Upper Bounds on the Critical Temperature for Kac Potentials

We consider an Ising system in two dimensions with a two body ferromagnetic interaction J _γ(x, y) that depends on the Kac scaling parameter γ. We prove that the inverse critical temperature β_cr(γ) is strictly above the mean-field value (equal to 1), namely that there exists C>0 so that for any b<C, β_cr(γ)> 1 + bγ²log γ^?1 for all γ sufficiently small. The temperature shift Cγ²log γ^?1 is to leading orders equal to the covariance of the magnetization fluctuations.     

Rotational spectra of quinoline and of isoquinoline: spectroscopic constants and electric dipole moments

Rotational spectra of quinoline and of isoquinoline have been observed in the centimeter- and millimeter-wave regions. The spectra were assigned on the basis of bands formed by high-J transitions, which were measured up to J″?128 and ν?234 GHz. Complementary measurements were also made on low-J, centimeter-wave spectra observed in supersonic expansion and with fully resolved nuclear quadrupole hyperfine structure. Accurate rotational, centrifugal distortion and hyperfine splitting constants for the ground states of both molecules are reported. The electric dipole moments for the two molecules were also determined from Stark effect measurements and are μ_a=0.14355(19), μ_b=2.0146(17), μ_tot=2.0197(17) D for quinoline, and μ_a=2.3602(21), μ_b=0.9051(14), μ_tot=2.5278(20) D for isoquinoline. The experimental observables were found to be rather accurately predicted by MP2/6-31G** ab initio calculations, and corresponding molecular geometries are also reported.     

The parity of regge cuts

The exchange of two reggeons of naturalities η_a and η_b will in general produce a J plane cut in amplitudes of both naturalities ± η_aη_b. We show that the amplitudes of naturality ? η_aη_b are suppressed, and this suppression grows with the energy, regardless of the particular model used for the vertices coupling the reggeons to the external particles. In consequence, for cuts where the two reggeons are any of ?, A₂, f, ω, or the pomeron, the natural-parity cut (if it is present) will dominate over the unnatural parity. We also show that cut vertices which contribute to both naturalities satisfy the conspiracy condition at t = 0 by suppressing both contributions equally. Away from t = 0, the η = + η_aη_b contribution can recover from this suppression. This behaviour is of importance in, for example, the pion-pomeron cut.We compare these conclusions with experiment.     

Chiral spin liquid in a two-dimensional helical XY magnet with two chiral order parameters

The critical properties of an XY helimagnet on a square lattice with two chiral order parameters are studied by Monte Carlo simulations. This model is a modification of the J ₁-J ₂-J ₃ model with J ₂ = 0. The case of different third range order interactions J ₃ are considered, J ₃ ^a ?? J ₃ ^b . A first order transition is found away from the Lifshitz points 4J ₃ ^a = J ₁ and 4 J ₃ ^b = J ₁. It is pointed out that a chiral spin liquid phase possibly exists near the Lifshitz points.     

Adiabatic hyperspherical approach to describing low-energy mesic-atom scattering

The adiabatic hyperspherical approach developed previously is used to describe the asymmetric mesic-atom scattering aμ+b → aμ+b, a+bμ (a, b=p, d, t) in the collision-energy range 10^?3≤?≤10² eV. Boundary conditions for J≠0 scattering states are formulated, and partial cross sections for J=0–3 are calculated. Effective numerical codes are developed, and a fast convergence of the adiabatic hyperspherical approach is demonstrated: to achieve a precision of about 1% in the calculated cross sections, it is sufficient to use a basis of not more than ten adiabatic hyperspherical functions. The results that we obtained are compared with the previous ones.     

