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.     

Coriolis intensity perturbations in the SO2 molecule: Experimental determination of the relative signs of (∂μ∂Qi)

The Coriolis interactions between ν₁ and ν₃, and between ν₂ and ν₃ in SO₂ have been analyzed to obtain the signs of the products $\text{ζ}{}_{3.1}{}^{\mathrm{c}}\text{(}\text{?μ}{}^{\mathrm{a}}\text{?Q}{}_3\text{)(}\text{?μ}{}^{\mathrm{b}}\text{?Q}{}_1\text{)}$ and $\text{ζ}{}_{3.2}{}^{\mathrm{c}}\text{(}\text{?μ}{}^{\mathrm{a}}\text{?Q}{}_3\text{)(}\text{?μ}{}^{\mathrm{b}}\text{?Q}{}_2\text{)}$. It has been found that both of the signs of these products are positive. Then, relative signs of ($\text{?μ}\text{?Q}{}_1$) have been determined using the calculated values of the Coriolis zeta constants for the present definition of the normal coordinates. The obtained sign combination of ($\text{?μ}\text{?Q}{}_{\mathrm{i}}$) is ±(+?+), which agrees with the one predicted by the molecular orbital calculations. Using the sign combination (+?+), the polar tensors of S and O atoms were also calculated.     

Gravitational collapse in quantum mechanics with relativistic kinetic energy

It is proved that the quantum mechanical Hamiltonian $\text{H = Σ}{}_{\mathrm{i=1}}{}^{\mathrm{N}}\text{(p}{}^2\text{+ m}{}^2\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{? κ Σ}{}_{\mathrm{i>j}}\text{|x}{}_{\mathrm{i}}\text{? x}{}_{\mathrm{j}}\text{|}{}^{\mathrm{?1}}$ for bosons (resp, fermions) is bounded from below if N ≤ c_bκ^?1 (resp. $\text{N ≤ c}{}_{\mathrm{f}}\text{κ}{}^{\mathrm{<mtext>?3</mtext><mtext>2</mtext>}}$). H is unbounded from below if N ≥ c_b^lκ^?1 (resp. $\text{N ≥ c}{}_{\mathrm{f}}{}^{\mathrm{l}}\text{κ}{}^{\mathrm{<mtext>?3</mtext><mtext>2</mtext>}}$). The constants c_b and c_b^l (resp. c_f and c_f^l) differ by about a factor 2 (resp. 4).     

Metal-nonmetal transition in solid argon-lanthanum mixtures

A continuous metal-nonmetal transition is observed in solid ArLa mixtures. The d.c. conductivity σ starts at a La atomic fraction c_La ? 0.15 with $\text{σ = 2 × 10}{}^{-2}\text{[Ω-cm]}{}^{-1}$ and increases exponentially with c_La until σ reaches the minimum metallic conductivity $\text{σ}{}_{\min }\text{= 300 ± 100[Ω-cm]}{}^{-1}$ at c_La ? 0.4. The temperature dependence of σ shows variable range hopping between localized states for c>_La ? 0.4 and metallic behaviour for $\text{c}{}_{\mathrm{<mtext>La</mtext>}}\text{? 0.4.}$     

Surface cyclotron resonance in Si under uniaxial stress

The cyclotron resonance of inversion-layer electrons on (100)p-type Si is found to depend sensitively on an externally applied compressive stress. At low temperatures (T ? 10 K) we observe a considerable increase of the cyclotron mass m¹_c with stress S along the [001] direction. The effect is most strongly observed at low electron densities n_s. For $\text{S～1.5 × 10}{}^9\text{dyne}\text{cm}{}^2$ and n_s～2 × 10¹¹cm^-2 we obtain $\text{m}{}^1{}_{\mathrm{c}}\text{～0.4 m}{}_0$ instead of the expected 0.2m₀. Along with this change of $\text{m}{}^1{}_{\mathrm{c}}$ a strong narrowing of the resonance is noted. Raising the temperature gives an additional n_s- dependent increase of $\text{m}{}^1{}_{\mathrm{c}}$.     

