Omega Tau Research Articles

Simplification of the resonance fluorescence spectrum by detuning from absorption features

Detuning the incident laser from any of the stationary vibrational features identified by the Smalley group in the long-tail alkylbenzenes is proposed. It is suggested that, in a relative sense, relaxed fluorescence lines will disappear and resonance fluorescence lines will grow back as the detuning frequency is increased. The proposed claim is based on the time-energy uncertainty principle ..delta.. omega tau similarly order 1. By detuning ..delta.. omega increases, tau goes down, and the zeroth-order vibrational state has less and less time to evolve into the tail.

The accuracy of Braginskii's transport coefficients for a Lorentz plasma

Transport coefficients appropriate to Ohm's Law and electron heat flow are derived for a Lorentz plasma. Their values are calculated directly from a cartesian tensor expansion of the electron distribution function without the use of Laguerre polynomials. Significant inaccuracies are found in Braginskii's thermoelectric and heat flow coefficients, for certain values of omega tau (where omega is the electron cyclotron frequency and tau its mean collision time with ions).

Logarithmic frequency dependence of the dynamical conductivity of one-dimensional disordered systems at low frequencies: a computer simulation for a very long chain

The low-frequency behaviour of the dynamical conductivity sigma ( omega ) for electrons on very long (106 sites) one-dimensional disordered chains is investigated by computer simulation. Berezinskii's result (1974) which is asymptotically exact in the limit of weak disorder and shows the behaviour sigma ( omega )/ sigma 0 to 32( omega tau )2(ln2(4 omega tau )- pi 2/4+(2C-3)ln(4 omega tau )+ ...) at low frequencies ( sigma 0, tau and C denote the Drude value of the conductivity, the relaxation time of the electrons and Euler's constant, respectively), is established for the first time by a direct numerical method. A discussion is given of a simple derivation of the coefficient 32. It is also found that this low-frequency behaviour remains almost when disorder is introduced, unchanged even when the disorder is strong.

Laser-enhanced mobility in semiconducting layered structures

The influence of a laser field on the scattering rate for the electron-phonon interaction in semiconductor layered heterojunction structures is discussed. It is found that for a laser beam polarised in the layer plane and with a frequency omega such that omega tau >1, where tau is the carrier relaxation time, the phonon-limited mobility increases with increasing laser field strength.

Diffusion with drift on a finite line

The authors consider diffusion in the presence of drift (caused, e.g. by a constant external field) on a finite continuous line terminated by reflecting boundaries. Exact analytical expressions are obtained for the positional probability density and the generalised diffusion coefficient (or the dynamic mobility), and thence the frequency-dependent dielectric response. For a given ratio of the diffusion and drift time scales, the generalized diffusivity is shown to be a universal function of omega tau L where tau L is the diffusion time on a strand of length L. They also present an exact solution for the strand-length-averaged diffusion coefficient in the absence of drift, which is the continuum analogue of the corresponding solution in the bond-percolation model. Finally, they apply their results to spectral diffusion and recover the nonDebye pulse relaxation known to occur in certain time regimes owing to the interplay of diffusion and drift.

Shear viscoelasticity of suspensions of biological cells with fluid membrane.

In order to consider the effect of membrane fluidity upon the mechanical property of biological cell suspensions, we have calculated the complex intrinsic viscosity [eta*] = [eta'] - i[eta"] of spherical shell structures with material incompressibility in suspension as a function of the dimensionless frequency x = omega eta'a/gamma' together with the parameters of hm = eta m/eta', g = gamma/gamma', h = eta/eta', delta = d/a, where a is the radius of the cell, d is the width of the membrane, eta, eta m, and eta' are the viscosities of the medium, of the membrane and of the internal region of the cell, gamma and gamma' the surface tensions at the outer and the inner side of the membrane respectively, and omega the angular frequency. The result is simply represented by two dispersions as follows: [eta*]/[eta] = A1 + B1/(1 + i omega tau 1) + B2/(1 + i omega tau 2). Here i is the imaginary unit, A1 = 2(1 - h)/(2 + 3h) + O(delta), B1 = 3h/(5 + 5h) + O(delta), B2 = h (19 + 16h)/[5(1 + h) (2 + 3h)] + O(delta), tau 1 = [(5/24) (1 + h) (1 + 1/g) delta-2 + O(delta-1)] a eta'/gamma', tau 2 = [(2 + 3h) (19 + 16h)/[40 (1 + h) (1 + g)] + O(delta)] a eta'/gamma', and [eta] = (5/2) [96hmg + 32g (5 + 5h - 12hm)delta + O(delta 2)]/[96hmg + 32g (5 + 2h - 12hm) delta + O(delta 2)].

