Quantum oscillations in screening in a two-dimensional electron gas

The static dielectric constant of a two-dimensional electron gas is studied as a function of the strength of a dc magnetic field applied normal to the plane of the electron gas. At high temperatures $\text{(kT ?}\text{h}\text{?}\text{ω}{}_{\mathrm{c}}\text{)}$ the static dielectric function is independent of magnetic field, and for long wavelengths is given by ? ? ?₀ + 2n_vme²/q, where ?₀ is the background dielectric constant and n_v is the valley degeneracy. At low-temperatures, quantum oscillations become important and dramatically modify the screening.     

Verification of the laws of luminescence of solids for manganese complexes of benzyl-trimethylammonium and 2-chloropyridinium

A formula at low temperature for the function G($\text{1}\text{λ}$) = I_λλ⁶ has been derived in terms of configuration curve theory and checked on luminescence spectra near 77 K. The vibrational quantum in the excited state has been calculated from the decrease of G($\text{1}\text{λ}{}_{\mathrm{M}}$), where λ_M is the wavelength of the maxima of G at low temperature, as a function of temperature.     

Phase transition in strongly inhomogeneous ferromagnets

A field theoretical model is proposed to describe the critical behaviour of a strongly inhomogeneous spin system with a position dependent concentration of magnetic atoms C(R) and magnetisation M(R). Assuming a finite number of $\text{n}$ Fouriermodes $\text{C}{}_{\mathrm{<mtext>Q</mtext>}}{}_{\mathrm{<mtext>v</mtext>}}\text{v}\text{= 1}$,..., $\text{n}$, to express C(R), the quenched randomness requires to interpret {$\text{Q}{}_{\mathrm{<mtext>v</mtext>}}\text{|}\text{Q}{}_{\mathrm{<mtext>v</mtext>}}\text{|}{}^2$} on a set of invariant or marginal lengths. As consequence, M(R) can be described by n Fourier-modes M_Qv, where $\text{n ?}\text{n}$. For short range spin-spin interaction, we find for strong inhomogeneity, i.e. large n, the critical exponent between those of the related homogeneous system and those of the spherical model.     

Temperature quenching of luminescence for linear and derivative nuclear operators

An earlier study of the thermal quenching of luminescence using the single-configurational-coordinate model is extended from Condon-approximation overlap integrals 〈u_n|v_m〉² to the linear and derivative integrals 〈u_n|z_v|v_m〉² and 〈u_n|?/?z_v|v_m〉². For non-radiative transitions, the thermally weighted nuclear factor in the transition rate is, for the linear and derivative integrals, the corresponding factor for 〈u_n|v_m〉² integrals multiplied by 2E_Xv/?ω_v and $\text{2[E}{}_{\mathrm{Xv}}\text{- E}{}_{\mathrm{p}}{}_{\mathrm{U}}\text{(T)]/}\text{h}\text{?}\text{ω}{}_{\mathrm{v}}$, respectively. E_Xv is the energy of the crossover above the initial- v-parabola minimum, and E_pU(T) is the single activation energy fitted to the nuclear factor's temperature dependence for 〈u_n|v_m〉² integrals. These multiplying factors are exact for equal parabola force constants and good approximations for unequal force constants. These multiplying factors will be difficult to distinguish experimentally. The more important considerations for fitting the model to thermal-quenching data are the parabola placement and the Condon-approximation integrals described previously.     

The D′ → A′ transition in I2

A detailed vibrational analysis is given for the D′(2g) → A′(2u³Π) transition (3300–3460 Å) in I₂. The assignments include ～ 150 v′-v″ bands in ¹²⁷I₂ and ～100 in ¹²⁹I₂, spanning v′ levels 0–15 and v″ levels 4–30. These bands are mainly red-degraded but include some violet-degraded and line-like features. The analysis is corroborated by Franck-Condon and band profile calculations. The least-squares fit yields the following constants (cm^?1); ΔT_c = 30 340.8, ω′_e = 103.95, ω_eχ′_e = 0.206, ω″_e = 106.1, ω_eχ″_e = 0.81. Anomalous behavior in the vibrational level structure above v″ = 23 makes the extrapolation to the A′ dissociation limit uncertain, so the absolute energies of both states remain ill-defined. However there is a possibility that the D′ state is the state labeled α by King et al. [Chem. Phys. 56, 145–156 (1981)], in which case the energies are known precisely. There is evidence of weak emission from at least two other electronic transitions in this spectral region, probably $\text{D(0}{}^{\mathrm{+}}\text{u) → X(}{}^1\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{+}}\text{)}$ ($\text{λ}\text{< 3300}\text{A}\text{?}$) and β → A(1u³Π) ($\text{λ}\text{> 3300}\text{A}\text{?}$).     