Phase diagram and exotic spin-spin correlations of anisotropic Ising model on the Sierpiński gasket

The anisotropic antiferromagnetic Ising model on the fractal Sierpiński gasket is intensively studied, and a number of exotic properties are disclosed. The ground state phase diagram in the plane of magnetic field-interaction of the system is obtained. The thermodynamic properties of the three plateau phases are probed by exploring the temperature-dependence of magnetization, specific heat, susceptibility and spin-spin correlations. No phase transitions are observed in this model. In the absence of a magnetic field, the unusual temperature dependence of the spin correlation length is obtained with 0 ≤ J_b/J_a< 1, and an interesting crossover behavior between different phases at J_b/J_a = 1 is unveiled, whose dynamics can be described by the J_b/J_a-dependence of the specific heat, susceptibility and spin correlation functions. The exotic spin-spin correlation patterns that share the same special rotational symmetry as that of the Sierpiński gasket are obtained in both the 1 / 3 plateau disordered phase and the 5/9 plateau partially ordered ferrimagnetic phase. Moreover, a quantum scheme is formulated to study the thermodynamics of the fractal Sierpiński gasket with Heisenberg interactions. We find that the unusual temperature dependence of the correlation length remains intact in a small quantum fluctuation.     

Magnetic rotation observation of the C2b3Σg− ← a3Πu transition using a color center laser

The magnetic rotation observation of the C₂b³Σ_g^? ← a³Π_u Ballik-Ramsay system using a color center laser is reported. This is the first detection of this system in absorption. Three bands, 0 ← 1, 1 ← 2, and 2 ← 3, were identified in the spectral range 3650–4030 cm^?1. The last two bands were observed for the first time. In magnetic rotation many satellite lines (ΔN ≠ ΔJ) which would be very weak in normal absorption have been observed with intensity comparable to the main branch lines. This permits a slight improvement in the accuracy of some of the fine structure constants. A variety of lineshapes are observed for the various branches by magnetic rotation. Because the b³Σ_g^? fine structure is small, giving a partial overlap, the peak frequency of a magnetic rotation signal usually does not correspond to the center frequency of the normal absorption signal of that transition. A computer program has been written to predict magnetic rotation lineshapes and obtain the peak frequency displacements. Various observed and calculated lineshapes are displayed and compared.     

1-Butyne microwave spectrum,barrier to internal rotation,and molecular dipole moment

Measurements of rotational transitions of 1-butyne have been made in the range of ～20–130 GHz. Both a-type transitions up to J = 46 and b-type transitions up to J = 42 have been measured and fitted to a rotational Hamiltonian which includes centrifugal distortion terms. In addition to the five quartic centrifugal distortion constants, three sextic coefficients had to be included to reproduce the observed frequencies to within experimental error. The results of the analysis are sufficient for the prediction of all strong transitions throughout the millimeterwave range. A barrier to internal rotation of the methyl group of 3.260 kcal/mole (1 kcal/mole = 4.18 kJ/mole) has been derived from the first excited torsional state. Analysis of the second-order Stark effect has led to an accurate determination of both μ_a and μ_b with μ_a = 0.763(3) D and μ_b = 0.170(4) D.     

Millimeter and submillimeter wave spectroscopic investigations into the rotation-tunneling spectrum of gGg ethylene glycol, HOCH2CH2OH

The rotation-tunneling spectrum of the second most stable gGg^′ conformer of ethylene glycol (1,2-ethanediol) in its ground vibrational state has been studied in selected regions between 77 and 579 GHz. Compared to the study of the more stable aGg^′ conformer, a much larger frequency range was studied, resulting in a much extended frequency list covering similar quantum numbers, J?55 and K_a?19. While the input data were reproduced within experimental uncertainties up to moderately high values of J and K_a larger residuals remain at higher quantum numbers. The severe mixing of the states caused by the Coriolis interaction between the two tunneling substates is suggested to provide a considerable part of the explanation. In addition, a Coriolis interaction of the gGg^′ ground vibrational state with an excited state of the aGg^′ conformer may also contribute. Relative intensities of closely spaced lines have been investigated to determine the signs of the Coriolis constants between the two tunneling substates relative to the dipole moment components and to estimate the magnitudes of the dipole moment components and the energy difference between the gGg^′ and the aGg^′ conformers. Results of ab initio calculations on the total dipole moment and the vibrational spectrum were needed for these estimates. The current analysis is limited to transitions with quantum numbers J?40 and K_a?6 plus those having J?22 and K_a?17 which could be reproduced within experimental uncertainties. The results are aimed at aiding radioastronomers to search for gGg^′ ethylene glycol in comets and in interstellar space.     

