Nonlinear Bogolyubov-Valatin transformations: Two modes

Extending our earlier study of nonlinear Bogolyubov-Valatin transformations (canonical transformations for fermions) for one fermionic mode, in the present paper, we perform a thorough study of general (nonlinear) canonical transformations for two fermionic modes. We find that the Bogolyubov-Valatin group for n=2 fermionic modes, which can be implemented by means of unitary transformations, is isomorphic to SO(6;R)/Z₂. The investigation touches on a number of subjects. As a novelty from a mathematical point of view, we study the structure of nonlinear basis transformations in a Clifford algebra [specifically, in the Clifford algebra C(0,4)] entailing (supersymmetric) transformations among multivectors of different grades. A prominent algebraic role in this context is being played by biparavectors (linear combinations of products of Dirac matrices, quadriquaternions, sedenions) and spin bivectors (antisymmetric complex matrices). The studied biparavectors are equivalent to Eddington’s E-numbers and can be understood in terms of the tensor product of two commuting copies of the division algebra of quaternions H. From a physical point of view, we present a method to diagonalize any arbitrary two-fermion Hamiltonians. Relying on Jordan-Wigner transformations for two-spin- and single-spin- systems, we also study nonlinear spin transformations and the related problem of diagonalizing arbitrary two-spin- and single-spin- Hamiltonians. Finally, from a calculational point of view, we pay due attention to explicit parametrizations of and SO(6;R) matrices (of respective sizes 4×4 and 6×6) and their mutual relation.     

Prospects of reactor neutrino experiments

Since the energy of a reactor neutrino is a few MeV, all , and oscillations are accessible by reactor neutrino experiments. KamLAND observed the oscillation and currently Double Chooz, RENO and Dayabay experiments are under construction aiming to detect oscillation. There are still good prospects for future reactor neutrino experiments after them. For example, there is room to further improve sin²2θ₁₃ accuracy at a baseline of ∼1.5 km, a very precise sin²2θ₁₂ measurement and the determination of mass hierarchy may be possible at a baseline ∼50 km, and if KamLAND is enlarged to the SuperKamiokande size, better measurement of and sin²2θ₁₂ will be anticipated. It is important to take into account such possibilities when planning future neutrino program after θ₁₃ is measured by current experiments.     

Terahertz spectroscopy of oxygen, O2, in its Σg and Δ electronic states : THz Spectroscopy of O2

High precision rotational spectra of isotopic oxygen O₂ (with or ) in its electronic ground state have been measured in selected frequency regions between 0.4 and 2.0 THz. The main isotopic species, , was also investigated in its first excited electronic state . The new data, analyzed together with previous measurements, yielded improved spectroscopic parameters.     

Parametric characterization of Mathieu-Gauss beams

Based on the irradiance moments definitions, the expression of factor of truncated zeroth-order Mathieu-Gauss beams (MGBs) is derived analytically. Furthermore, the propagation equation of kurtosis parameter of non-truncated MBGs passing through a paraxial ABCD optical system is established. Particularly, the dependence of factor and kurtosis parameter on the spatial profile of the beam are illustrated numerically and analyzed in details.     

Compton scattering by the proton through θcms = 75° and 90° in the Δ-resonance region

Differential cross sections for Compton scattering by the proton have been measured in the energy interval between 200 and 500 MeV at scattering angles of θ_cms = 75° and θ_cms = 90° using the CATS, the CATS/TRAJAN, and the COPP setups with the Glasgow Tagger at MAMI (Mainz). The data are compared with predictions from dispersion theory using photo-meson amplitudes from the recent VPI solution SM95. The experiment and the theoretical procedure are described in detail. It is found that the experiment and predictions are in agreement as far as the energy dependence of the differential cross sections in the Δ-range is concerned. However, there is evidence that a scaling down of the resonance part of the photo-meson amplitude by (2.8 ± 0.9)% is required in comparison with the VPI analysis. The deduced value of the amplitude at the resonance energy of 320 MeV is: .     