An ultrasonic study of stress-induced ordering of hydrogen in single-crystal palladium hydride

The attenuation of longitudinal acoustic waves propagating along the (110) axis in single-crystal PdH0.64 has been investigated over the temperature range 80-300K and the frequency range 10-270 MHz. At a given frequency the attenuation exhibits a maximum as a function of temperature. The attenuation peaks are attributed to the stress-induced ordering of hydrogen atoms on the interstitial sites. These peaks occur when omega tau R=1, where omega /2 pi is the frequency of the ultrasonic wave and tau R is the relaxation time for stress-induced ordering. An Arrhenius plot of tau R-1 against inverse temperature gives an activation energy of 0.23+or-0.02 eV over the temperature range 190-240K, approximately the same as that deduced by other techniques for the hopping of hydrogen between interstitial sites. Surprisingly, the experimental value of tau R at any particular temperature is about an order of magnitude shorter than the mean time of stay of hydrogen on an interstitial site as determined by other experimental techniques. Possible reasons for this discrepancy are discussed.

Spin waves in sodium and potassium at 80 GHz

Measurements are presented of spin waves observed in the nearly free-electron metals sodium and potassium, utilising a transmission microwave spectrometer operating at 80 GHz. With very pure material and careful sample preparation it has been possible to detect up to fifty distinct spin waves. The samples, studied at 1.4K, have values of omega tau of the order of 150 where omega is the observational frequency and tau is the momentum relaxation time determined from the linewidth and amplitude decay of the spin waves. Consequently the signals approximate very closely to the infinite omega tau limit. This allows a simple comparison of theory with experiment yielding values for B0, B1 and B2, the first three parameters characterising the many-body spin interaction. For sodium B0=-0.210+or-0.015, B1=-0.010+or-0.015 and mod B2 mod <or=0.02 while for potassium B0=-0.293+or-0.01, B1=-0.076+or-0.01 and mod B2 mod <or=0.01.

Conductivity of 1D electrons in anisotropic 3D medium

Discusses the phonon limited high-temperature conductivity of 1D electrons within the quasistatic limit for lattice vibrations ( omega tau <<1 where omega is the phonon frequency and tau is the electron scattering time) using both first and second Born approximations and electron-one-phonon interaction. The second-order contribution of acoustic phonons to tau -1 is shown to be divergent when the phonons are 1D as well. This divergence indicates that the second-order contribution to the resistivity may be important in the case of anisotropic 3D acoustic phonons. The authors show that the ratio between the first- and second-order electron scattering rates is: tau 2-1/ tau 1-1 varies as ( lambda / alpha )(T/ epsilon F); where lambda is the dimensionless /electron-phonon coupling constant and alpha =vperpendicular to /v/sub /// is the ratio of the sound velocities perpendicular to and along the chain direction. Thus the second-order contribution is seen to be enhanced for small alpha . The theory is applied to the resistivity of mercury chains in Hg3- delta AsF6 where alpha is known to be very small. It is compared with previous experimental results of rho (T) as well as with a newly obtained one at an extended temperature region, up to 430K. It is shown that the expression for the resistivity which follows from the authors' theory; rho =AT+BT2 can account for the experimental data in the temperature range 235K-430K. The electron-multiphonon series in first Born approximation for atomic chains is summed in the quasi-static limit and is shown to be strongly suppressed. The organic conductor TTF-TCNQ is also discussed. Here the present-second order contribution is shown to be smaller because the phonons are isotropic ( alpha approximately=1).

Nuclear spin relaxation by translational diffusion in solids. VI. Monovacancy limit

For pt.V see ibid., vol.14, p.447 (1981). The theory of the two-spin correlation functions J(p)( omega ) that determine nuclear spin relaxation rates has been developed for the monovacancy limit of high spin concentrations using the encounter model of Einenstadt and Redfield. The theory is based upon a rate equation for the spin pair probability function and avoids the assumption of a Poisson distribution used by Wolf which is only valid if the spin motions are uncorrelated. In the high-frequency limit omega tau s>>1 and omega tau v >1 the results obtained disagree with those obtained by Feeders (1979) using a moment expansion.

Elastic behaviour of YAG under pressure

Measurements of the effects of hydrostatic and uniaxial pressures on ultrasonic wave velocities are used to obtain the six third-order elastic constants of yttrium aluminium garnet (YAG). Results are used to investigate whether the shear isotropy and the conformity with the Cauchy relation (indicative of central forces), which hold for the second-order elastic constants of YAG, extend into the region of finite strain which determines higher-order elasticity. The compression has been extrapolated up to 150*108 Pa using the Murnaghan equation of state. The vibrational anharmonicity of YAG and yttrium iron garnet (YIG) are compared through the acoustic-mode Gruneisen gammas computed from the pressure dependences of the elastic constants. The attenuation of transverse microwave ultrasonic waves propagated along the (001) direction (the mode used in acoustic devices) due to anharmonic interactions with thermal phonons, calculated at the limits omega tau >>1 and omega tau <1, is shown to be in good agreement with previous experimental attenuation measurements for this mode.

Acoustic shear impedance of superfluid3He at low temperatures

The acoustic impedance of superfluid 3He for the transverse mode in the collisionless limit ( omega tau = infinity ) is calculated under conditions h(cross) omega <<2 Delta and h(cross) omega <<kT. The boundary condition is chosen to be consistent with diffuse scattering for quasiparticles. Graphs for the temperature dependence of the impedance in the B phase are given as results of numerical calculations. In the A phase, at low temperatures, leading contributions are either like T3, T4 or T5 for l//e, l//q or l perpendicular to e, q respectively.