How chaotic is a state of a quantum system?

A concept related to the entropy is studied. Let A and B be two density matrices, with eigenvalues a₁, a₂,… and b₁, b₂,…, arranged in decreasing order and repeated according to multiplicity. Then A is said to be “more mixed”, or “more chaotic”, than B, if a₁?b₁, a₁+a₂?b₁+b₂,…,a₁+…+a_m?b₁+…+b_m,…; It turns out that if A is more mixed than B, then the entropy of A is larger than the entropy of B. However, more generally, let v be an arbitrary concave function, ?0, and vanishing at 0. Then, if A is more mixed than B, trv(A)?trv(B). It is shown that also the converse is true. Furthermore, a variety of other characterizations of the relation “A is more mixed than B” is obtained, and several applications to quantum statistical mechanics are given.     

Inversion of the Ka = 0 and 1 rotational levels in the lowest excited vibrational state of HNCS

Fairly strong, regularly spaced absorption lines have been observed in the microwave spectrum of HNCS and assigned to b-type, K_a = 0 ← 1, Q-branch transitions arising from molecules in the lowest excited vibrational state. The Fortrat diagram of these lines has the appearance of a c-type Q branch, which is impossible in HNCS because of its symmetry. This anomalous b-type Q-branch spectrum is caused by strong a-type Coriolis interactions among the three low-lying bending modes; the K_a = 1 levels of the lowest excited vibrational state are perturbed and shifted lower in energy than the K_a = 0 levels for each J. This interpretation has been confirmed by the observation of P- and R-branch transitions associated with this Q branch. The band origin has been determined to be ?40 104.287 MHz (?1.3377 cm^?1). The inversion of the K_a = 0 and 1 energy levels is consistent with the interpretation of HNCS as a quasi-linear molecule.     

Die Hyperfeinstruktur des 32P3/2-Zustands von Natrium im starken Magnetfeld

The hyperfine structure of the 3²P_3/2 State of Na²³has been measured by the optical double resonance technique in a magnetic field of 3.1 kG sufficiently strong to decouple completelyI andJ. In the case of π or (σ⁺+σ^?) excitation the double resonance signal represents the superposition curve of eight unresolved radio-frequency transitions. The dependence of the signal on the pressure of sodium vapour and the radio-frequency field strength has been studied. The analysis of the experimental curves yields for the hyperfine coupling constants the valuesa=(18.7±0.4) Mc/s andb=(3.4±0.4) Mc/s. The nuclear electric quadrupole moment derived from the ratio ofb/a isQ=(0.146±0.02) · 10^?24cm². The Lande factor and the lifetime for the 3²P_3/2state are g_J=1.3344±0.0004 and τ=(1.61±0.07) · 10^?8 sec.     

Experimentally favoured potential for mesons

We show first that a natural potential to be used in a semirelativistic wave equation for theS=1,J=J _max light and heavy mesons is, forr?1 Fermi,V(r)=ar+b/r withb??π/2, forr?1 Fermi,V(r)=cln(r/r ₀). Next we show that this particularb value favours in fact a QCD-like potential forr?1 Fermi so that a logarithmic potential is only an effective one in a smallr region.     

Relation between contiguous Mie coefficients for perfectly conducting spheres

It is shown that when the size parameter x = ka in the scattering of electromagnetic waves by a perfectly conducting sphere is equal to an integer n, the Mie coefficients a_n and a_n−1 are equal. It is also shown that the other Mie coefficient b_n cannot be equal to b_n−1 for any finite x. The latter conclusion also holds in the case of scattering of a scalar particle by a hard sphere in quantum mechanics.     

