Comparison of |Q|=1 and |Q|=2 gauge-field configurations on the lattice four-torus

It is known that exactly self-dual gauge-field configurations with topological charge |Q|=1 cannot exist on the untwisted continuum four-torus. We explore the manifestation of this remarkable fact on the lattice four-torus for SU(3) using advanced techniques for controlling lattice discretization errors, extending earlier work of De Forcrand et al. for SU(2). We identify three distinct signals for the instability of |Q|=1 configurations, and show that these signals manifest themselves early in the cooling process, long before the would-be instanton has shrunk to a size comparable to the lattice discretization threshold. These signals do not appear for the individual instantons which make up our |Q|=2 configurations. This indicates that these signals reflect the truly global nature of the instability, rather than the local discretization effects which cause the eventual disappearance of the would-be single instanton. Monte-Carlo generated SU(3) gauge-field configurations are cooled to the self-dual limit using an -improved gauge action chosen to have small but positive errors. This choice prevents lattice discretization errors from destroying instantons provided their size exceeds the dislocation threshold of the cooling algorithm. Lattice discretization errors are evaluated by comparing the -improved gauge-field action with an -improved action constructed from the square of an -improved lattice field-strength tensor, thus having different discretization errors. The number of action-density peaks, the instanton size, and the topological charge of configurations is monitored. We observe a fluctuation in the total topological charge of |Q|=1 configurations, and demonstrate that the onset of this unusual behavior corresponds with the disappearance of multiple-peaks in the action density. At the same time discretization errors are minimal.     

On the Q(M) depolarization metric

In this work, we have derived a depolarization metric, named Q(M) here, from the nine bilinear constraints between the 16 Mueller-Jones matrix elements, reported previously by several authors following different approaches. This metric Q(M) is sensitive to the internal nature of the depolarization Mueller matrix and does not depend on the incident Stokes vector. Q(M) provides explicit information about the inner 3 × 3 internal matrix. Four bounds are associated to Q(M) for a totally depolarizing, partially depolarizing, non-depolarizing diattenuating or partially depolarizing, and non-depolarizing non-diattenuating optical system, respectively. To our best knowledge, Q(M) is the unique depolarization metric that provides such information in one single number.     

Ultra high Q crystalline microcavities

We report on the fabrication technique of ultra high Q optical crystalline whispering gallery mode microresonators and discuss their properties. The technique is suitable for the majority of available optical crystals and for production of resonators with small size. To validate the method, we made CaF₂ resonators with Q factors exceeding 4 × 10⁸ and a diameter smaller than 100 μm. A single mode resonator has also been fabricated. Possible utilization of these new resonators in quantum optics is discussed.     

The forbidden rotational Q branch of CH3SiF3: A study in internal rotation

The pure rotational spectrum driven by the small dipole moment produced perpendicular to the symmetry axis by centrifugal distortion has been investigated for CH₃SiF₃ in the ground vibrational state using a Fourier transform waveguide spectrometer. Between 10.9 and 17.0 GHz, four (k + 3 ← k) series in the Q branch have been measured in the lowest torsional state v₆ = 0 for k = 4, 5, 6, and 7 with 54 ? J ? 65. In each transition, the quantum number σ = 0, +1, −1 labelling the different torsional sub-levels is conserved. For given (J,k), splittings from ∼10 to ∼45 MHz have been observed between lines with different values of σ. The global data set includes the anticrossing molecular beam energy differences of [W.L. Meerts, I. Ozier, Chem. Phys. 71 (1982) 401-415] as well as the mm-wave R branch frequencies and (A₁ − A₂) splittings of [P. Dréan, J.-M. Colmont, J. Demaison, L. Dore, C. Degli Esposti, J. Mol. Spectrosc. 176 (1996) 23-27]). A good fit was obtained by varying 15 molecular parameters characterizing the torsion-rotation Hamiltonian H_TR for the vibrational ground state. Because of the strong correlation between two of the quartic torsion-distortion parameters (F_0,3K and D_0,Km) and a redundancy connecting the centrifugal distortion constants, four models were obtained yielding comparable fits. In each case, effective values were determined for the A-rotational constant and the height of the potential hindering the internal rotation. A high precision determination of the structural parameter ρ was made that is the same in all four models. For the off-diagonal quartic centrifugal distortion constant ε₀ and the sextic constants H_0,J, H_0,JK, H_0,KJ, and h_0,3, the differences in the values obtained in the two different reductions used have been explained in terms of the redundancy connecting these parameters. For σ = 0, +1, −1, the energy level pattern for (|k| = 3) is discussed for the case where the pure torsional energy splitting and the matrix elements off-diagonal in k are of comparable magnitude. A method is described of using an R branch study of the resulting σ-splittings for (|k| = 3) to probe the zeroth-order torsional Hamiltonian.     