On triviality of the :expλϕ:4 quantum field theory in a finite volume

The ?dν(λ):expλ?:_n (without counterterms) quantum field theory is considered. Here ν(·) is a finite positive measure.Let n ? 3, or n = 2 and supp$\text{ν ∩ [?}\text{8π}\text{,}\text{8π}\text{] = ?}$. Under these conditions the theory ?dν(λ):expλ?:_n (without counterterms)converges to the free-field theory when the cut- offs are removed.     

On the theory of the low-temperature electrical resistivity of potassium

Expressing the residual resistivity ?₀ as a force-force correlation, a first-principles basis is afforded for the low temperature expansion of the electrical resistivity ? as

(I)$\text{? = ?}{}_0\text{[1 +}\text{λ1}\text{λ}\text{+ … ]}$

where λ = const T^-2 is the non-resistive mean free path arising from electron-electron scattering. λ¹ is found to reflect directly long-range correlations in the electronic motions via the off-diagonal behaviour of the local density of states at the Fermi energy.     

Quantum integrable systems related to lie algebras

Some quantum integrable finite-dimensional systems related to Lie algebras are considered. This review continues the previous review of the same authors [83] devoted to the classical aspects of these systems. The dynamics of some of these systems is closely related to free motion in symmetric spaces. Using this connection with the theory of symmetric spaces some results such as the forms of spectra, wave functions, S-matrices, quantum integrals of motion are derived. In specific cases the considered systems describe the one-dimensional n-body systems interacting pairwise via potentials g²v(q) of the following 5 types: v_I(q) = q^?2, v_II(q) = sinh^?2q, v_III(q) = sin^?2q, $\text{v}{}_{\mathrm{<mtext>IV</mtext>}}\text{(q) =}\text{P}\text{(q)}$, v_V(q) = q^?2 + ω²q². Here $\text{P}\text{(q)}$ is the Weierstrass function, so that the first three cases are merely subcases of the fourth. The system characterized by the Toda nearest-neighbour potential exp(q_jq_{j+ 1}) is moreover considered.This review presents from a general and universal point of view results obtained mainly over the past fifteen years. Besides, it contains some new results both of physical and mathematical interest.     

On universality for area-preserving maps of the plane

We present detailed evidence that one-parameter families of area-preserving maps exhibit cascades of period doubling with universal geometric scaling in the parameter. We relate this behaviour to a fixed point equation of the form

$\text{Λ}{}^{\mathrm{?1}}\text{°Φ°Φ°Λ = Φ}$

and

$\text{det}\text{DΦ = 1}$

, Φ:$\text{R}$²→$\text{R}$². In particular we argue that the scaling transformation Λ:$\text{R}$²→$\text{R}$² is conjugate to the transformation Λ₀:(x, y)→(λx, μy), with λ² ≠ μ, and in fact λ² >μ. We present some numerical evidence that

$\text{δ = 8.721}$

…,

$\text{?}\text{1}\text{λ}\text{= 4.018}$

…,

$\text{1}\text{μ}\text{= 16.36}$

…, where δ is the asymptotic ratio of the differences of the parameter values corresponding to the successive periods 2^k described above.     

On the definition of the pressure of an infinite system

A microcanonical system $\text{L}$^o_Λ is considered together with a manometer $\text{M}$_Λ. The thermodynamic limit Λ → ∞ is taken for the system $\text{L}$_Λ composed of $\text{L}$^o_Λ and $\text{M}$_Λ. This yields a definition of the pressure P(v, ε) of $\text{{}\text{L}{}^{\mathrm{o}}{}_{\mathrm{\Lambda }}\text{; Λ → ∞}}$ for given values ε and v of the energy and particle densities. P(v, ε) is shown to be equal to the thermodynamic function p(z, β) derived from the grand canonical ensemble for almost all values of ε and v provided the appropriate equilibrium values of the temperature β^?1 and the chemical potential μ = β^?1 log z are inserted.     

