0(the deviation ofh(0) is about 6% atT=0.9T _c forκ=1 andα=0). The ratioH _c1/H _c (where the thermodynamic criticalH _c has the BCS-temperature-dependence) is found to increase slightly in the “clean” limit (α=0), and to decrease slightly in the “dirty” limit (α=∞) asT decreases (the variation ofH _c 1/H _c is always less than 3% for arbitrary values ofκ andα asT decreases fromT _c to 0.9T _c ).     

Evolution of an optically pumped ensemble of cold ground-state atoms in weak light fields

The evolution of multipole moments is analyzed for optically pumped cold ground-state atoms in the limit of low saturation of a closed j₀ → j₁ dipole transition. The longest multipole-moment relaxation times are analyzed as functions of ellipticity and frequency detuning from resonance for transitions with j₀ ? 5. The qualitative difference between the evolution toward steady-state Zeeman sublevel populations and dynamics of transient spontaneous emission is demonstrated for transitions of the following types: j → j?1, j → j with integer j, j → j with half-integer j, and j → j + 1.     

Derivation of Hamaker Dispersion Energy of Amorphous Carbon Surfaces in Contact with Liquids Using Photoelectron Energy-Loss Spectra

Hamaker interaction energies and cutoff distances have been calculated for disordered carbon films, in contact with purely dispersive (diiodomethane) or polar (water) liquids, using their experimental dielectric functions ε (q, ω) obtained over a broad energy range. In contrast with previous works, a q-averaged <ε (q, ω) >  _q is derived from photoelectron energy-loss spectroscopy (XPS-PEELS) where the energy loss function (ELF) < Im[?1/ε (q, ω)] >  _q is a weighted average over allowed transferred wave vector values, q, given by the physics of bulk plasmon excitation. For microcrystalline diamond and amorphous carbon films with a wide range of (sp³/sp² + sp³) hybridization, non-retarded Hamaker energies, A ₁₃₂ (L < 1 nm), were calculated in several configurations, and distance and wavenumber cutoff values were then calculated based on A ₁₃₂ and the dispersive work of adhesion obtained from contact angles. A geometric average approximation, H _0?CVL ?=?(H _0?CVC H _0?LVL )^1/2, holds for the cutoff separation distances obtained for carbon-vacuum-liquid (CVL), carbon-vacuum-carbon (CVC) and liquid-vacuum-liquid (LVL) equilibrium configurations. The linear dependence found for A _CVL, A _CLC and A _CLV values as a function of A _CVC, for each liquid, allows predictive relationships for Hamaker energies (in any configuration) using experimental determination of the dispersive component of the surface tension, \( {\gamma}_{CV}^d \), and a guess value of the cutoff distance H _0?CVC of the solid.

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Depolarizing collisions in ytterbium vapor: Isotropic and anisotropic relaxation

Isotropic depolarizing collisions are studied using a stimulated photon echo with a specific polarization of the excitation radiation pulses in a mixture of ytterbium with krypton for the J = 1 ? J = 0 transition of ¹⁷⁴Yb. The difference between the relaxation rates of orientation and alignment γ _b ⁽²⁾ ? γ _b ⁽¹⁾ of the ³ P ₁(6s6p) ¹⁷⁴Yb level is measured as a function of the krypton pressure. The collision photon echo at the J = 1 ? J = 0 transition induced by the anisotropic relaxation is studied for the Yb + Xe mixture. The power of the collision echo increases from zero with the addition of a buffer gas to ytterbium, reaches an optimal level, and decreases with an increase in the buffer gas pressure. The polarization of this collision-induced echo differs from the polarization of the conventional echo. The experimental results are in qualitative agreement with theoretical predictions.     