Accurate Q value for the Se double-electron-capture decay

The Q   value of the neutrinoless double-electron-capture (0νECEC$0\nu \text{ECEC}$) decay of ⁷⁴Se was measured by using the JYFLTRAP Penning trap. The determined value is 1209.169(49) keV, which practically excludes the possibility of a complete energy degeneracy with the second ²⁺$2^{+}$ state (1204.205(7) keV) of ⁷⁴Ge in a resonant 0νECEC$0\nu \text{ECEC}$ decay. We have also computed the associated nuclear matrix element by using a microscopic nuclear model with realistic two-nucleon interactions. The computed matrix element is found to be quite small. The failure of the resonant condition, combined with the small nuclear matrix element and needed p-wave capture, suppresses the decay rate strongly and thus excludes ⁷⁴Se as a possible candidate to search for resonant 0νECEC$0\nu \text{ECEC}$ processes.     

Q values of the Ge and Mo double-beta decays

Penning trap measurements using mixed beams of ⁷⁶Ge–⁷⁶Se and ¹⁰⁰Mo–¹⁰⁰Ru have been utilized to determine the double-beta decay Q-values of ⁷⁶Ge and ¹⁰⁰Mo with uncertainties less than 200 eV. The value for ⁷⁶Ge, 2039.04(16) keV is in agreement with the published SMILETRAP value, 2039.006(50) keV. The new value for ¹⁰⁰Mo, 3034.40(17) keV is 30 times more precise than the previous literature value, sufficient for the ongoing neutrinoless double-beta decay searches in ¹⁰⁰Mo. Moreover, the precise Q-value is used to calculate the phase-space integrals and the experimental nuclear matrix element of double-beta decay.     

Double-beta decay Q values of Cd and Te

The Q values of the ¹¹⁶Cd and ¹³⁰Te double-beta decaying nuclei were determined by using a Penning trap mass spectrometer. The new atomic mass difference between ¹¹⁶Cd and ¹¹⁶Sn of 2813.50(13) keV differs by 4.5 keV and is 30 times more precise than the previous value of 2809(4) keV. The new value for ¹³⁰Te, 2526.97(23) keV is close to the Canadian Penning trap value of 2527.01 ± 0.32 keV (Scielzo et al., 2009) [1], but differs from the Florida State University trap value of 2527.518 ± 0.013 keV (Redshaw et al., 2009) [2] by 0.55 keV (2σ). These values are sufficiently precise for ongoing neutrinoless double-beta decay searches in ¹¹⁶Cd and ¹³⁰Te. Hence, our Q values were used to compute accurate phase-space integrals for these double-beta decay nuclei. In addition, experimental two-neutrino double-beta decay nuclear matrix elements were determined and compared with the theoretical values. The neutrinoless double-beta decay half-lives for these nuclei were estimated using our precise phase-space integrals and considering the range of the best available matrix elements values.     

Infrared-radio frequency double resonance observations of pure rotational Q-branch transitions of methane

The $\text{F}{}_2{}^{\mathrm{(2)}}\text{← F}{}_1{}^{\mathrm{(2)}}$ and $\text{F}{}_2{}^{\mathrm{(2)}}\text{← F}{}_1{}^{\mathrm{(1)}}$ transitions of the J = 7 levels of the ground state of CH₄ have been observed by infrared-radio frequency double resonance using the 3.39 μ HeNe laser line. The transition frequencies are 423.02 ± 0.02 MHz and 1246.55 ± 0.02 MHz, respectively. Using these frequencies and the splitting of the E and F₂ levels of the J = 2 state calculated from the molecular beam magnetic resonance spectra of Ozier, the centrifugal distortion constants are derived to be D_t = 132933 ± 10 Hz, H_4t = ? 16.65 ± 0.2 Hz, and H_6t = 10 ± 1 Hz. The J = 15 E⁽¹⁾ → E⁽²⁾ microwave transition is predicted as 14150 ± 9 MHz.     

Methyl isocyanate: An analysis of the low-J rotational spectrum using the quasi-symmetric top molecule approach

The low-J rotational spectrum of methyl isocyanate (CH₃NCO) has been analyzed in terms of the quasi-symmetric top molecule model, accounting explicitly for the large-amplitude CNC bending motion, and internal and overall rotation. An assignment of 25 J = 1 ← 0 and 2 ← 1 rotational transitions arising from the various CNC bending and torsional states is proposed. The molecule is found to be a nearly freely internally rotating quasi-symmetric top, with a barrier to linearity of the CNCO skeleton of 1049 cm^?1 and an equilibrium CNC valence angle of 140.2°.     

The microwave spectrum of trans 1-nitropropene

Rotational transitions of 1-nitropropene arising from the ground vibrational state and from three excited states of the nitro torsional vibration have been assigned. The values of the rotational constants in MHz are: A₀=10 650B₀=2028.56C₀1722.16A₁10 615 B₁=2028.47 C₁=1725.11 A₂10 570 B₂ 2028.31 C₂= 1727.32 A₃= 10 512 B₃2028.11 C₃=1729.37The dipole moment components are μ_a = 4.52 D, μ_b = 0.42 D and μ_total = 4.54 D. From the lack of observable internal rotation splittings the barrier to internal rotation of the methyl group is shown to be greater than 2250 cal/mole.     

