Thickness dependence of the surface-polariton relaxation rates in a crystal slab

A few useful formulas are derived concerning the damping properties of long-wavelength surface polaritons (SP) in a crystal slab. For example, it is shown that the SP propagation length in a metal slab with thickness 2a satisfying $\text{ω}{}_{\mathrm{p}}\text{a}\text{c}\text{< 1}$ (c is the velocity of light and ω_p the electronic plasma frequency) is increased by the factor $\text{3}\text{2}\text{(}\text{c}\text{ω}{}_{\mathrm{p}}\text{a}\text{)}{}^4$ in comparison with the corresponding value for SP in a semi-infinite metal.     

Derivation of the dielectric loss formula (a theory of dielectric relaxation in glassy systems)

The derivation is given of the empirical formula tan $\text{σ = A(ω)[}\text{1}\text{B}\text{(T?T}{}_{\mathrm{c}}\text{)]}{}^2\text{sech}{}^2\text{[}\text{1}\text{B}\text{(T?T}{}_{\mathrm{c}}\text{)]}$, where A (ω), B and T_c are constants of the dipolar material at constant applied frequency ω, which has been shown to be in excellent agreement with experimental dielectric loss data on polymers and other amorphous glasses. The derivation is based on the dynamics of a two-level model. The energy splitting, Δ, of the system is derived and determined experimentally for polymers.     

Rydberg atoms in crossed electric and magnetic fields. Experimental evidence for the Pauli quantization

The experimental evidence for the Pauli quantization obeyed by the Rydberg spectrum of rubidium, in crossed electric and magnetic fields, is reported. When the external field perturbation associated with Zeeman and linear Stark effects are of the same order but small compared to the Coulomb binding energy, the energy levels of the system are given by $\text{E}{}_{\mathrm{n,k}}\text{= -R/n}{}^2\text{+ ɡK (ω}{}^2{}_{\mathrm{L}}\text{+ ω}{}^2{}_{\mathrm{E}}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$, where K is an integer ω_L, ω_E the Larmor and linear Stark frequencies respectively.     

On some recent results concerning the superconducting transition temperature

The Eliashberg gap equations relate the transition temperature T_c of an isotropic superconductor to its electron-phonon spectral function α²F(ω) and Coulomb pseudopotential parameter $\text{μ}{}^1$. Recently the Eliashberg theory has been used to derive some supposedly rigorous results bearing on the problem of attaining higher superconducting transition temperatures: Bergmann and Rainer derived an expression for the functional derivative $\text{δT}{}_{\mathrm{c}}\text{δα}{}^2\text{F(ω)}$; Allen and Dynes showed that in the asymptotic limit of very large $\text{λ(λ?10)k}{}_{\mathrm{B}}\text{T}{}_{\mathrm{c}}\text{=f(μ}{}^1\text{)(λ〈ω}{}^2\text{〉)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ and Leavens proved that for any isotropic superconductor k_BT_c ?0.2309A, where A is the area under its electron-phonon spectral function. In this letter we show that the result of Allen and Dynes is not compatible with the other results and is, in fact, incorrect.     

Polariton modes at the interface between two conducting or dielectric media

A review of polariton modes at interfaces composed of two semiinfinite, homogeneous, and isotropic media is given. Both media are characterized by frequency-dependent dielectric functions ?_i(ω), i = 1, 2, and may become “interface-wave-active” in different frequency regions. The conditions for the existance of propagation windows are analyzed and applied to two particular cases: an interface composed of (a) two dielectrics with dielectric functions $\text{?}{}_{\mathrm{i}}\text{= ?}{}_{\mathrm{?\infty i}}\text{(}\text{ω}{}^2\text{ω}{}_{\mathrm{<mtext>Li</mtext>}}{}^2\text{ω}{}^2\text{ω}{}_{\mathrm{<mtext>T</mtext><mtext>i</mtext>}}{}^2$, where ?_t8i are the dielectric constants for very large frequencies and ωTi and ωLi are the transverse and longitudinal phonon frequencies; (b) two conductors with dielectric functions $\text{?}{}_{\mathrm{i}}\text{= ?}{}_{\mathrm{\infty i}}\text{(}\text{1 ?ω}{}_{\mathrm{i}}{}^2\text{ω}{}^2\text{)}$, where ω_iare the plasma frequencies. In the first case there exist two propagation windows in the infrared region, while in the second case there is one propagation window in the ultraviolet, visible, or infrared region. The dispersion relations of the modes and their decay distances into the two media are presented, and various damping effects are discussed. The review is concluded with theoretical results on the optical excitation and detection (ATR) of the interface modes.     

