Multiple Peak Structure Research Articles

On a Generating Function and its Probability Distributions. A Contribution to the Theory of Transition Rates I

A function of two complex variables with two real parameters a and b is described, which generates a sequence of probability distributions of two integer variables m ≥ 0 and n ≥ 0. Closed expressions for the special b = 0 and general case b≠ 0 and recurrence equations for calculating the probability distributions are derived. The probability distribution for m = 0 and a large enough is qualitatively bell-shaped, and that for m ≠ 0 has multiple peak structures. In both cases, the b parameter influences solely the skewness of the curves. For small a values, the distributions fall rapidly from a value of nearly one, decreasing by a factor of 1010 or more as n increases from zero to n = 10. The influence of the b parameter on their properties can be pronounced. Finally, we note an important property of the distributions when two or several of them are convoluted with one another. The result is expressed in terms of an addition theorem in respect to the parameter a and describes a multidimensional distribution.

High energy-resolution electron energy-loss spectroscopy study of the electric structure of double-walled carbon nanotubes

Electron energy-loss spectra were obtained from two double-walled carbon nanotubes (DWCNTs) with an energy resolution of 85 meV. The spectra showed multiple peak structures between 2 and 3 eV. However, peak positions are different for these two DWCNTs. The chiral indices of CNT layers of the two DWCNTs were determined to be (29,4)(in) (17,8)(out) and (46,6)(out) (26,21)(in), respectively, by comparing experimental electron diffraction patterns with simulated ones. The spectra were also compared with simulated joint density of states, which were derived from the determined chiral indices. It was confirmed that the peak structures in the spectra are due to interband transitions intrinsic for tubular structures of graphitic sheets.

Quantum size dependence of electron distribution on carbon nanotubes and its influence on field emission

A two-dimensional model of quasi-free-electrons is used to compute the electron axial distribution on a carbon nanotube and the energy distribution of the field emitted electrons. The nature of the substrate-nanotube contact is taken into account by varying the boundary condition for the electronic wave function. In qualitative agreement with the experimental results to date, regular patterns of the axial electron density and electron accumulation on the nanotube cap are obtained. The energy distribution of the field emitted electrons shows a multiple peak structure superimposed over a very fine distribution of maxima. Such a multiple peak structure is also qualitatively confirmed in experiments. The behavior of the distribution of the emitted electrons with the extraction voltage and with the operation temperature is investigated.

Ｓｒ２ＦｅＭｏＯ６エピタキシャル薄膜の表面特性

Thin films of ordered double perovskite Sr2FeMoO6 were sputter-deposited on Ba0.4Sr0.6TiO3-buffered SrTiO3 substrates, and their surface properties were examined by atomic force microscopy (AFM) and X-ray photoemission spectroscopy (XPS). The Mo 3d spectra of Sr2FeMoO6 films showed a multiple peak structure, which originated from the unusual electronic state of metallic Sr2FeMoO6. Systematic XPS studies of the air-exposed surface of Sr2FeMoO6 film indicated that the surface native barrier was an insulating SrMoO4. In addition, a TMR junction with the native barrier was fabricated using a convention photolithographic technique, and an MR ratio of 10 % was observed at 4.2 K.

Overtone spectroscopy of C–H ethyl stretches of 1-butyne

Room-temperature photoacoustic (PA) spectra and jet-cooled action spectra of the first to third overtone regions of the ethyl C-H stretches in vapor phase 1-butyne, CH3CH2C[Triple Bond]C-H, were measured. Both the PA and action spectra exhibit a complex multiple peak structure being better resolved and more pronounced in the latter, due to inhomogeneous structure reduction. The observed manifolds were analyzed in terms of a simplified joint local-/normal-mode (LM/NM) model accounting for two types of C-H stretches (methyl and methylene) and for Fermi resonances between stretches and deformations. The retrieved parameters, used for calculation of the eigenstates, come from the best-fit parameters based on the diagonalization of the vibrational Hamiltonian in the LM/NM basis. The parameters were obtained by comparing the eigenvalues and the sum of the squares of the expansion coefficients of the eigenvectors of the C-H stretches of methyl and methylene to the action spectra peak positions and intensities, respectively. This approximate model vibrational Hamiltonian is proposed to explain most observed spectral features, corresponding to C-H stretch bands and to combinations of C-H stretches and deformations, indicating the importance of the Fermi resonance. The model was also applied to calculate the dynamics of the C-H stretching modes resulting from coupling with the deformations, implying rapid initial state decay on subpicosecond time scale. Decays of several picoseconds were found for complete transfer of probability from the initially prepared state of methylene and methyl to the counterpart LM states.