Nuclear magnetic relaxation of spin<Emphasis Type="Italic">I</Emphasis>=1/2 scalar coupled to a quadrupolar nucleus in the presence of cross-correlation effects

The rigorous treatment of relaxation for the dipolar-multipolarAX spin system (I=1/2,S>1/2) in the presence of the dipolarI-S coupling, anisotropy chemical shift and quadrupolar interaction ofS spin is proposed. The calculations of the spin evolution under the relaxation Hamiltonian are based on the second-order time-dependent perturbation theory and are carried out in the operator representation. For this task the double commutator identities of the type [[I _±S _z ⁿ ,A _q ^μp ]A _?q ^μp ] and [[I _zS _z ⁿ ,A _q ^μp ]A _?q ^μp. ] are derived. The fist-order differential equations for the evolution of longitudinal two-spin orderI _zS _z ⁿ , z=magnetization ofS spinS _z ⁿ and coherences <I _±S _z ⁿ > in the spin systemIS with scalar coupling between spin 1/2 and quadrupolar spinS>1/2 were obtained. These equations are used to get equations for the evolutions of each component of the multiplet structure of spinI. The imaginary part of the cross-correlation spectral density function and indirect spin-spin coupling Hamiltonian are taken into account. Equations for the longitudinal components of theI spin spectrum in the presence of cross-correlation effects were obtained also. Longitudinal and transverse relaxation times and cross-relaxation times in the presence of cross-correlation D-CSA, Q-CSA, Q-D were analyzed.     

Decoherence control mechanisms of a charged magneto-oscillator in contact with different environments

In this work, we consider two different techniques based on reservoir engineering process and quantum Zeno control method to analyze the decoherence control mechanism of a charged magneto-oscillator in contact with different type of environment. Our analysis reveals that both the control mechanisms are very much sensitive on the details of different environmental spectrum (J?(ω)), and also on different system and reservoir parameters, e.g., external magnetic field (r _c ), confinement length (r ₀), temperature (T), cut-off frequency of reservoir spectrum (ω _cut ), and measurement interval (τ). We also demonstrate the manipulation scheme of the continuous passage from decay suppression to decay acceleration by tuning the above mentioned system or reservoir parameters, e.g., r _c , r ₀, T and τ.     

A first-principle study on the phase transition,electronic structure,and mechanical properties of three-phase ZrTi<Subscript>2</Subscript> alloy under high pressure*

We employed density-functional theory (DFT) within the generalized gradient approximation(GGA) to investigate the ZrTi₂ alloy, and obtained its structural phase transition,mechanical behavior, Gibbs free energy as a function of pressure, P-V equation of state,electronic and Mulliken population analysis results. The lattice parameters andP-V EOS for α, β and ω phases revealed by ourcalculations are consistent with other experimental and computational values. The elasticconstants obtained suggest that ω-ZrTi₂ and α-ZrTi₂ are mechanically stable, and that β-ZrTi₂ is mechanically unstableat 0 GPa, but becomes more stable with increasing pressure. Our calculated resultsindicate a phase transition sequence of α → ω → β forZrTi₂. Both thebulk modulus B and shear modulus G increase linearly withincreasing pressure for three phases. The G/B values illustrated goodductility of ZrTi₂alloy for three phases, with ω<α<β at0 GPa. The Mulliken population analysis showed that the increment of d electron occupancystabilized the β phase. A low value for B '₀ is the feature of EOS for ZrTi₂ and this softness in the EOS isrepresentative of pressure induced s-d electron transfer.     

The non-Markovian stochastic Liouville equation and anomalous quantum relaxation kinetics

We analyze within the continuous-time random walk approach, the kinetics of phase and population relaxation in quantum systems induced by noise with the anomalously slowly decaying correlation function P(t) ∝ (wt)^-α, where 0 < α < 1. The relaxation kinetics is shown to be anomalously slow. Moreover, for α < 1, in the limit of a short characteristic time of fluctuations w^-1, the kinetics is independent of w. As α → 1, the relaxation regime changes from the static limit to narrowing of fluctuation. Simple analytical expressions are obtained that describe the specific features of the kinetics.     