Correlation functions of the transverse Ising chain at the critical field for large temporal and spatial separations

We study the behavior of 〈σ₀^x(t)σ_n^x(0)〉 and 〈σ₀^y(t)σ_n^y(0)〉 for the transverse Ising chain at the critical magnetic field at T = 0. Explicit results are obtained for the three distinct regions where t → ∞ and n → ∞with $\text{0 ?}\text{n}\text{t}\text{<1}$, $\text{1 <}\text{n}\text{t}$, or $\text{t = n + n}{}^{\mathrm{<mtext>1</mtext><mtext>3</mtext>}}\text{(}\text{z}\text{2}\text{)}$ where z is fixed of order one. In this latter region the general Painlevé V solution is shown to reduce to a Painlevé II function. We use our results to discuss the general problem of long-time behavior of Toda equations with slowly decaying initial values.     

An identity for T-ordered exponentials with applications to quantum mechanics

The solution of the Cauchy problem for Liouville's equation φ_xy = e^φ is shown to be equivalent to the calculation of a T-ordered exponential of a two-dimensional variable matrix. This gives rise to an identity for the T-ordered exponential involving two arbitrary functions. The formalism is applied to the time evolution of a magnetic dipole in a time dependent magnetic field and to the one-dimensional Dirac equation with external potential $\text{V(x) = (n +}\text{1}\text{2}\text{)λ}$ tanh λx which is relevant for field theoretic applications. A generalization to n-dimensional matrices is also given.     

Scaling of the “superstable” fraction of the 2D period-doubling interval

The scaling properties of a “superstable” parameter interval, $\text{C}$, where the eigenvalues about a period-2n orbit are complex, are derived for 2D period-doubling maps. The ratio of $\text{C}$ to the whole parameter interval, between the nth and the (n+1)st bifurcation, is shown to be a universal function of the effective jacobian, B_e, only (B_e≡B²ⁿ, B is thejacobian of th e map). Unlike the whole period-2ⁿ interval, $\text{C}$ has a convergence rate that behaves as $\text{4.6692016×B}{}^{\mathrm{<mtext>-1</mtext><mtext>4</mtext>}}{}_{\mathrm{e}}$ as B_e↓), wh ile its complement has a convergence rate 8.7210972/4 as B_e↑1.     

Rotational analysis and radiative lifetime measurement on the 2B1 (K′ = 0) excited state of NO2 with v′2 = 6, 7, 8, and 9

The rotational structure of the ²B₁ (K′ = 0) subbands of NO₂ with v′₂ = 6, 7, 8, and 9 were analyzed by means of the time-gated excitation spectrum. The excitation spectrum monitored at ν₂, 2ν₂, or 3ν₂ fluorescence band was fairly simplified in comparison to its corresponding absorption spectrum. The band origins and rotational constants are evaluated from the observed data: ν₀ = 20205.0 cm^?1, $\text{B}\text{′ = 0.374}\text{cm}{}^{\mathrm{?1}}$ for v′₂ = 6; ν₀ = 21104.4 cm^?1, $\text{B}\text{′ = 0.374}\text{cm}{}^{\mathrm{?1}}$ for v′₂ = 7; ν₀ = 22001.9 cm^?1, $\text{B}\text{′ = 0.375}\text{cm}{}^{\mathrm{?1}}$ for v′₂ = 8ν₀ = 22898.0 cm^?1, $\text{B}\text{′ = 0.375}\text{cm}{}^{\mathrm{?1}}$ for v′₂ = 9. The value of $\text{B}\text{′}$ extrapolated to v′ = 0 is 0.370 cm^?1. This value corresponds to the bond length of 1.19 Å. Fluorescence decays of these excited levels were also studied. Radiative lifetimes obtained by extrapolation to zero pressure from the $\text{1}\text{τ}\text{– P}$ plots were 25–40 μsec. The short-lived excited levels previously reported by some authors were not found.     