Ion kinetic effects in radio-frequency sheaths

The kinetic effects of ions on the radio-frequency collisionless sheath dynamics are explored by solving the ion Vlasov equation with an ion source term. The ion velocity distribution function is obtained numerically. It is found to depend strongly on the source term. The macroscopic variables such as the ion density, velocity, electric field, and sheath voltage predicted by the kinetic model are in good agreement with the fluid model. The predicted period-averaged ion energy distributions at the cathodes, however, are different. In the high frequency regime, multiple peaks can be formed with some process parameters such as bias voltage and rf frequency. The mechanism for this multiple-peak structure can be attributed to the rf modulation of the sheath potential in combination with the creation of cold ions in the sheath as shown by Wild and Koidl for charge-exchange collisional plasma [J. Appl. Phys. 69, 2909 (1991)]. It is also found that the ion source temperature plays an important role in determining the ion velocity distribution function.

Cavity quantum electrodynamics in superconducting circuits: Susceptibility at elevated temperatures

We study the properties of superconducting electrical circuits, realizing cavity quantum electrodynamics. In particular we explore the limit of strong coupling, low dissipation, and elevated temperatures relevant for current and future experiments. We concentrate on the cavity susceptibility as it can be directly experimentally addressed, i.e., as the impedance or the reflection coefficient of the cavity. To this end we investigate the dissipative Jaynes-Cummings model in the strong coupling regime at high temperatures. The dynamics is investigated within the Bloch-Redfield formalism. At low temperatures, when only the few lowest levels are occupied, the susceptibility can be presented as a sum of contributions from independent level-to-level transitions. This corresponds to the secular (random phase) approximation in the Bloch-Redfield formalism. At temperatures comparable to and higher than the oscillator frequency, many transitions become important and a multiple-peak structure appears. We show that in this regime the secular approximation breaks down, as soon as the peaks start to overlap. In other words, the susceptibility is no longer a sum of contributions from independent transitions. We treat the dynamics of the system numerically by exact diagonalization of the Hamiltonian of the qubit plus up to 200 states of the oscillator. We compare the results obtained with and without the secular approximation and find a qualitative discrepancy already at moderate temperatures.

Intramolecular Dynamics in the Photofragmentation of Initially Vibrationally Excited CH2Cl2

The intramolecular dynamics of dichloromethane was studied by applying vibrationally mediated photodissociation and photoacoustic spectroscopy. The parent species were initially excited to the second, third, and fourth C-H stretch overtone regions and subsequently photodissociated by ∼235 nm photons that also tagged the ground, Cl( 2 P 3 / 2 ) [Cl], and spin-orbit-excited, Cl( 2 P 1 / 2 ) [Cl*], state photofragments via resonantly enhanced multiphoton ionization. The Cl and Cl* action spectra revealed enhancement of their yield as a result of rovibrational excitation with a Cl*/Cl ratio of about ½. The action and photoacoustic spectra manifested a multiple-peak structure, which in terms of normal- and local-mode models is shown to be related to overtones of C-H stretches or combination bands of C-H stretches and bends. The measured time-of-flight profiles together with the determined Cl*/Cl branching ratios suggest fast dissociation and involvement of upper states of A' and A symmetry, mixing via curve crossing and releasing both Cl and Cl*. The determined Cl*/Cl ratios in photodissociation of vibrationally excited CH 2 Cl 2 are higher than those obtained previously in 193 nm photodissociation of the vibrationless ground state, implying higher nonadiabaticity for the former.

