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.     

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.     

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.     

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.     

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.     

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.     

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     

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.     

On the difference between pp and pp topological cross sections up to 100 GeV/c

New 100 GeV/c$\text{p}$p data are used to find moments of the difference between the $\text{p}$p and pp topological cross sections. The mean multiplicity for annihilations at 100 GeV/c is estimated to be 9.06 ± 0.56, and the value of the quantity 〈n〉/D to be 2.75 ± 0.33. It is shown that $\text{R}{}_{\mathrm{n}}\text{= {σ}{}_{\mathrm{n}}\text{(}\text{p}\text{p) ? σ}{}_{\mathrm{n}}\text{(pp)}/σ}{}_{\mathrm{n}}\text{(pp)}$ appears at 100 GeV/c to have acquired an asymptotic form, R_n = s^?αβⁿ, with α and β constant.     

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.     

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.     

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.     

The law of corresponding states for metals

Using the similarity of the effective potentials seen by ions in metals a reduced phonon equation of state is derived. It is shown that the melting point T_m(0) and the atomic volume Ω₀ at T = 0 K and at p = 0 are suitable macroscopic parameters for scaling ? and σ characterizing the interatomic potentials of metals having similar structures. The temperature and pressure dependence of thermodynamical quantities reduced with the above parameters are discussed and the results are compared with the experiment. It is shown that the pressure dependence of the reduced thermodynamic quantities can be described by the pressure dependence of the scaling parameters T_m(p) and Ω₀(p).The general form of the reduced equation of state (containing the electronic contributions as well) obtained gives that the reduced pressure is a universal function of the following reduced variables: the volume, temperature, de Broglie wavelength, Gibbs free energy of electrons $\text{3}\text{5}\text{zE}{}_{\mathrm{fo}}\text{?}$ (E_fo is the Fermi energy at T = 0 K) and depe of the valence z as well. It is shown that $\text{E}{}_{\mathrm{fo}}\text{?}$ is a function of $\text{Ω}{}_{\mathrm{o}}{}^{\mathrm{<mtext>?1</mtext><mtext>2</mtext>}}$ and $\text{(}\text{E}{}_{\mathrm{fo}}\text{/?}\text{)Ω}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ is approximately constant within the same sub-group of the periodic table.     

Infrared study of lattice and free carrier effects in p-type CuInTe2 single crystals

Infrared reflectivity spectra of p-type CuInTe₂ single crystals were measured at room temperature for the polarization direction E ⊥ c and E | c in the wavenumber range from 55 to 4000 cm^?1. Fits to a dielectric function including contributions from lattice oscillators and free carriers gave the first determination of the effective hole masses of $\text{m}{}_{\mathrm{p\perp }}\text{m}{}_0\text{= 0.85}$ and $\text{m}{}_{\mathrm{p|}}\text{m}{}_0\text{= 0.66}$. Two optical phonon modes were found for both polarization directions.     

An inequality for the trace of matrix products

In this paper we consider a product of n complex m×m matrices A_k (k=1,…,n) with singular values ∝^(k)_i ordered in decreasing magnitude. Using the spectral resolution for the operators $\text{A}{}^{\mathrm{dagger;}}{}_{\mathrm{k}}\text{A}{}_{\mathrm{k}}$, it is shown that $\text{|}\text{Tr}\text{A}{}_1\text{…A}{}_{\mathrm{n}}\text{|≤}\text{∑}\text{i=1}\text{m}\text{Φ}\text{i=1}\text{n}\text{α}{}^{\mathrm{(k)}}{}_{\mathrm{i}}\text{.}$This inequality is an extension of an inequality of von Neumann in the simple case that n=2. The necessary and sufficient condition for the equality sign to hold is established. Application of Hölder's inequality leads to further inequalities which can be useful in statistical mechanics.     

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.     

A compact configuration interaction wavefunction for the helium atom and the hydride ion

Using expansion functions $\text{Φ}{}_0\text{and}\text{{}\text{G}{}^{\mathrm{+}}{}_{\mathrm{k}}\text{Φ}{}_0\text{},}\text{where}\text{{}\text{G}{}^{\mathrm{+}}{}_{\mathrm{k}}\text{Φ}{}_0\text{}}$ is approximately strongly orthogonal to Φ₀, the self-consistent determinant, a correlated wavefunction for the helium atom and the hydride ion is presented. Using only one of these functions an energy of ?2.89731 au is obtained, for the helium atom and -0.519820 au for the hydride ion. The wavefunction is compact and is composed entirely of gaussians and correlated gaussians.     

Search for parity-nonconservation effects in deep-inelastic μ-N interaction

The difference of the cross sections for deep inelastic scattering of muons with average momenta 21 GeV/c with right and left helicity at large angles, i.e., with large momentum transfer, has been measured. No statistically-significant dependence of cross sections on the longitudinal polarization of muons has been found, i.e. no parity-nonconservation effects in deep inelastic μN interaction have been observed. The magnitude of the cross-section asymmetry $\text{R =}\text{[〈σ}{}_{\mathrm{<mtext>R</mtext>}}\text{〉 ? 〈σ}{}_{\mathrm{<mtext>L</mtext>}}\text{〉]}\text{[〈σ}{}_{\mathrm{<mtext>R</mtext>}}\text{〉+ + 〈σ}{}_{\mathrm{<mtext>L</mtext>}}\text{〉]}$ may be represented as R = β〈Q²〉 = (? 4 ± 6) × 10^?3 〈Q², (GeV/c)²〉. The limitations G_o^(μ) = (+ 6 ± 10)G have been obtained for the constant G_o^(μ) of vector-axial interaction $\text{(}\text{G}{}_{\mathrm{<mtext>o</mtext>}}{}^{\mathrm{(\mu )}}\text{2}\text{) [}\text{μ}\text{γα(1 + γ}{}_5\text{)μ] J}{}_{\mathrm{\alpha }}{}^{\mathrm{<mtext>o</mtext>}}$ (hadron, V-A).