Functional derivative δTc/δα2 (Ω)F(Ω) for weak coupling superconductors

We present approximate analytic calculation of the functional derivative $\text{δT}{}_{\mathrm{c}}\text{δα}{}^2\text{(Ω)F(Ω)}$, where T_c is the superconducting critical temperature and $\text{α}{}^2\text{(Ω)F(Ω)}$ is the electron-phonon spectral function, within the “square-well model” for the phonon mediated electron-electron interaction and weak coupling limit $\text{ω}{}_{\mathrm{D}}\text{(2πT}{}_{\mathrm{c}}\text{)? 1 (ω}{}_{\mathrm{D}}$ is the Debye energy). It is found that $\text{δT}{}_{\mathrm{c}}\text{δα}{}^2\text{(Ω)F(Ω) = (1 + λ)}{}^{-1}\text{G(Ω)}$ where λ is the familiar electron-phonon coupling parameter and $\text{G(Ω)}$ is a universal function of the reduced frequency $\text{Ω}\text{=}\text{Ω}\text{T}{}_{\mathrm{c}}$. We compare this formula with accurate numerical results for several weak coupling superconductors. The overall agreement is good     

νW2 at small ω′ and resonance form factors in a quark model with broken SU(6)

The small ω′ behaviour of F₂^en/F₂^ep and the apparent difference in the q² dependences of the magnetic form factor of the proton and of the transition to Δ⁺(1236) are quantitatively correlated in a model where nucleon consistes of a quarks and a scalar or vector core. The proton and Δ transition form factors suggest that only the scalar core contributes at large q² and small ω′. As a result the ω′ dependence of $\text{F}{}_2{}^{\mathrm{<mtext>en</mtext>}}\text{F}{}_2{}^{\mathrm{<mtext>ep</mtext>}}$ is obtained for ω′ < 3 and predictions for the weak structure functions and polarisation asymmetries at smallω′ are presented. We predict $\text{F}{}^{\mathrm{<mtext>\nu </mtext><mtext>p</mtext>}}\text{F}{}^{\mathrm{<mtext>\nu </mtext><mtext>n</mtext><mtext>\omega \prime \to 1</mtext><mtext>0</mtext>}}$ asymmetries $\text{ω′→1}\text{1}$ and also expect that $\text{G}{}_{\mathrm{<mtext>m</mtext>}}{}^{\mathrm{<mtext>n</mtext>}}\text{G}{}_{\mathrm{<mtext>m</mtext>}}{}^{\mathrm{<mtext>p</mtext>}}\text{→}\text{?1}\text{2}$ as q²→∞.     

The superconducting transition temperature for very large electron-phonon coupling

A rigorous derivation of the range of validity of the asymptotic relation $\text{k}{}_{\mathrm{B}}\text{T}{}_{\mathrm{c}}\text{?0.1827[λ<ω}{}^2\text{>]}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ is presented.     

Measurements of the high frequency resistence of a deuterium plasma near the lower hybrid resonance

The resistance of a deuterium plasma generated by a radio frequency discharge near the lower hybrid resonance —power transfer into the plasma between 400W and 1500W — is measured and compared with the theory of a bounded cold plasma. Reasonable agreement is found between measurement and theory only by introducing an effective collision frequency in the range from $\text{ν}{}^1\text{= 0.01 ω}{}_{\mathrm{p}}$ up to $\text{ν}{}^1\text{= 0.1 ω}{}_{\mathrm{p}}$. The effective collision frequency introduced in this manner exhibits an almost linear dependence on the power transferred into the plasma ($\text{ν}{}^1\text{ω}{}_{\mathrm{p}}\text{～?P}$).     

Resonant motion of a spherical pendulum

The weakly nonlinear, resonant response of a damped, spherical pendulum (length l, damping ratio δ, natural frequency ω₀) to the planar displacement εl cos ωt (ε ? 1) of its point of suspension is examined in a four-dimensional phase space in which the coordinates are slowly varying amplitudes of a sinusoidal motion. The loci of equilibrium points and the corresponding bifurcation points in this space are determined. The control parameters are $\text{α= 2δ/ε}{}^{\mathrm{<mtext>2</mtext><mtext>3</mtext>}}$ and . If α < 0.441 there is a finite interval of v within which no stable equilibrium points exist. As v decreases through the upper bound (a Hopf-bifurcation point) of this interval the motion in the phase space becomes periodic and then, following a period-doubling cascade, chaotic. There may be alternating sub-intervals of chaotic and periodic motion. The chaotic trajectories in the phase space appear to lie on fractal attractors.     