A comparative study of the P and Q representations of a feedback controlled two-qubit system

In this Letter the Master equation of a two qubit system is transformed into Fokker-Planck equations in order to find the Glauber-Sudarshan P function representation. For the two qubit system examined in this Letter, the P representation is ill defined, which indicates the system is non-classical. A qualitative measure of the non-classical nature of the system is found by taking the semi-classical limit of the Fokker-Planck equation and obtaining a simplified Glauber-Sudarshan P representation. The agreement between the simplified P representation and the Q representation as well as the system stability are discussed when feedback is present and absent.     

The rotational spectrum of tertiary-butyl alcohol

The rotational spectrum of tertiary-butyl alcohol has been recorded in selected regions between 8 and 500 GHz. Early data from the University of Wisconsin in the 8-40 GHz region have been combined with recent measurements from the University of Bologna and the Jet Propulsion Laboratory in the millimeter and submillimeter wavelength regions. The spectrum was fit over a wide range of J’s and K’s using a common set of parameters for both the A and E states. This paper describes the initial assignment at Wisconsin and the final procedure used to assign and fit the higher rotational states. The resulting molecular constants and their interpretation are discussed.     

Hadronic jets with a large Q⊥ lepton pair trigger

We propose to observe hadron jets in correlation with large Q⊥ transverse momentum lepton pairs. This would allow to test the theoretical idea that the large transverse momentum of the pair is mainly produced through a scattering subprocess $\text{a}\text{+}\text{b}\text{→}\text{c}\text{+γ}{}^1$. The quantum number content of these jets is a specific signature of the subprocess, especially of those involved in perturbative QCD.     

The isotopic dependence of the spin-rotation interaction: the rotational spectrum of cadmium hydride in its XΣ state

Far-infrared rotational transitions within the X²Σ⁺ (v=0) state of cadmium hydride (CdH) were recorded over the range N″=2-17 for 12 different isotopomers, using the technique of tunable far-infrared (TuFIR) spectroscopy. The molecule was made by heating cadmium metal in the presence of a DC electric discharge in hydrogen. Fine structure arising from the electron spin-rotation interaction and hyperfine structure from the ¹¹¹Cd, ¹¹³Cd, and ¹H nuclei were resolved and analyzed. All of the isotopic data were fitted together using a Hamiltonian containing mass-independent, Dunham-type rotational parameters U_kl and small correction terms Δ_kl described by Watson [J. Mol. Spectrosc. 80 (1980) 411]. The spin-rotation interaction was modeled in an analogous way using Dunham-like U_γ,kl parameters, and fitting its isotopic dependence properly required the use of four Δ_γ,kl correction terms.     

The methane ν1(a1) vibrational state rotational structure obtained from high-resolution CARS-spectra of the Q-branch

The gaseous methane ν₁(a₁), Q-branch coherent anti-Stokes Raman scattering (CARS) spectra have been investigated at a resolution of 0.002 cm^?1. A complex rotational structure of the resolved Q-branch has been experimentally observed. This structure can be ascribed to strong tetrahedral splitting of the rotational levels of the upper vibrational state, which possibly occurs due to Fermi resonance between the ν₁(a₁) and 2ν₂(a₁) vibrational energy levels which are close to each other. An assignment of the observed spectral lines has been made, yielding the rotational constants B, D, and D_t for the ν₁(a₁) vibrational state of the methane molecule. The absolute Raman frequency ν₁ of the purely vibrational transition has been found.     

Structure in the aluminum 1s soft x-ray appearance potential spectrum

The Al 1s level soft X-ray appearance potential spectrum for clean and oxidized Al has been observed. In the spectrum of the clean metal, structure related to an edge singularity and a plasmon satellite is distinguished. The plasmon coupling strength in the appearance potential spectrum is found to be almost equal to that in X-ray photoelectron spectroscopy and bremsstrahlung isochromat spectroscopy.     

Lost branches in the spectrum of Parekh waves

It has been shown that a traditional approach to the calculation of a Parekh wave (a shear surface acoustic wave propagating along the mechanically free surface of a ferromagnet laterally magnetized by a static external magnetic field) including magnetoelastic interaction and neglecting magnetostriction inadequately describes the spectrum of the wave in the high-frequency range.     

Millimeterwave rotational spectrum and internal rotation in o-chlorotoluene

The millimeterwave rotational spectrum of o-chlorotoluene is investigated in the frequency region 150-250 GHz. Many rotational lines show splitting due to internal rotation of the methyl group. The analysis of the internal rotation splitting allows us to determine with precision the potential barrier to internal rotation of the methyl group. However, it is found that the moment of inertia of the methyl top is probably much smaller than usually assumed, which significantly affects the value of the barrier. Accurate centrifugal distortion constants are obtained for the ground states of ³⁵Cl and ³⁷Cl isotopologues as well as for an excited vibrational state.