Cluster approximation in the theory of the AC hopping conductivity in disordered systems. II. The three-dimensional case

For pt.I see ibid., vol.12, p.2797 (1979). AC hopping conductivity calculations are performed using a method analogous to the one used in percolation theory for frequencies lower than those described by two-site models. An expression was obtained for sigma ( omega ) approximately omega f( omega tau c), f being a slowly decreasing function of omega tau c( tau c is a few orders of magnitude larger than the characteristic time in two-site models, tau 0 approximately 1/ nu ph). Over a wide frequency range sigma ( omega ) approximately omega s, with s<1, and s may depend on omega , temperature and concentration of localisation centres. Agreement between the theory and the available experimental data is discussed.

Cyclotron resonance line shape and cyclotron waves for a spherical Fermi surface

A recently developed formalism is applied to the evaluation of the surface impedance for a metal in a magnetic field. A spherical Fermi surface is assumed for the metal and the field configuration considered is the Azbel-Kaner geometry. The formalism makes use of the dispersion relation for extraordinary cyclotron waves in an essential way and the authors therefore give a detailed treatment of this dispersion relation for a finite value of omega tau and for frequencies of the order of 25-50 GHz. The fundamental cyclotron resonance and the surface impedance anomalies, occurring above the fundamental resonance, observed experimentally in potassium by Dunifer and co-workers are calculated. The correlation between the surface impedance and the dispersion relation for the cyclotron waves is pointed out and the significance of the polarisation properties of the waves is emphasised.

Transport coefficients in strong magnetic fields

Formulae describing the electron transport coefficients as functions of the conductivity tensor are derived on the basis of the linear response theory. It is shown that the Wiedemann-Franz law and the Mott rule are obeyed even in the presence of a quantizing magnetic field omega tau >1 if the scattering of electrons is elastic and if h(cross) omega >>kT. As no assumptions about the form of the one-electron potential are made, the conclusions are valid not only in the case of the Shubnikov-de Haas oscillations but also if effects such as magnetic breakdown and the size-effect appear.

Plasma diagnosis of a Hall accelerator discharge

The results of plasma measurements on a two-stage, high-current-density ( approximately 50 A cm-2) Hall accelerator hydrogen plasma are described. These measurements show that although Omega tau is large so that the electrons are collisionless, the observed electron conductivity is anomalously high. This appears to arise because of the existence of an approximately 5 MHz fluctuation in which the associated azimuthal electric field drives collisionless electron drift currents. Momentum and total energy balances are investigated. These are consistent with a large wall loss of ions which is to be expected since the instability-dominated accelerating voltage gives a small ratio of ion Larmor radius to stage length. The electron energy balance is studied so that this might provide the basis for a stability analysis.

A study of the virtual bound state dielectric constant

It is shown that existing theoretical expressions for the dielectric constant of virtual bound state alloys can only be valid in the frequency range omega tau >>1. A general expression is proposed which is valid at both low and high frequencies. Use of the conductivity sum rule then indicates changes in the electronic effective mass. Earlier expressions are not consistent with the sum rule, nor indeed with Kramers-Kronig relation between real and imaginary parts of the dielectric constant.

Ultrasonic attenuation in GaAs from 2K to 300K

Ultrasonic attenuation measurements have been made in GaAs (n-type carrier density 1.3*1016cm-3) between 2K and room temperature at 40 MHz 80 MHz 160 MHz and 320 MHz. The ultrasonic attenuation is dominated by damping due to phonon-phonon interactions and is interpreted in terms of the Woodruff-Ehrenreich theory (1961). In GaAs the attenuation frequency exponent approaches 2 at the highest temperatures and falls towards 1 in the region omega tau =1 (about 30K) these results confirm the predictions of the Woodruff-Ehrenreich theory. Details are given of the Gruneisen parameter average which is operative in this model for the phonon damping.

Exact solution of the AC hopping conductivity problem at low site densities

A sum rule is derived for the hopping conductivity ( sigma ( omega )) in the rate equation formalism. It is shown that the pair approximation to ( sigma ( omega )) satisfies the sum rule exactly in the limit of low site densities. Detailed comparison of the exact high-frequency expansion of ( sigma ( omega )) with that derived from the pair approximation shows that the pair approximation becomes exact for all omega in the limit of low site densities. The real and imaginary parts of ( sigma ( omega )) are calculated numerically in this limit on the basis of model assumptions about the site statistics and the intersite transition rates which are appropriate to doped crystalline semiconductors. The magnitude of the ratio of the imaginary to the real part of ( sigma ( omega )) is shown to be 0.293 lg ( omega tau 0)-1 in this case where tau 0 is the minimum pair relaxation time.

The dispersion of transverse zero sound in liquid helium 3

The dispersion relation for transverse sound in a Fermi liquid has been derived for all omega tau ( omega is the sound frequency, tau is the quasi-particle relaxation time), and using this the shear wave properties of liquid 3He have been calculated. For omega tau >1) transverse zero sound should propagate if the liquid is pressurized. The nature and properties of this zero sound are discussed, and suggestions are offered as to how it could be studied experimentally.