Prediction of strong magnetic quantum oscillations of the nuclear spin relaxation in a quasi-two-dimensional metal

The nuclear spin lattice relaxation rate in a quasi-two-dimensional (2-D) metal under strong magnetic fields is studied in a special case where the electronic cyclotron mass is small compared with the free electron mass. In the pure limit (ω_cτ ? 1) and for sufficiently low temperatures ($\text{h}\text{?}\text{ω}{}_{\mathrm{c}}\text{> 2π}{}^2\text{k}{}_{\mathrm{B}}\text{T}$) we find remarkable quantum oscillations of the relaxation rate as a function of the magnetic field. The period of these oscillations is identical to that of the de Haas-van Alphen oscillations and their amplitude grows linearly with the magnetic field. The possibility of observing such oscillations experimentally in the quasi-2-D mercury chain compound Hg_3?δAsF₆ is discussed.     

Derivation of the Gribov—Lipatov reciprocity relation in a scaling bootstrap model

The Gribov—Lipatov reciprocity relation $\text{ν}\text{W}{}_2\text{(ω) = ? ω}{}^{-3}\text{νW}{}_2\text{(ω}{}^{-1}\text{)}$ is shown to be valid in scaling bootstrap model under certain assumptions.     

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.     

Quantum theory of longitudinal dielectric response properties of a two-dimensional plasma in a magnetic field

An analysis of dynamic and nonlocal longitudinal dielectric response properties of a two-dimensional Landau-quantized plasma is carried out, using a thermodynamic Green's function formulation of the RPA with a two-dimensional thermal Green's function for electron propagation in a magnetic field developed in closed form. The longitudinal-electrostatic plasmon dispersion relation is discussed in the low wavenumber regime with nonlocal corrections, and Bernstein mode structure is studied for arbitrary wavenumber. All regimes of magnetic field strength and statistics are investigated. The class of integrals treated here should have broad applicability in other two-dimensional and finite slab plasma studies.The two-dimensional static shielding law in a magnetic field is analyzed for low wavenumber, and for large distances we find $\text{V(}\text{r}\text{) ～}\text{Q}\text{k}{}_0{}^2\text{r}{}^3$. The inverse screening length $\text{k}{}_0\text{=}\text{2πe}{}^2\text{??}\text{?ξ}$ (? = density, ξ = chemical potential) is evaluated in all regimes of magnetic field strength and all statistical regimes. k₀ exhibits violent DHVA oscillatory behavior in the degenerate zero-temperature case at higher field strengths, and the shielding is complete when $\text{ξ = r′}\text{l}\text{z.shtsls;}\text{ω}$, but there is no shielding when $\text{ξ ≠ r′}\text{l}\text{z.shtsls;}\text{ω}{}_{\mathrm{c}}$. A careful analysis confirms that there is no shielding at large distances in the degenerate quantum strong field limit $\text{l}\text{z.shtsls;}\text{ω}{}_{\mathrm{c}}\text{> ξ}$. Since shielding does persist in the nondegenerate quantum strong field limit $\text{l}\text{z.shtsls;}\text{ω}{}_{\mathrm{c}}\text{> KT}$, there should be a pronounced change in physical properties that depend on shielding if the system is driven through a high field statistical transition. (It should be noted that the static shielding law of semiclassical and classical models has no dependence on magnetic field in two dimensions, as in three dimensions.) Finally, we find that the zero field two-dimensional Freidel-Kohn “wiggle” static shielding phenomenon is destroyed by the dispersal of the zero field continuum of electron states into the discrete set of Landau-quantized orbitals due to the imposition of the magnetic field.     

Production of A20and ω1 (1675) in the reaction π−p → π+π−π0n at 12 and 15 GeV/c

Data on the reaction π^?p → π⁺π^?π⁰ have been taken at 12 and 15 GeV/c with the CERN Omega multiparticle spectrometer. In a 3-pion partial-wave analysis strong production of $\text{A}{}_2{}^0\text{(1310)}\text{and}\text{ω}{}^1\text{(1675)}$ is observed. Total and differential cross sections are determined and density matrix elements presented as a function of t in the t- and s-channel frames. The energy dependence of A₂⁰ production is studied, and a comparison of $\text{ω(780),}\text{A}{}_2{}^0\text{(1310)}\text{and}\text{ω}{}^1\text{(1675)}$ production is made.     