Measurement of the decay-probability of metastable hydrogen by two-photon emission

The two-photon-decay probability of the metastable 2² S_{$\text{1}\text{2}$} level of hydrogen has been measured. The result A(λ)dλ = 1.5 sec^?1 ± 43% in the spectral range dλ = (255.4?232)nm ± 5% is in agreement with the theoretical prediction.     

Thirring model with U(n) symmetry: Scale invariant only for fixed values of a coupling constant

Generalizations of the Thirring model to Fermi fields with U(n) symmetry are treated. When interactions quadratic in the SU(n) currents are introduced, scale invariance (with anomalous dimensions) is maintained only for values of the coupling g_v=0 or $\text{g}{}_{\mathrm{<mtext>v</mtext>}}\text{=}\text{4φ}\text{(n+1)}$.     

Rotational analyses and vibrational assignments of the 463- and 474-nm bands of NO2

The excitation spectrum of NO₂ was investigated in the blue region by using a Nd:YAG laser-pumped dye laser. The 463- and 474-nm bands of the ²B₂-²A₁ system were identified and analyzed using the simplification that occurs if the excitation spectrum is monitored at particular wavelengths. Band origins and rotational constants were obtained. Vibrational assignments have been given to these bands by comparing the Franck-Condon Factors calculated for the ²B₂-²A₁ system with the fluorescence intensities of bands going to different vibrational levels of the ground state. The vibrational assignments and molecular constants obtained in this work are (v′₁, v′₂, v′₃) = (3, 11, 0)ν₀(K′ = 0) = 21584.1, $\text{B}\text{= 0.405}$, and $\text{∥}\text{?}\text{′∥ = 0.05}\text{cm}{}^{\mathrm{?1}}$ for the 463-nm band; and (v′₁, v′₂, v′₃) = (2, 12, 0), ν₀(K′ = 1) = 21104.9, $\text{B}\text{= 0.408}$, and $\text{∥}\text{?}\text{′∥ = 0.03}\text{cm}{}^{\mathrm{?1}}$ for the 474-nm band.     

(p, γ) reaction studies on 60Ni

The γ-ray spectra from the ⁶⁰Ni(p, γ)⁶¹Cu reaction were measured for 27 isolated resonances. From these studies the J^π assignment of the compound states in ⁶¹Cu were made. Moreover, a value for the El photon strength function k(El) = 1.03 × 10^?9 MeV^?3 was obtained from seven l = 0 resonances to the 16 low-lying states. This value was then compared with the theoretical estimates of El strengths as predicted from the s.p. and giant dipole resonance models. The distribution of partial radiative widths about their mean value was determined from a Monte Carlo technique and was found to be consistent with the Porter-Thomas distribution when the Γ_{γ, ij} were divided by the E_γ⁵ energy dependence.Values for the coefficients of the correlation R between Γ_{λ, p} and Γ_{λ, γj} and T between Γ_{λ, yj} and $\text{Γ}{}_{\mathrm{\lambda ,\; \gamma ?}}$ where f ≠ j, were computed with the values R = 0.14 and T = 0.39, respectively. Also the correlation coefficients C(〈 Γ_{λ, yj}〉, I₃He, d, j) and $\text{C(〈Γ}{}_{\mathrm{\lambda ,\; y?}}\text{〉 I}{}_{\mathrm{<mtext>d,\; n</mtext><mtext>,\; ?</mtext>}}\text{)}$ yielded the values ρ = 0.87 and ρ = 0.80 respectively. All these correlations which are found to be statistically significant, imply that the (p, γ) reaction in ⁶⁰Ni is partly due to direct capture such as given by valence and doorway state contributions.     

Energy of a muonic X-ray transition measured with a crystal spectrometer

The wavelength of the $\text{3}\text{d}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}\text{?2}\text{p}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ muonic X-ray transition in ²⁸Si has been measured relative to the wavelength of the 84 keV gamma ray from a ¹⁷⁰Tm source. The result is λ^Si/λ^Tm = 1.099675 (39). Using the reported value for λ^Tm we find (λ_exp^Si-λ_th^Si)/λ_th^Si = (?9±35) × 10^?6.