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.     

Sound attenuation in one-dimensional magnetic systems at finite temperatures

Sound attenuattion constants are calculated for the one-dimensional ferro- and antiferromagnetic systems at finite temperatures. Their frequency dependences, in both cases, turn out to be $\text{ω}{}^{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}{}_{\mathrm{<mtext>k</mtext>}}\text{if}\text{ω}{}_{\mathrm{<mtext>k</mtext>}}\text{? ω}{}_{\mathrm{c}}\text{and}\text{ω}{}^2{}_{\mathrm{<mtext>k</mtext>}}\text{if}\text{ω}{}_{\mathrm{<mtext>k</mtext>}}\text{?ω}{}_{\mathrm{c}}$, where ω_c is a “cut-off” frequency related to the three-dimensional anisotropic interactions.     

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.     

Spectroscopic information on ground-state Ar2, Kr2, and Xe2 from interatomic potentials

Calculations of vibrational and rotational level spacings of homonuclear inert gas diatomic molecules by numerical integration of the radial Schrödinger equation are presented. The potentials which were used for the ground states of Ar₂, Kr₂, and Xe₂ were obtained from accurate fits to the molecular beam scattering data. From the calculated $\text{Δ}\text{G}{}_{\mathrm{<mtext>v+</mtext><mtext>1</mtext><mtext>2</mtext>}}\text{'}\text{s}$ and B_v's, the following spectroscopic constants (in cm^?1) were fitted: for Ar₂ω_e = 31.92, ω_ex_e = 3.31, ω_ey_e = 0.11, B_e = 0.060, α_e = 0.004; for $\text{Kr}{}_2\text{ω}{}_{\mathrm{e}}\text{? 23.99}$, $\text{ω}{}_{\mathrm{e}}\text{x}{}_{\mathrm{e}}\text{? 1.30}$, $\text{ω}{}_{\mathrm{e}}\text{y}{}_{\mathrm{e}}\text{? 0.021}$, $\text{B}{}_{\mathrm{e}}\text{? 0.024}$, $\text{α}{}_{\mathrm{e}}\text{? 0.001}$; for $\text{Xe}{}_2\text{ω}{}_{\mathrm{e}}\text{? 21.26}$, $\text{ω}{}_{\mathrm{e}}\text{x}{}_{\mathrm{e}}\text{? 0.75}$, $\text{ω}{}_{\mathrm{e}}\text{y}{}_{\mathrm{e}}\text{? 0.008}$, $\text{B}{}_{\mathrm{e}}\text{? 0.013}$, $\text{α}{}_{\mathrm{e}}\text{? 0.0004}$.     

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.     

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→∞.     

Determination of effective interaction between two plasmons

Using the Bohm-Pines hamiltonian the problem of the bound state of two plasmons is investigated following two different decoupling procedures where the energy transfer $\text{Ω = 0}$ or 2ω_pl. The effective interaction g₄ between the two plasmons is found to be repulsive for $\text{Ω = 2ω}{}_{\mathrm{pl}}$ and attractive when $\text{Ω = 0}$. The case of $\text{Ω= 2ω}{}_{\mathrm{pl}}$ is shown to be analogous to the situation under which the critical coupling g_4c is determined.     

Parametric excitation of relativistic plasma oscillations by strong electromagnetic waves

Parametric interaction of strong waves ($\text{?=}\text{eE}{}_{\mathrm{<mtext>o</mtext>}}\text{m}{}_{\mathrm{<mtext>e</mtext>}}\text{cω}{}_{\mathrm{<mtext>o</mtext>}}\text{～ 1}$) with a cold, two-fluid (ion and electron) plasma is studied in the limits of high frequency (ω_o?ω_Le) and resonance (ω_o ≈ ω_Le). Unstable oscillations of both electrons and ions are found in the resonance limit.     

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.     

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     

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.     

Zero field steps in short Josephson junction

A theoretical investigation is carried out on the zero field current steps of a short Josephson junction under both the d.c. voltage V_d.c. and a.c. voltage V_a.c. cos ωt. The steps occur when the condition $\text{Ω + pω = 2Nω}{}_{\mathrm{n}}$ is fulfilled, where $\text{Ω = 2eV}{}_{\mathrm{d.c.}}\text{/}\text{h}\text{?}$, ω_n is the nth eigenfrequency in the eigenfrequency in the junction cavity, p and N are integers.     

On the asymptotic behaviour of the mass operator near the Fermi energy

By taking due account of momentum conservation, it is shown that, when ω is near the Fermi energy ω_F, the imaginary part of the mass operator $\text{M(}\text{k}\text{, ω)}$ for an infinite Fermi system behaves like (ω ? ω_F)^p(k) where the exponent p(k) ? 2 depends on the interval in which $\text{|}\text{k}\text{|}$ is lying. In particular, the commonly asserted quadratic behaviour (ω ? ω_F² is shown to be true only for $\text{|}\text{k}\text{| ? 3k}{}_{\mathrm{<mtext>F</mtext>}}$. It is explicity assumed that the Fermi system admits a perturbative type treatment.     

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.     

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.     

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.     

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.     

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.     

Surface wave second harmonic generation over a n-type semiconductor

The sharp gradient in the intensity of a surface wave over a simiconductor-vacuum interface gives rise to a strong ponderomotive force on electrons and thus generates a second harmonic wave. The power of the second harmonic shows a resonance at $\text{ω =}\text{ω}{}_{\mathrm{p}}\text{2}$ (ω and ω_p being the wave and plasma frequencies) and tends to a saturation value at very high values of ω_p.     

Possible beat effect of specific heat due to impurities in semi-metal in external magnetic field

The simple model of a single-band semi-metal or degenerate semiconductor with impurities in an external quantizing magnetic field is discussed. The susceptibility and specific heat are studied in their dependence on the field-induced quasi-local levels, due to the impurities. These levels are shown to cause additional oscillations in the thermodynamical quantities as functions of the magnetic field. Their contribution to the susceptibility and specific heat is comparable to the values for the undoped system if the impurity concentration c_i fulfils the condition $\text{c}{}_{\mathrm{i}}\text{= (c}{}_{\mathrm{e}}\text{/4√π)(}\text{h}\text{?}\text{ω/ε}{}_{\mathrm{F}}\text{)}{}^{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$, with c_e the electron concentration.