A least upper bound on the superconducting transition temperature

It is rigorously shown that the superconducting transition temperature of any material for which the Eliashberg theory is valid must satisfy k_BT_c ? 0.2309 A, where A is the area under its electron-phonon spectral function α²F(ω). This relation is a least upper bound, not just an upper bound, in the sense that there is an optimal situation in which the equality holds. This occurs when the Coulomb pseudopotential parameter $\text{μ}{}^1$ is zero and the spectral function is the Einstein spectrum Aδ(ω ? 1.750 A). These results are generalized in an approximate, but sufficiently accurate, way to the case $\text{μ}{}^1\text{≠ 0}$ to obtain the more useful least upper bound $\text{k}{}_{\mathrm{<mtext>B</mtext>}}\text{T}{}_{\mathrm{<mtext>c</mtext>}}\text{? c(μ}{}^1\text{) A}$ and the corresponding optimal spectrum $\text{Aδ[ω ? d(μ}{}^1\text{)A]}$. Numerical results for the functions $\text{c(μ}{}^1\text{)}$ and d(μ¹) are presented for $\text{0 ? μ}{}^1\text{? 0.20}$. It is shown that the T_c's of many materials (including Nb₃Sn), for which experimental values of A and $\text{μ}{}^1$ are available, do not lie very far below the upper bound.     

Multidimensional elastic waves excited by oscillating domain walls

Magnetoelastic excitations with a fine structure in the 50kHz range have been observed in the study of the domain wall resonance (DWR) in magnetic garnet thin films. DWR excites standing transverse elastic waves which have a resonance frequency given by $\text{f=}\text{nv}\text{2d}$, where f is the frequency, n is an integer, v=3.5×10⁵ cm/sec is the transversal velocity of the elastic wave, and d=0.05 cm is thickness of the film/substrate system. A fine structure associated with each of these modes has been identified as due to two dimensional bulk elastic waves by using a set of parallel microstrip lines. The dispersion relation of these elastic waves is ω²=v²(k²₁+k²₂), where ω is the radial frequency, k₁ and k₂ are the wave vectors in the orientation perpendicular and parallel to the sample surface respectively. In the case of k₁?k₂, $\text{f=}\text{f}{}_0\text{+v}{}^2\text{k}{}^2{}_2\text{f}{}_0$, where f₀ is the resonance when k₂=0. The experimental results are in excellent agreement with this model. A linear dispersion, observed when using a shorted slot-line structure, is understood as the excitation of three dimensional modes due to the complex structure of the slot-line and the sample geometry.     

On a least upper bound Tc of superconductors with paramagnetic impurities

We have obtained a least upper bound, $\text{k}{}_{\mathrm{B}}\text{T}{}_{\mathrm{c}}\text{? c(μ}{}^1\text{, t)A}$, on the critical temperature T_c of an isotropic superconductor with paramagnetic impurities described by the scattering matrix t for fixed values of μ¹. We have also obtained the corresponding optimal spectrum $\text{α}{}^2\text{F(m) = Aδ[ω?d(μ}{}^1\text{, A]}$. The numerical results for the functions $\text{c(μ}{}^1\text{, t)}\text{and}\text{d(μ}{}^1\text{, t)}$ are presented for $\text{α}{}^1\text{= 0.1}$ and 0.16 in the form of universal curves representing $\text{c(μ}{}^1\text{, t)}\text{and}\text{d(μ}{}^1\text{, t)}$ as functions of the reduced impurity concentration $\text{t}\text{= t/A}$. We have also established an upper limit to the reduced critical concentration $\text{t}{}_{\mathrm{crit}}$ for an arbitrary shape of α²F(ω)1.     

Dielectric susceptibility and correlation length of one-dimensional CDW with impurties. II. weak disorder

Dependence of static dielectric susceptibility and correlation length of charge density waves (CDW) with weak defects on parameter of incommensurability with lattice is investigated. In almost commensurate phase (h?h_ch_c), $\text{χ ～ (h?h}{}_{\mathrm{c}}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>3</mtext>}}\text{In}{}^{\mathrm{<mtext>-4</mtext><mtext>3</mtext>}}\text{h}{}_{\mathrm{c}}\text{/h?h}{}_{\mathrm{c}}$ and R_c ～ (h ? h_c)^{$\text{2}\text{3}$}. In${}^{\mathrm{<mtext>1</mtext><mtext>3</mtext>}}\text{h}{}_{\mathrm{c}}\text{/h ? h}{}_{\mathrm{c}}$. Far from commensurability $\text{(h?h}{}_{\mathrm{c}}\text{) χ～ (a+h}{}^2{}_{\mathrm{c}}\text{/h}{}^2\text{)}{}^{\mathrm{<mtext>-2</mtext><mtext>3</mtext>}}$, $\text{R}{}_{\mathrm{c}}\text{～ (a + h}{}^2{}_{\mathrm{c}}\text{/h}{}^2\text{)}{}^{\mathrm{<mtext>-2</mtext><mtext>3</mtext>}}$, where a is the dimensionless ratio of random potential intensities, corresponding to backward and forward scattering impurities.