Divisors on elliptic Calabi-Yau 4-folds and the superpotential in F-theory — I

Each smooth elliptic Calabi-Yau 4-fold determines both a three-dimensional physical theory (a compactification of “M-theory”) and a four-dimensional physical theory (using the “F-theory” construction). A key issue in both theories is the calculation of the “superpotential” of the theory, which by a result of Witten is determined by the divisors D on the 4-fold satisfying X( _D = 1. We propose a systematic approach to identify these divisors, and derive some criteria to determine whether a given divisor indeed contributes. We then apply our techniques in explicit examples, in particular, when the base B of the elliptic fibration is a toric variety or a Fano 3-fold.

When B is Fano, we show how divisors contributing to the superpotential are always “exceptional” (in some sense) for the Calabi-Yau 4-fold X. This naturally leads to certain transitions of X, i.e., birational tranformations to a singular model (where the image of D no longer contributes) as well as certain smoothings of the singular model. The singularities which occur are “canonical”, the same type of singularities of a (singular) Weierstrass model. We work out the transitions. If a smoothing exists, then the Hodge numbers change.

We speculate that divisors contributing to the superpotential are always “exceptional” (in some sense) for X, also in M-theory. In fact we show that this is a consequence of the (log)-minimal model algorithm in dimension 4, which is still conjectural in its generality, but it has been worked out in various cases, among which are toric varieties.     

Optical pumping with laser-induced-fluorescence

We describe a new procedure for optical pumping that is based on laser-induced fluorescence (LIF). The procedure is demonstrated by optically exciting a sample of Rb⁸⁵ atoms, which then creates a population imbalance between the ground state hyperfine levels of Rb⁸⁷ by “LIF depopulation pumping”. Though optical pumping with this technique increases the intensity dependent light-shift coefficient (i.e., ac Stark shift) of the Rb⁸⁷ 0-0 hyperfine transition, it reduces the frequency dependent light-shift coefficient by at least an order of magnitude. Since the stabilization of the diode laser wavelength is a significant challenge in the development of laser-pumped gas-cell atomic clocks, it is anticipated that optical pumping with LIF will be of benefit to atomic clock technology.     

Fano resonances in the impurity photocurrent spectra of GaAs samples and an InGaAs/GaAsP quantum-well heterostructure doped with shallow acceptors

The photocurrent spectra of p-GaAs samples and a p-InGaAs/GaAsP quantum-well heterostructure doped with shallow acceptors (C, Be, Zn) are investigated. Fano resonances associated with the ground and excited acceptor states are revealed and analyzed. It is found that sharp change in dielectric constant in the GaAs reststrahlen region strongly affects the lineshape of the Fano resonance associated with the acceptor ground state.     

He原子体系中偶极子响应的周期性量子相位调控的理论研究

基于激光诱导相位模型, 研究了周期性相位调控的He原子体系的光谱响应. 研究发现,周期性的相位调控会导致He原子吸收谱由单个孤立的洛伦兹线型转化为等间隔的“梳状”结构. “梳状”光谱的性质主要由原子系统和控制脉冲链的性质决定, 并给出了表征“梳状”光谱的理论公式. 该机理具有普遍适用性, 它可以应用到任意原子体系, 进而推广到任意波段, 并且为任意波段的脉冲整形提供了可能.     

High field magnetization in Pr(Ni1-xCox)5 single crystals

Magnetization measurements in fields up to 38 T performed at low temperature on single crystals of the hexagonal Pr(Ni_1-xCo_x)₅ compounds for x = 0, 0.05, 0.10 and 0.20 are presented. In PrNi₅ we observe highly original behaviour predicted by the knowledge of the Crystalline Electric Field parameters and arising from the existence of a non-magnetic singlet ground state; namely transitions associated with the field induced “anticrossing” and “crossing” of the two lowest states along the [100] and [120] directions, respectively. The measurements performed on the other compounds have allowed us to study the dependence of this behaviour on Co substitutions.     