Antiproton-proton total elastic cross sections in the T and U regions (0.69−2.43 GeV/c)

Antiproton-proton total elastic cross sections at 21 incident momenta in the range 0.69 to 2.43 GeV/c have been deduced by combining p?p elastic differential cross sections over a c.m. angular range $\text{?0.95 ?}\text{cos}\text{θ}{}^1\text{? 0.93}$ with forward elastic cross sections derived from recent real-part measurements and p?p total cross sections. Two bumps are observed, at $\text{M}{}_1\text{? 2.155}$ and $\text{M}{}_2\text{? 2.345}\text{GeV}\text{/c}{}^2$, having widths of Г₁ ～ 0.135 and $\text{Г}{}_2\text{～ 0.135}\text{GeV}\text{/c}{}^2$. Corresponding structures in other p?p reaction channels are discussed.     

Complexified Pöschl–Teller II potential model

With the help of complexifying a five-parameter exponential-type potential model, we obtain a general complex version of the Pöschl–Teller II potential, , where q_c=q₀e^2iαε, real V₁>0, q₀>0 and $\text{0<λε<}\text{π}\text{2}$. It has been shown that this complex potential is P-pseudo-Hermitian and PT-symmetric, where the parity operator P acts on the position operator as $\text{PxP}{}^{\mathrm{-1}}\text{=}\text{ln}\text{q}{}_0\text{λ}\text{−x}$. The discrete energy eigenvalues are shown to be real when $\text{V}{}_2\text{⩾−}\text{q}{}_0\text{λ}{}^2\text{4}$ while they are complex conjugate pairs if $\text{V}{}_2\text{<−}\text{q}{}_0\text{λ}{}^2\text{4}$.     

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     

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.     

Evidence for double dissociation in K-p interactions at 14.3 GeV/c

We have studied the reaction K^-p → K^-π⁺π^-π⁺π^-p at 14.3 GeV/c to search for evidence of the double dissociation process $\text{K}{}^{\mathrm{-}}\text{p}\text{→}\text{QN}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}{}^1$. In the channel $\text{K}{}^{\mathrm{-}}\text{p}\text{→}\text{K}{}^{10}\text{(890)}$π₁^-π₂^-Δ⁺⁺ (1236) there is evidence for simultaneous production of low-mass enhancements in the $\text{K}{}^{10}\text{π}{}_1{}^{\mathrm{-}}$ and Δ⁺⁺(1236)π₂^- subsystems which correspond to the $\text{Q}\text{→}\text{K}{}^1\text{(890)π}$ and $\text{N}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}{}^1\text{→ Δπ}$ decay modes. In this particular final state the double fragmentation system is produced with a cross section of the order of a few microbarns. Our data are consistent with the factorizable pomeron exchange model of double diffractive dissociation.     

Elastoresistivity of TTF-TCNQ and related compounds

Elastoresistances of TCNQ high conducting salts have been measured at room temperature by an original strain gauge technique. The effects, on the longitudinal and transverse resistivities ?, of an elementary uniaxial strain ? applied along one of the three axes, a, b or c¹ respectively, have been estimated.For TTF-TCNQ, they are:

$\text{K}{}^{\mathrm{b}}{}_{\mathrm{a}}\text{=? ln ?}{}^{\mathrm{b}}\text{/??}{}_{\mathrm{a}}\text{= 16±3}$

;

$\text{K}{}^{\mathrm{b}}{}_{\mathrm{b}}\text{= ? ln α}{}^{\mathrm{b}}\text{/??}{}_{\mathrm{b}}\text{= 34±4}$

;

(5% risk).So, in an hydrostatic pressure experiment, the fraction of piezoresistivity attributable to transverse effects is 43± 10% of the total value χ^b (K^b_a and K^b_c effects accumulated).Low values have been found for the anisotropy (?^a/?^b) variations due to strains. So one may write:

$\text{K}{}^{\mathrm{a}}{}_{\mathrm{a}}\text{= ? ln ?}{}^{\mathrm{a}}\text{/??}{}_{\mathrm{a}}\text{≌K}{}^{\mathrm{a}}{}_{\mathrm{b}}$

;

$\text{K}{}^{\mathrm{a}}{}_{\mathrm{b}}\text{= ? ln ?}{}^{\mathrm{a}}\text{/??}{}_{\mathrm{b}}\text{≌ K}{}^{\mathrm{b}}{}_{\mathrm{b}}$

;

.The TTF-, HMTTF-, TSF-, HMTSF-TCNQ elastoresistance values are coherent with the previously measured hydrostatic pressure piezoresistivity values.All these experimental results are in good agreement with a model where the longitudinal but also the transverse elastoresistivities are essentially due to variations with strains of the longitudinal scattering time τ_ν defined by σ^b = ne²τ_ν/m¹.     