The effect of the spatial variation of the order parameter on the tunneling density of states of superconducting alloys

In the first part of the paper we derive expressions of the Ginzburg-Landau (GL) type for the local tunneling density of states of superconducting alloys. These expressions are quite generally applicable at high excitation energies. One can see immediately that the density of states,N(r, ω), at any positionr and high energiesω is always larger than the local BCS density of states if the space dependence of the order parameter is governed by the GL-equation. This effect is largest for long mean free pathsl. In the second part of the paper we calculate the spatial average of the density of states,¯N, at all energiesω for a lattice of vortex lines in a magnetic field slightly below the upper critical field. The resulting curve of [¯N? N(0)]/N(0) versus co shows no gap and has a zero at about the gap value in zero field. Its value at ω=0 depends onl like ln(ξ₀/l) for l?ξ₀ [N(0) denotes the normal density of states, and ξ₀ is the BCS coherence length].     

The Schrödinger Equation,the Zero-Point Electromagnetic Radiation,and the Photoelectric Effect

A Schrödinger type equation for a mathematical probability amplitude Ψ(x,t) is derived from the generalized phase space Liouville equation valid for the motion of a microscopic particle, with mass M and charge e, moving in a potential V(x). The particle phase space probability density is denoted Q(x,p,t), and the entire system is immersed in the “vacuum” zero-point electromagnetic radiation. We show, in the first part of the paper, that the generalized Liouville equation is reduced to a simpler Liouville equation in the equilibrium limit where the small radiative corrections cancel each other approximately. This leads us to a simpler Liouville equation that will facilitate the calculations in the second part of the paper. Within this second part, we address ourselves to the following task: Since the Schrödinger equation depends on \(\hbar \), and the zero-point electromagnetic spectral distribution, given by \(\rho _{0}{(\omega )} = \hbar \omega ^{3}/2 \pi ^{2} c^{3}\), also depends on \(\hbar \), it is interesting to verify the possible dynamical connection between ρ₀(ω) and the Schrödinger equation. We shall prove that the Planck’s constant, present in the momentum operator of the Schrödinger equation, is deeply related with the ubiquitous zero-point electromagnetic radiation with spectral distribution ρ₀(ω). For simplicity, we do not use the hypothesis of the existence of the L. de Broglie matter-waves. The implications of our study for the standard interpretation of the photoelectric effect are discussed by considering the main characteristics of the phenomenon. We also mention, briefly, the effects of the zero-point radiation in the tunneling phenomenon and the Compton’s effect.     

Isospin violation in mixing and decays of <Emphasis Type="Italic">ρ</Emphasis> and <Emphasis Type="Italic">ω</Emphasis> mesons

The influence of isospin-violating (ρ⁰, ω) mixing is discussed for any pair of decays of ρ⁰, ω into the same final state. It is demonstrated, in analogy to the CP violation in neutral kaon decays, that isospin violation can manifest itself in various forms: direct violation in amplitudes and/or violation due to mixing. In addition to the known decays (ρ⁰, ω) → π⁺π^? and (ρ⁰, ω) → π⁰γ, the pair of decays to e⁺e^? and the whole set of radiative decays with participation of ρ⁰, ω (in initial or final states) are also shown to be useful and promising for studies. Existing data on these decays agree with the universal character of the mixing parameter and indirectly support enhancement of ρ⁰ → π⁰γ in respect to ρ^± → π^±γ. Future precise measurements will allow one to separate different forms of isospin violation and elucidate their mechanisms.     

Geometric resonance in the optical properties of microinhomogeneous PdMn<Subscript>x</Subscript>Fe<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript> alloys

The optical properties of PdMn_xFe_1?x ternary alloys in the homogeneous ferromagnetic (F₁, for x ～ 0) and antiferromagnetic (A, for x ～ 1) states, as well as in the microinhomogeneous state (at x=0.7), are discussed. In the x=0.7 alloy, the presence of nuclei of the low-resistivity, PdFe-type F₁ phase in the high-resistivity, PdMn-type A matrix was shown to produce a narrow maximum on the optical-conductivity σ(ω) curve at E ～ 0.1 eV, which is due to a geometric resonance associated with light scattering from phase inhomogeneities of the sample. The behavior of σ(ω) in the interband transition region is dominated by parameters of the electronic spectrum of both the A and F₁ phases.