Differential structure on the κ-Minkowski spacetime from twist

We study four-dimensional κ  -Minkowski spacetime constructed by the twist deformation of U(igl(4,R))$U(\mathit{igl}(4,R))$. We demonstrate that the differential structure of such twist-deformed κ-Minkowski spacetime is closed in four dimensions contrary to the construction of κ-Poincaré bicovariant calculus which needs an extra fifth dimension. Our construction holds in arbitrary dimensional spacetimes.     

Poincaré covariance and κ-Minkowski spacetime

A fully Poincaré covariant model is constructed as an extension of the κ-Minkowski spacetime. Covariance is implemented by a unitary representation of the Poincaré group, and thus complies with the original Wigner approach to quantum symmetries. This provides yet another example (besides the DFR model), where Poincaré covariance is realised à la Wigner in the presence of two characteristic dimensionful parameters: the light speed and the Planck length. In other words, a Doubly Special Relativity (DSR) framework may well be realised without deforming the meaning of “Poincaré covariance”.     

Speed of particles and a relativity of locality in κ-Minkowski quantum spacetime

The last decade of research on κ-Minkowski noncommutative spacetime has been strongly characterized by a controversy concerning the speed of propagation of massless particles. Most arguments suggested that this speed should depend on the momentum of the particle strongly enough to be of interest for some ongoing experimental studies. But the only explicit derivations of worldlines in κ-Minkowski predicted no momentum dependence for the speed of massless particles. We return to this controversy equipped with the recent understanding that in some quantum spacetimes coincidences of events assessed by an observer who is distant from the events can be artifactual. We therefore set up our investigation in such a way that we never rely on the assessment of coincidences of events by distant observers. This allows us to verify explicitly that in κ-Minkowski simultaneously-emitted massless particles of different momentum are detected at different times, and establish a linear dependence of the detection times on momentum.     

κ-Poincaré–Hopf algebra and Hopf algebroid structure of phase space from twist

We unify κ-Poincaré algebra and κ-Minkowski spacetime by embedding them into quantum phase space. The quantum phase space has Hopf algebroid structure to which we apply the twist in order to get κ-deformed Hopf algebroid structure and κ-deformed Heisenberg algebra. We explicitly construct κ-Poincaré–Hopf algebra and κ-Minkowski spacetime from twist. It is outlined how this construction can be extended to κ-deformed super-algebra including exterior derivative and forms. Our results are relevant for constructing physical theories on noncommutative spacetime by twisting Hopf algebroid phase space structure.     

On κ-deformation and triangular quasibialgebra structure

We show that, up to terms of order κ⁻⁵${\kappa }^{\mathrm{-5}}$, the κ-deformed Poincaré algebra can be endowed with a triangular quasibialgebra structure. The universal R matrix and coassociator are given explicitly to the first few orders. In the context of κ-deformed quantum field theory, we argue that this structure, assuming it exists to all orders, ensures that states of any number of identical particles, in any representation, can be defined in a κ-covariant fashion.     

Photonic band structure and effect of ε and μ on the reflectivity of one-dimensional magnetic photonic crystal structure

In this paper, we study the photonic band structure and reflection properties in one-dimensional magnetic photonic crystals (MPCs). Investigation of dispersion characteristics shows that in the case of MPCs, photonic band gaps arise due to the contrast in the wave impedance, not due to the contrast in the refractive index, while contrast in the refractive index of the two layers decides the position and number of the band gaps. We also study the effect of permittivity and permeability on reflection bands, which shows that the structure that has larger values of magnetic permeability (μ) than dielectric permittivity (ε) have wider TM-reflection bands, whereas the structure for which ε is greater than μ has wider TE-reflection bands. But the gap to mid-gap frequency ratio for TM-reflection bands is larger than TE-reflection bands. Thus, magnetic permeability has greater impact on the reflectivity of MPCs than dielectric permittivity. Finally, the analysis of the omni-reflectance in MPCs has also been studied.     

The property of κ-deformed statistics for a relativistic gas in an electromagnetic field: κ parameter and κ-distribution

We investigate the physical property of the κ parameter and the κ-distribution in the κ-deformed statistics, based on Kaniadakis entropy, for a relativistic gas in an electromagnetic field. We derive two relations for the relativistic gas in the framework of κ-deformed statistics, which describe the physical situation represented by the relativistic κ-distribution function, provide a reasonable connection between the parameter κ  , the temperature four-gradient and the four-vector potential gradient, and thus present for the case κ≠0$\kappa \ne 0$ one clearly physical meaning. It is shown that such a physical situation is a meta-equilibrium state of the system, but has a new physical characteristic.     