A microscopic three-cluster model in the hyperspherical formalism

The hyperspherical formalism is applied in the framework of the microscopic generator-coordinate method. Three-cluster systems are described with a single generator coordinate, the hyperradius. This model is a natural extension of previous microscopic theories, and can be applied to bound states and resonances in a range of nuclei exhibiting a cluster structure. As an illustrative example, the model is applied to ⁶He and ⁶Li. Density distributions and electric dipole transition strengths are calculated, including B(E2;0⁺→2⁺) in ⁶He. The results are consistent with a neutron halo structure for the ground state of ⁶He, and with a proton–neutron halo structure of its isobaric analog state in ⁶Li. No 1⁻ “soft dipole” resonance is found in ⁶He.     

DIET in the bulk: evidence for hot electron cleavage of Si---H bonds in SiO2 films

The observed increase in leakage current through SiO₂ films after hot electron exposure is ascribed to dissociation induced by electronic transitions (“DIET”) of bulk Si---H bonds, producing mobile hydrogen. We use ab initio supercell bandstructure calculations at the local density functional level to locate features produced by hydrogen-containing defects in -SiO₂. The edge of the Si---H σ* resonance is found to be about 2.7 eV above the conduction band rise, in good agreement with the observed threshold for hot electron induced damage in amorphous SiO₂ films grown on Si substrates. The O---H σ* resonance is almost 4 eV higher. Removing H from O---H in the supercell does not affect the gap region (---O⁻ forms); however, removing H from Si---H produces a mid-gap state, suggesting leakage current by hopping conductivity between Si dangling bonds. A Morse potential model is used to explore the dynamics of bond scission by short-lived (<1 fs) hot electron σ* capture. Supercell calculations on interstitial atomic hydrogen indicate the energy cost to break an embedded Si---H bond is about 0.6 eV less than in the gas phase. The DIET yield is substantially increased by reducing both ground and electron-attached state binding by this amount. While uncertainty over the displaced equilibrium in the electron-attached excited state remains, the computed DIET cross-section for reasonable parameters is ≈10⁻¹⁸ cm², and is in agreement with the semi-empirically derived value for trap creation. Comparisons are made to surface DIET processes involving Si---H bonds.     

Quantum coherence in quantum dot—Aharonov–Bohm ring hybrid systems

We investigate coherent transport through hybrid systems of quantum dots and Aharonov–Bohm (AB) rings. Strong coherence over the entire system leads to the Fano effect, which originates from the interference and the phase shift caused by the discrete states in the dots. The high controllability of the system parameters reveals that the Fano effect in mesoscopic transport can be a powerful tool for detecting the phase shift of electrons. We apply it to detect electrostatic phase modulation and the phase shift in a quantum wire with a side-coupled dot. Finally, we provide an experimental answer to the problem of “neighboring in-phase Coulomb peaks”.     

Photoelectron ionization spectra in a system interacting with a neighbor atom

We study long-time photoelectron ionization spectra of a system interacting with a neighbor two-level atom under the influence of a laser field. The system has at least a ground state and a continuum of states that are free with respect to one electron. In a weak light field, a Fano resonance is revealed. Also we consider an atomic autoionization level of the system, which leads to two Fano resonances under the influence of a weak field.     

Measurement of the average polarization of B produced by polarized muons in the μ + C → νμ + B reaction

The average polarization of ¹²B produced by the capture of polarized muons in ¹²C has been measured using recoil implantation techniques. From the result we deduce the average polarization of the ¹²B ground state ¹²B(0) corresponding to the ¹²C → ¹²B(0) Gamow-Teller reaction: J_μ(0) = 0.43 ± 0.10. The sizeable deviation of this polarization from the value of 2/3, characteristic of a “bare” 0⁺ → 1⁺ process, is a fair evidence for induced axial-vector interaction(s) in muon capture. The ratio of the induced pseudoscalar and the axial-vector coupling constants is deduced to be: g^μ_P/g^μ_A = 12 ± 5.     