A Mössbauer study of amorphous Fe40Ni40B20

Amorphous Fe₄₀Ni₄₀B₂₀ (VITROVAC 0040) alloy has been investigated using ⁵⁷Fe Mössbauer Spectroscopy. The Curie temperature T_c is found to be well defined and is 695 ± 1 K. The quadrupole splitting just above T_c is 0.64 mm sec^?1. The crystallization temperature is 698 ± 2 K, close to but definitely above T_c. The average hyperfine field H_eff(T) of the glassy state shows a temperature dependence of $\text{H}{}_{\mathrm{<mtext>eff</mtext>}}\text{(0)[1 ? B}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{(T/T}{}_{\mathrm{c}}\text{)}{}^{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{? C}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}\text{(T/T}{}_{\mathrm{c}}\text{)}{}^{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}\text{? …]}$ indicative of the existence of spin wave excitations. The values of $\text{B}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ and $\text{C}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}$ are found to be 0.40 and 0.06, respectively, for T/T_c ? 0.72. At temperatures close to T_c, H_eff(T) varies as (1 ? T/T_c)^β where β is one of the critical exponents and its value is found to be 0.29 ± 0.02.     

Charge transport in layer semiconductors

Electron and hole-drift velocity is measured in the layer semiconductors HgI₂, GaSe, PbI₂ and GaS, mainly on the direction parallel to the c-axis between 80 and 400 K. In the electric field range in question, electron and hole-drift velocity is proportional to the field except in the case of GaS, where a superohmic behaviour is observed. At 300 K the mobility parallel to the c-axis is $\text{μ}{}_{\mathrm{e}}\text{, = 100}\text{cm}{}^2\text{Vsec}$, $\text{μ}{}_{\mathrm{h}}\text{= 4}\text{cm}{}^2\text{Vsec}$ for HgI₂; $\text{μ}{}_{\mathrm{e}}\text{= 80}\text{cm}{}^2\text{Vsec}$, $\text{μ}{}_{\mathrm{h}}\text{= 210}\text{cm}{}^2\text{Vsec}$ for GaSe; $\text{μ}{}_{\mathrm{e}}\text{, = 8}\text{cm}{}^2\text{Vsec}$, $\text{μ}{}_{\mathrm{h}}\text{= 2}\text{cm}{}^2\text{Vsec}$ for PbI₂. The highest hole mobility observed in GaS is $\text{μ}{}_{\mathrm{h}}\text{= 80}\text{cm}{}^2\text{Vsec}$.Where it is possible to compare these data with mobility values perpendicular to the c-axis, the three-dimensional character of the energy bands near the fundamental gap is proved.For HgI₂ and GaSe we find no evidence for the large anisotropy of charge-carrier transport properties usually attributed to layered semiconductors. The mobility-temperature dependences found are interpreted on the basis of polar and non-polar optical phonon scattering mechanisms, except in the case of GaS, where a trapping model is used. The effective masses of electrons and holes are reported for PbI₂ and, for the first time, for HgI₂.     

The A-dependence of J/ψ-particle inclusive distributions

The differential cross sections $\text{d}\text{σ}\text{d}\text{x}$ and $\text{d}\text{σ}\text{d}\text{p}{}_{\mathrm{t}}{}^2$ of inclusive J/ψ production by 43 GeV/c π^? off Be, Cu and W nuclei have been measured. Fitting $\text{d}\text{σ}\text{d}\text{p}{}_{\mathrm{t}}{}^2\text{～ A}{}^{\mathrm{\alpha }}\text{(p}{}_{\mathrm{t}}{}^2\text{)}$ we observed the increase of α with p_t².     

Density of states in dirty type II superconductors near Tc

We have determined the behavior of the density of states in the mixed state of superconducting alloys for T → T_c. The local density of states tends towards the BCS expression with the order parameter playing the role of the energy gap. The singularities are smeared out by the spatial average. The effective normal core radius of a vortex diverges like $\text{(1 ?}\text{T}\text{T}{}_{\mathrm{c}}\text{)}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>3</mtext>}}$ for T → T_c unlike the coherence length which diverges like $\text{(1 ?}\text{T}\text{T}{}_{\mathrm{c}}\text{)}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>2</mtext>}}$.     