Tight-binding parameterization of α-Sn quasiparticle band structure

The diamond structure of tin (α-Sn) can be stabilized in nanocrystals embedded in a suitable host. We developed highly accurate parameterizations for tight-binding simulation of such structures incorporating strain and spin-orbit interaction. Parameters are obtained by fitting to ab initio GW quasiparticle band structures of unstrained α-Sn as well as geometries under uniform compressive or tensile strain. The optical response calculated from this fit is in excellent agreement with experiments. As an application, confinement induced band gaps in strained and unstrained 3 nm nanocrystals are computed. It is found that compressive and tensile strain raises and lowers the gap, respectively.     

Differential operators on the algebra of densities and factorization of the generalized Sturm–Liouville operator

Letters in Mathematical Physics - We consider factorization problem for differential operators on the commutative algebra of densities (defined either algebraically or in terms of an auxiliary...     

Theoretical investigation on the optical absorption spectra and local lattice structure of α-Al2O3:Yb crystals

In this paper, the optical absorption spectra of Yb³⁺ in the α-Al₂O₃ crystal are reasonably explained by using the superposition model and local lattice structure analysis. Based on these studies, we find that the local geometrical structure around the Yb³⁺ ions possesses an elongated trigonal distortion above the O²⁻-triangle and a compressed trigonal distortion in the lower one.     

High-resolution study of the ν1/ν5 and 2ν1/ν1+ν5 P-H stretching bands of PH2D

The P-H stretching bands ν₁/ν₅ and 2ν₁/ν₁+ν₅ were recorded using a Bruker 120 HR interferometer with a resolution of 0.0042 and 0.0088 cm⁻¹, respectively, and analyzed. From the fits 33 and 50, respectively, vibrational, rotational, centrifugal distortion, and resonance interaction parameters were obtained. These reproduce 668 and 497 rovibrational energies of the pairs of states ν₁/ν₅ and 2ν₁/ν₁+ν₅ with experimental accuracies, rms=0.00016 and , respectively. “Local mode” behavior of the PH₂ fragment is established and discussed in detail.     

New analysis of the ν5+ν9−ν9 hot band of HNO3

Nitric acid which is an important NO_x atmospheric reservoir molecule exhibits a strong absorption in the spectral region. Since this region, which corresponds to an atmospheric window, is one of the most commonly used for the retrieval of HNO₃ in the atmosphere it is essential to have the best possible corresponding spectral parameters. Updates of these spectral line parameters were recently performed in the last versions of the atmospheric databases. They concern the line positions and intensities not only of the two interfering cold bands ν₅ and 2ν₉ but also of the ν₅+ν₉−ν₉ hot band. This hot band exhibits indeed a sharp and strong Q branch at which is clearly observable in atmospheric spectra and is used for the retrievals. However, in spite of these recent updates, it proved that the spectral parameters of the hot band are not accurate enough to reproduce accurately the observed atmospheric HNO₃ absorption in ATMOS spectra. The present paper is dedicated to a more accurate analysis of this hot band using new laboratory high-resolution (0.002-) Fourier transform spectra. As a consequence, new and more precise line positions and line intensities (about 35% weaker than in HITRAN2K) were derived leading to a significant improvement in the simulation of atmospheric spectra.     

High-resolution infrared and theoretical study of the fundamental bands ν6, ν7, ν9 and ν13 of 1,2,3-thiadiazole

The Fourier transform gas-phase IR spectrum of 1,2,3-thiadiazole, C₂H₂N₂S, has been recorded with a resolution of ca. 0.003 cm⁻¹ in the 700-1100 cm⁻¹ spectral region. Four fundamental bands ν₆(A^/; 1101.8 cm⁻¹), ν₇(A^/; 1038.8 cm⁻¹), ν₉(A^/, 858.9 cm⁻¹), and ν₁₃(A^//; 746.2 cm⁻¹) have been analyzed using the Watson model in A-reduction. Two additional bands, ν₈ (A^/; 894.6 cm⁻¹) and ν₁₂(A^//; 881.2 cm⁻¹) were assigned by their weak Q-branches. Ground state rotational and quartic centrifugal distortion constants as well as upper state spectroscopic constants have been obtained from fits. A number of weak global and local interactions are present in the bands. The resonances identified were qualitatively explained by Coriolis type perturbations with neighboring levels. Ground state rotational and quartic centrifugal distortion constants, anharmonic frequencies, and vibration-rotational α-constants predicted by quantum chemical calculations using a cc-pVTZ basis and B3LYP methodology, have been compared with the present experimental data, where there is generally good agreement.     