Near-infrared diode laser spectroscopy of the HCSi radical

The , , and band spectra of HCSi radical were investigated by means of near-infrared diode laser spectroscopy to determine precise molecular constants for the and states. The detailed analysis of the rotationally resolved band spectra, studied for the first time in the present investigation, leads to the precise determination of molecular constants for the state associated with the Renner-Teller interaction. We obtained −0.15126663(53) and 495.00698(30) cm⁻¹ as the Renner-Teller parameter ε and the bending vibrational frequency ω₂, respectively. Based on the molecular constants for the and states, the rotational levels of the state were analyzed to obtain molecular constants and information on upper state perturbations. Using the available spectroscopic data, valence force fields for both the and states were estimated to aid in understanding the vibrational energy levels of the HCSi radical.     

Fe monolayers on InAs(0 0 1): An in situ study of surface, interface and volume magnetic anisotropy

The magnetic anisotropy of epitaxial Fe films with thicknesses in the range of 2-142 monolayers (ML) grown on {4×2} reconstructed InAs(0 0 1) was investigated by in situ ferromagnetic resonance. The easy magnetization direction was found to be parallel to the -direction for Fe films below 4 ML, while it rotates by 45^° toward the -direction. It is observed that both surface-interface and volume contribution to the perpendicular anisotropy favor an easy axis perpendicular to the film plane. The cubic surface-interface anisotropy is relatively large with easy axes along -directions in contrast to the volume contribution which favors easy axes along the -directions. The volume contribution is found to be larger than the Fe bulk cubic anisotropy. A thickness independent uniaxial anisotropy has been found in films with a thickness of 2 up to 142 ML.     

Electronic structure of dysprosium silicide films grown on a Si(1 1 1) surface

The thickness-dependent electronic structures of Dy silicide films grown on a Si(1 1 1) surface have been investigated by angle-resolved photoelectron spectroscopy. Two (1×1) periodic bands, both of them cross the Fermi level, have been observed in the silicide films formed by Dy coverages of 1.0 monolayer and below, and more than five () periodic bands have been observed in thicker films. Taking the () periodic structure of Dy atoms in the submonolayer silicide film into account, the periodicity of the two metallic bands indicate that they mainly originate from the orbitals of Si atoms, which form a (1×1) structure. Of the () periodic bands observed in thick films, four of them are well explained by the folding of the (1×1) bands into a () periodicity. Regarding the other band, the three () periodic bands would originate from the electronic states related to the inner Si layers that form a () structure, and the one observed in the 3.0 ML film only might originate from the electron located at the interface between bulk Si and the Dy silicide film.     

Molecular beam epitaxy of superconducting Pr2CuO4 films

Recent reports on superconductivity in parent compounds [RE = Pr, Nd, Sm, Eu, Gd] prepared by metal-organic decomposition (MOD) shed new light on the electronic and magnetic phase diagram of electron-doped cuprates. A thorough reduction process is the key to inducing superconductivity in square-planar coordinated cuprates. In this work, Pr₂CuO₄ films were grown epitaxially by molecular beam epitaxy (MBE) on (001)SrTiO₃, (110)GdScO₃ and (110)DyScO₃ substrates. A modified two-step reduction process is required in order to obtain single-phase superconducting samples. The optimized superconducting properties are , while the room-temperature resistivity is about . Hence, we show that even amorphous Pr₂CuO_y films deposited on (110)DyScO₃ become superconducting after the application of the two-step annealing process. These results indicate that superconductivity is induced to Pr₂CuO₄ by systematic optimization of the reduction conditions, irrespective of the synthesis route.     