Numerical Solution of the Spin-1 Heisenberg Antiferromagnetic Chains by Using a Projector Method

An eficient projector Monte Carlo method has been used to calculate the energies of the ground state and the first excited state, and hence the gap between them, of the spin-1 Heisenberg antiferromagnetic chains with linear sizes up to N = 40. We have computed them on chains up to N = 40. We have found that the size-dependence of the ground state energy per site has the form[e₀(N)-e₀]～1/N^5/2, which implies that there is a gap between the ground state and the first excited state. The value of the ground state energy per site as N→ ∞ is e₀ = -1.3996. The direct extrapolation of ΔE(N) also shows that a gap of ΔE = 0.36 exists as N→ ∞.     

Refractive index sensing of double Fano resonance excited by nano-cube array coupled with multilayer all-dielectric film

We propose a hybrid structure of a nano-cube array coupled with multilayer full-dielectric thin films for refractive index sensing.In this structure,discrete states generated by two-dimensional grating and continuous states generated by a photonic crystal were coupled at a specific wavelength to form two Fano resonances.The transmission spectra and electric field distributions of the structure were obtained via the finite-difference time-domain method.We obtained the optimal structural parameters after optimizing the geometrical parameters.Under the optimal parameters,the figure of merit(FOM)values of the two Fano resonances reached 1.7×10⁴and 3.9×10³,respectively.These results indicate that the proposed structure can achieve high FOM refractive index sensing,thus offering extensive application prospects in the biological and chemical fields.     

πN scattering and electromagnetic corrections in the perturbative chiral quark model

We apply the perturbative chiral quark model to give predictions for the electromagnetic O(p²) low-energy couplings of the ChPT effective Lagrangian that define the electromagnetic mass shifts of nucleons and first-order (e²) radiative corrections to the πN scattering amplitude. We estimate the leading isospin-breaking correction to the strong energy shift of the π⁻p atom in the 1s state, which is relevant for the experiment “Pionic Hydrogen” at PSI.     

High resolution X-ray photoelectron spectroscopy on nitrogen molecules

This paper summarizes recent developments for experimental and theoretical studies on core-level photoelectron spectroscopy of N₂. Analysis of experimental spectra reveals that the 1σ_g and 1σ_u core-hole states differ in energy by ~100meV and in equilibrium bond length by ~0.04pm, in agreement with ab initio predictions. The ratio of the 1σ_g and 1σ_u photoionization cross sections measured in the photon energy range up to 1 keV reveals oscillatory structure due to two-center interference, equivalent to Young’s double-slit experiment, as Cohen and Fano predicted. The experimental Auger rates for the transition to the dicationic ground state are found to be different by a factor of two for 1σ_g and 1σ_u hole states and are well reproduced by the ab initio calculations. All these findings support the delocalized picture of the core hole. Discussion is given how many-body processes involved and observations for these processes affect the observation of the localized and/or delocalized core hole.     

A study of the Li(p,n)Be reaction by the neutron threshold technique

The reaction ⁶Li(p,n)⁶Be has been studied by slow-neutron detection, with particular attention to the ⁶Be ground state threshold. The detector response was calculated by a Monte Carlo technique and verified with a measurement of the ⁷Li(,n)¹⁰B threshold. An analysis of the shape of the ⁶Be threshold indicated that both s- and p-wave neutrons contribute significantly to the reaction. The results depend on what mode of decay is assumed for the ground state of ⁶Be. If a two-stage process is assumed, with either an alpha particle and an unbound diproton or ⁵Li and a proton as intermediate state, the width is found to be 95±28 keV and the Q-value obtained for the ⁶Li(p,n)⁶Be reaction is −5074±13 keV. It was not possible to detertmine which process is predominant. No higher thresholds in the slow neutron yield up to 4 MeV of excitation in ⁶Be were observed. The data above the ground state threshold are consistent with a broad excited state of ⁶Be or with the occurrence of other neutron-producing reactions.     