High resolution analysis of the ν7 and ν9 bands of DCOOH

The 7¹ and 9¹ vibrational states of deuterated species of formic acid molecule DCOOH have been recorded by a FTIR spectrometer in the region 450- at a resolution of and a millimeter wave spectrometer. In the analysis microwave transitions from literature were used in addition to 14 835 assigned IR and 114 millimeter wave lines in the 7¹ and 9¹ vibrational states. The analysis resulted in band origins, rotational, centrifugal distortion, and eight interaction parameters of the Coriolis coupled 7¹ and 9¹ vibrational states. RMS deviation of the fit was for the IR data and the maximum values of J and K_a quantum numbers in the fit were 64, 28 and 64, 30 for 7¹ and 9¹ states, respectively.     

High-resolution infrared and theoretical study of the fundamental bands ν2, ν4 and ν9 and the c-Coriolis interacting dyad ν5, ν14 of 1,3,4-thiadiazole

The Fourier transform gas-phase IR spectrum of 1,3,4-thiadiazole, C₂H₂N₂S, has been recorded with a resolution of ca. 0.003 cm⁻¹ in the 800-1500 cm⁻¹ spectral region. Five fundamental bands ν₂(A₁; 1391.9 cm⁻¹), ν₄(A₁; 964.4 cm⁻¹), ν₅(A₁; 894.6 cm⁻¹), ν₉(B₁; 821.5 cm⁻¹), and ν₁₄(B₂; 898.4 cm⁻¹) have been analysed using the Watson model. Ground state rotational and quartic centrifugal distortion constants as well as upper state spectroscopic constants have been obtained from fits. The ν₄ and ν₉ bands are unperturbed while a strong c-Coriolis resonance perturbs the close-lying ν₅ and ν₁₄ bands. This dyad system has been analysed by a model including first and second order c-Coriolis resonance using the theoretically predicted Coriolis coupling constant . The ν₂ band is strongly perturbed by a local resonance, and we obtain a set of spectroscopic parameters using a model including second order a-Coriolis resonance with the inactive ν₁₀ + ν₁₄ band. Ground state rotational and quartic centrifugal distortion constants, anharmonic frequencies, and vibration-rotational α-constants predicted by quantum chemical calculations using a cc-pVTZ basis and B3LYP methodology, have been compared with the present experimental data, where there is generally good agreement.     

Simultaneous analysis of the 2ν2, 2ν5, and ν2 + ν5 vibration-rotation bands of CH3Br

Previous studies of the parallel bands 2ν₂ and $\text{2ν}{}_5{}^0$ of CH₃Br by the two first authors have been completed by the analysis of the weaker perpendicular band ν₂ + ν₅, centered near 2745 cm^?1. It is well known that the v₂ = 1 and v₅ = 1 states of methylbromide are linked by an x-y-type Coriolis interaction. Therefore, in the 2500–2900-cm^?1 range, the levels

$\text{(v}{}_2\text{=2), (v}{}_5\text{2, l}{}_5\text{=0), (v}{}_5\text{=2, l}{}_5\text{±2), (v}{}_5\text{=v}{}_2\text{=1, l=5±1)}$

are linked by a similar interaction. Least-squares and prediction programs have been written to treat this kind of problems and they have been satisfactorily applied to both isotopic species, CH₃⁷⁹Br and CH₃⁸¹Br. A localized resonance in the K = 0 subband of ν₂ + ν₅ has been shown to be due to the 3ν₃ + ν₆ band. No evidence for a strong Fermi resonance between ν₁ and $\text{2ν}{}_5{}^0$ has been found.     

Measurement of the branching ratios for the decays J/ψ → ϱπ and J/ψ → γη′

Decays of the J/ψ (3.1) resonance into final states with two charged hadrons and two photons are investigated. Branching ratios for the decays J/ψ → ?π and J/ψ → γη′ are determined to be

$\text{Г(J/ψ → pφ)}\text{Г(J/ψ → all)}\text{= (1.0± 0.2) ·10}{}^{\mathrm{?2}}\text{,}\text{Г(J/ψ → γη′)}\text{ГJ/ψ → all)}\text{= (2.0± 0.7) ·}{}^{\mathrm{?3}}$

Upper limits for the same decay modes of ψ′ (3.7) are also determined.