Quantization and instability of the damped harmonic oscillator subject to a time-dependent force

We consider the one-dimensional motion of a particle immersed in a potential field U(x) under the influence of a frictional (dissipative) force linear in velocity () and a time-dependent external force (K(t)). The dissipative system subject to these forces is discussed by introducing the extended Bateman’s system, which is described by the Lagrangian: which leads to the familiar classical equations of motion for the dissipative (open) system. The equation for a variable y is the time-reversed of the x motion. We discuss the extended Bateman dual Lagrangian and Hamiltonian by setting specifically for a dual extended damped–amplified harmonic oscillator subject to the time-dependent external force. We show the method of quantizing such dissipative systems, namely the canonical quantization of the extended Bateman’s Hamiltonian ?. The Heisenberg equations of motion utilizing the quantized Hamiltonian surely lead to the equations of motion for the dissipative dynamical quantum systems, which are the quantum analog of the corresponding classical systems. To discuss the stability of the quantum dissipative system due to the influence of an external force K(t) and the dissipative force, we derived a formula for transition amplitudes of the dissipative system with the help of the perturbation analysis. The formula is specifically applied for a damped–amplified harmonic oscillator subject to the impulsive force. This formula is used to study the influence of dissipation such as the instability due to the dissipative force and/or the applied impulsive force.     

Dynamics of electrons and holes at surfaces

We present ab initio calculation results for electron-phonon (e-ph) contribution to hole lifetime broadening of the surface state on Al(0 0 1). We show that e-ph coupling in this state is significantly stronger than in bulk Al at the Fermi level. It makes the e-ph decay channel very important in the formation of the hole decay in the surface state at . We also present the results for e-e lifetime broadening in a quantum-well state in 1 ML K/Cu(1 1 1). We show that this contribution is not negligible and is much larger than that in a surface state on Ag(1 1 1).     

Observation of internal-conversion electrons induced by inelastic nuclear resonant scattering

Measurements of the internal-conversion electron emission due to the inelastic nuclear resonant excitation are reported. thin films of 20 and 1.3 nm thickness were deposited on Si(1 1 1), and the internal-conversion electrons were measured as a function of the photon energy. From the inelastic part of the spectra, the phonon density of states was obtained. Whereas the phonon density of states of 20-nm thick film resembles that of bulk -Fe, the 1.3-nm thick film revealed an obvious softening of the acoustic mode.     

Vibronic spectra, ab initio calculations, and structures of conformationally non-rigid molecules of oxalyl halides in the ground and lowest excited electronic states. Part IV: Analysis of the absorption spectra of oxalyl fluoride in the gas phase

The gas phase absorption spectrum of oxalyl fluoride in the region of 37 000–29 300 cm⁻¹ has been examined at high resolution. Singlet–singlet and singlet–triplet electronic transitions of the trans-conformer were found in the spectrum. The fundamental frequencies of trans-oxalyl fluoride in the and electronic states were determined.In the low resolution ultraviolet absorption spectrum of oxalyl fluoride in the gas phase the transition of the cis-conformer (ν_max) was found to be shifted to the blue by about 6000 cm⁻¹ relative to the transition of the trans-conformer.     

Submillimeter measurements of N2 and air broadening of hypochlorous acid

The pressure induced broadening of a several pure rotational transitions of hypochlorous acid, HOCl, have been measured as a function of temperature. This set of rotational transitions is the dominant feature of the submillimeter spectrum in the range where several remote sensing instruments currently operate. Additional features throughout the submillimeter spectrum have been recorded at the full-resolution of the room temperature Doppler linewidth using multiplier chains in the 110- wavelengths.     

Stability of matter–antimatter molecules

We examine the stability of matter–antimatter molecules by reducing the four-body problem into a simpler two-body problem with residual interactions. We find that matter–antimatter molecules with constituents possess bound states if their constituent mass ratio m₁/m₂ is greater than about 4. This stability condition suggests that the binding of matter–antimatter molecules is a rather common phenomenon. We evaluate the binding energies and eigenstates of matter–antimatter molecules , and (K⁺μ⁻) − (μ⁺K⁻), which satisfy the stability condition. We estimate the molecular annihilation lifetimes in their s states.