Fermion Coherent State Studies of One-Dimensional Hubbard Model

We present a comparative study of the ground state of the one-dimensional Hubbard model. We first use a new fermion coherent state method in the framework of Fermi liquid theory by introducing a hole operator and considering the interactions of two pairs electrons and holes. We construct the ground state of the Hubbard model as ｜〉=[f＋∑^tφk1σ1hk2σ2ck3σ3hk4σ4 ∏exp（ρck1σ1 hk2σ2）]｜〉0,where φ and ρ are the coupling constants. Our results are then compared to those of varlational methods, density functional theory based on the exact solvable Bethe ansatz solutions, variational Monto-Carlo method （VMC） as well as to the exact result of the infinite system. We find satisfactory agreement between the fermion coherent state scheme and the VMC data, and provide a new picture to deal with the strongly correlated system.     

ATOMIC COHERENT POPULATION TRAPPING AND ITS APPLICATION IN A RAMAN-TYPE PHOTOIONIZATION SYSTEM WITH THREE BOUND STATES

We have studied the atomic coherent population trapping in a Raman-type, photoionization system with three bound states. The conditions for the system having two or one stable eigenstate are given. The influences of Fano asymmetric factors on the coberent population transfer are also analyzed.It is found that the property of the system having on]y one population trapping state consisting of the ground state, and one excited state, can be utilized to transfer the atomic initial population into one excited state.     

Impurity photoconductivity in strained <Emphasis Type="Italic">p</Emphasis>-InGaAs/GaAsP heterostructures

The impurity-photoconductivity spectrum is observed for strained quantum wells of the p-InGaAs/GaAs solid solution at T= 4.2 K. In addition to the broad photoconductivity band attributed to the transitions from the acceptor ground state to the continuum of the first size-quantization subband, the spectrum exhibits a peak due to the transitions from the ground state to the excited localized acceptor state, a band corresponding to the transitions to the resonance states associated with the second heavy-hole size-quantization subband, and a narrow photoconductivity peak (Fano resonance) in the spectral range corresponding to the optical-phonon energy.     

Fano resonances in semiconductor superlattices

We use semiconductor superlattices as a model system for the investigation of Fano resonances. In absorption the excitonic transitions of the Wannier–Stark ladder show the typical asymmetric line shape due to coupling to the continuum of lower-lying transitions. The unique feature of these Fano resonances is that they allow to continuously tune the key parameter – the coupling strength Γ between the discrete state and the degenerate continuum – by varying the bias voltage. Using this feature, we directly show that the Fano coupling leads to a fast polarization decay. We also investigate the dependence of the Fano parameters on the structure of the superlattice and compare with an extensive theoretical model of the resonances.     

A relation between the atomic charge of carbon and the C1s core electron binding energy estimated from a comparison of gas phase and solid state data and the molar polarizabilities of the investigated molecules

A method for internal calibration of ESCA (XPS ) spectra is described that permits the use of a simple relation between binding energy (E_b) and atomic charge (q) : E_b = kq + E_b0. This relation has been shown to hold for a large number of elements. So far the relation for carbon has, however, not been very well established. A method is now described that allows the use of carbon charges determined from E_b, vs. q correlations for other elements and has also made it possible to establish a linear relation for carbon. The method does not use carbon charges determined directly from quantum chemical calculations.

As an essential part of this procedure we investigated empirically the possible relation between the difference between the gas phase calibration standard and that for the same element in the solid state, “a”, and the molar polarizability of the substance, P. It was found that “a” decreases with increasing polarizability, tentatively as a=4.15+8.30 P^−1/3. Therefore, knowledge of the polarizability of carbon-containing molecules from the literature made it possible to determine “a” and then the charge of all other atoms in the molecule. In this way a set of E_b and qc date was obtained. These data were complemented by another set using theoretical q_c snd solid state E_b of phenyl compounds previously made.

The results of the investigation show a linear relation between E_b(Cls) and q_c valid for the solid state: E_b,(Cls) = 4.68 q_c + 286.2 eV with a correlation coefficient of 0.945. This brings the previously obtained k value for carbon, which seemed anomalously high, down to a value of similar magnitude as for other light elements.