Microwave spectral studies of rotational isomerism in substituted ethanethiols: 2-Aminoethanethiol and 2-chloroethanethiol

Microwave spectra were observed and analyzed for 2-aminoethanethiol and 2-chloroethanethiol. The amino compound exists in two gauche rotameric conformations, one exhibiting an intramolecular SH?N hydrogen bond. The hydrogen-bonded conformer lies higher in energy by 274 ± 90 cal mole^?1 and has the following rotational constants (in MHz): A = 12 040.1 ± 11.3, B = 3352.24 ± 0.03, and C = 2881.99 ± 0.03. For the non-hydrogen-bonded conformer the rotational constants (in MHz) are A = 11 929.9 ± 10.2, B = 3395.01 ± 0.03, and C = 2877.82 ± 0.03. Dipole moment measurements for the H-bond conformer led to μ_a = 2.68 D, μ_b = 0.88 D, and μ_c = 0.37 D, while for the non-H-bond form the values are μ_a = 1.51 D, μ_b = 0.0 D, and μ_c = 0.62 D. In the case of chloroethanethiol, the only assigned spectral lines were the unresolved J → J + 1 a-type bands of a trans conformation. For this molecule the combination rotational constant B + C has the value 2955.17 ± 0.02 MHz for the ³⁵Cl species and 2879.73 ± 0.02 MHz for the ³⁷Cl species.     

Antiferromagnetic exchange mechanism of superconductivity in cuprates

The theory of superconducting pairing due to antiferromagnetic exchange is considered. The strong dependence of the superconducting transition temperature T _c on the lattice constant a observed recently in mercury superconductors is explained within the framework of this theory. Calculations have been performed based on the two-band p-d Hubbard model in the strong correlation limit. The large excitation energy Δ_pd for the antiferromagnetic exchange of two particles from different Hubbard subbands results in the suppression of the retardation effects and in the pairing of all the particles in the conduction subband with the Fermi energy E _F ?Δ_pd:T _c ?E _F exp(?1/λ), where λ∝J. The dependence T _c (a) and the isotope effect are explained by the dependence of the exchange interaction J on a and on zero-point vibrations of oxygen ions.     

Sub-Doppler laser-Stark and high-resolution Fourier transform spectroscopy of the ν3 band of formic acid

The 5.6-μm band of HCOOH, which is the strong carbonyl stretch mode, is analyzed using a combination of sub-Doppler resolution laser-Stark data obtained with a CO laser and Fourier transform data obtained from a Bomem interferometer. The Fourier transform data, including 647 lines with J′ ≤ 22 and K_a ≤ 11, are fit with a Watson-type Hamiltonian to determine excited state constants. The Coriolis interactions with v₅₊₉ and v₆₊₉, previously noted by Kuze et al., are included in the analysis; the former by using an exact diagonalization technique, the latter via perturbation theory. Taking the molecular parameters from this fit, the laser-Stark data are then analyzed to give ground and excited state dipole moments, yielding the following results in Debyes: μ″_a=1.4071(8)μ″_b=0.227(10)μ′_a=1.4353(9)μ′_b=0.214(9), where the errors are 3σ estimates. The laser-Stark data are limited to J′ ≤ 7 and give a ± 14 MHz fit to 191 lines.     

Unusual metal–insulator transition in disordered ferromagnetic films

We present a theoretical interpretation of recent data on the conductance near and farther away from the metal–insulator transition in thin ferromagnetic Gd films of thickness b≈2$b\approx 2$–10 nm. For increasing sheet resistances a dimensional crossover takes place from d=2 to d  =3 dimensions, since the large phase relaxation rate caused by scattering of quasiparticles off spin wave excitations renders the dephasing length L_??b$L_{?}?b$ at strong disorder. The conductivity data in the various regimes obey fractional power-law or logarithmic temperature dependence. One observes weak localization and interaction induced corrections at weaker disorder. At strong disorder, near the metal–insulator transition, the data show scaling and collapse onto two scaling curves for the metallic and insulating regimes. We interpret this unusual behavior as proof of two distinctly different correlation length exponents on both sides of the transition.     

Microwave and submillimeter-wave spectra of CH3OH

Frequency measurements and assignments have been made for CH₃OH lines in the 15- to 400-GHz region. The a-type R-branch multiplets are reported up to J = 8 ← 7 for the v_t=0 torsional ground state, and to J = 6 ← 5 for the v_t=1 and v_t=2 excited states. Several new Q branches are listed and many b-type P- and R-branch transitions have been identified over a wide range of J and k values.