Spectrum and structure of the He2 molecule: Characterization of the singlet and triplet states associated with the UAO's 4s, 4dσ, 4dπ, and 4dδ

The emission spectrum of the He₂ molecule has been rephotographed in the ～4000–～5700 Å region and the $\text{4d(}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}\text{,}{}^3\text{Π}{}_{\mathrm{u}}\text{,}{}^3\text{Δ}{}_{\mathrm{u}}\text{) → 2pπ}{}^3\text{Π}{}_{\mathrm{g}}$, $\text{4d(}{}^1\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}\text{,}{}^1\text{Π}{}_{\mathrm{u}}\text{,}{}^1\text{Δ}{}_{\mathrm{u}}\text{) → 2pπ}{}^1\text{Π}{}_{\mathrm{g}}$, $\text{4s}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}\text{→ 2pπ}{}^3\text{Π}{}_{\mathrm{g}}$ and $\text{4s}{}^1\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}\text{→ 2pπ}{}^1\text{Π}{}_{\mathrm{g}}$ transitions analyzed. The 4dδj³Δ_u, 4dπj³Π_u, $\text{4dσj}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}$ and $\text{4sh}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}$ states have been characterized through v = 2 and the 4dδJ¹Δ_u, 4dπJ¹Π_u, $\text{4dσJ}{}^1\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}$, and $\text{4sH}{}^1\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}$ states for v = 0. The term levels for these perturbed and l-uncoupled states have been confirmed (a) by analyses of bands with common levels from Δv = 0, ±1 sequences and (b) by analyses of the transitions between the above states from 4d and 4s and the $\text{c}{}^3\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{+}}$ and $\text{C}{}^1\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{+}}$ states associated with 3pσ. Molecular constants are reported which have been partially corrected for the effects of l-uncoupling and the homogeneous perturbations between the state pairs J, H and j, h.     

On the order of levels in charmonium

We prove a theorem concerning the energies of the 2S and 3D states in a potential $\text{V(r) =}\text{?g}{}^2\text{r}\text{+ V}{}_{\mathrm{<mtext>c</mtext>}}\text{(r)}$, where V_c is a non-singular confining potential. If $\text{(}\text{d}\text{d}\text{r)}{}^3\text{(r}{}^2\text{V}{}_{\mathrm{<mtext>c</mtext>}}\text{)}$ is positive, then the 3D state lies above the 2S state, provided

$\text{d}\text{d}\text{r}\text{1}\text{r}\text{d}\text{d}\text{r}\text{2V}{}_{\mathrm{<mtext>c</mtext>}}\text{+r}\text{d}\text{V}{}_{\mathrm{<mtext>c</mtext>}}\text{d}\text{r}\text{< 0, ?}{}_{\mathrm{r}}\text{>0.}$

For V_c = r^α, this corresponds to 0 < α < 2.     

The anharmonic force field of phosphorus trifluoride from the millimeter wave spectra of vibrationally excited states

The millimeter rotational spectra of PF₃ have been recorded for all four excited fundamental vibrational states. A coriolis resonance between ν₁ and ν₃ results in anomalous distortion constants for these states and can be analyzed to yield $\text{|ζ}{}_{13}{}^{\mathrm{y}}\text{| = 0.392}$. The value of $\text{ζ}{}_{33}{}^{\mathrm{c}}$ is found to be 0.4194 which does not fit the coriolis sum rule due to anharmonic resonance. Equilibrium values for the centrifugal distortion constants are determined and have been used to find the harmonic force field. All available data is used to determine some of the anharmonic force constants.     

Critical slowing down of fluctuations in squaric acid (H2C4O4) at the phase transition observed by 13C spin-lattice relaxation

Spin lattice relaxation T₁ of naturally abundant ¹³C nuclei in squaric acid was measured close to the antiferroelectric-paraelectric phase transition temperature T_c = 373 K. A rapid increase in $\text{1}\text{T}{}_1$ is observed close to T_c coming from above, which follows the power law $\text{1}\text{T}{}_1\text{～ ε}{}^{\mathrm{?1.4}}$ where $\text{ε =}\text{(T ? T}{}_{\mathrm{c}}\text{)}\text{T}{}_{\mathrm{c}}$. This behaviour is explained on the basis of the two-dimensional character of the fluctuations.     

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.