Doping dependence of crossing vortex lattice in Bi 2Sr 2CaCu 2O 8+ y

Local magnetization hysteresis is studied in a highly anisotropic superconductor Bi 2Sr 2CaCu 2O 8+ y under tilted magnetic fields using a micro Hall probe. At moderately high temperatures, we found novel multiple peak structures in the local magnetization hysteresis curves. These peaks appear only in the increasing branch of hysteresis curves when a magnetic field is applied nearly parallel to the superconducting plane. Possible origins of the novel peak structures are discussed on the basis of the evolution of the peaks with temperature.

Structural formation induced by electrode biasing in tokamaks: accessibility to a double-peaked Er shear layer**This paper is dedicated to Professor F Wagner on the occasion of the 60th anniversary of his birth.

Electrode biasing is one of the methods for controlling the radial electric field externally and can induce a transition to an improved confinement state. We have shown theoretically that a solitary Er structure with a single peak is formed selectively by electrode biasing in our previous works. That a multiple-peaked Er structure, which has a wider E × B flow shear region, can exist stably was also derived. In this paper, accessibility to a double-peaked Er structure is demonstrated theoretically by double electrode biasing with an applied voltage ramp-up.

Thermodynamic properties of the periodic Anderson model: X-boson treatment

We study the specific-heat dependence of the periodic Anderson model (PAM) in the limit of $U=\ensuremath{\infty}$ employing the X-boson treatment in two different regimes of the PAM: the heavy fermion Kondo (HF-K) and the local magnetic moment regime (HF-LMM). We obtain a multiple peak structure for the specific heat in agreement with the experimental results as well as the increase of the electronic effective mass at low temperatures associated with the HF-K regime. The entropy per site at low T tends to zero in the HF-K regime, corresponding to a singlet ground state, and it tends to ${k}_{B}\mathrm{ln}2$ in the HF-LMM, corresponding to a doublet ground state at each site. The linear coefficient $\ensuremath{\gamma}{(T)=C}_{v}(T)/T$ of the specific heat qualitatively agrees with the experimental results obtained for different materials in the two regimes considered here.

Propagation effects in spectrally resolved transient four wave mixing measurements on excitons in GaAs multiple quantum wells

We perform spectrally resolved degenerate four wave mixing (DFWM) measurements by resonantly exciting 1s heavy hole excitons in 8 and 17.5 nm wide GaAs multiple quantum wells (MQW) with subpicosecond laser pulses. The signal is detected in a self-diffraction mode in backward geometry. The DFWM spectra reveal a multiple peak structure, evolving into a double peak for positive delays. This may be related to the propagation effects in MQWs due to strong photon–exciton coupling. The different peaks in the DFWM spectra show a dissimilar dependence on pulse excitation intensity, delay and polarization.

Optical, magneto-optical, and magnetic properties of stoichiometric and off-stoichiometricγ′−phaseNi3Alalloys

The optical and magneto-optical properties of two ${\ensuremath{\gamma}}^{\ensuremath{'}}\ensuremath{-}\mathrm{p}\mathrm{h}\mathrm{a}\mathrm{s}\mathrm{e}$${\mathrm{Ni}}_{3}\mathrm{Al}$ alloys $({\mathrm{Ni}}_{0.752}{\mathrm{Al}}_{0.248}$ and ${\mathrm{Ni}}_{0.771}{\mathrm{Al}}_{0.229})$ have been investigated experimentally and theoretically. In the optical-conductivity spectra of the investigated alloys two intense interband absorption features at $\ensuremath{\sim}0.8\mathrm{eV}$ and $\ensuremath{\sim}4.2\mathrm{eV}$ were experimentally observed. The peak at $\ensuremath{\sim}0.8\mathrm{eV}$ was theoretically predicted, but not experimentally confirmed in the previous investigations. The low-energy peak exhibits a multiple-peak structure for ${\mathrm{Ni}}_{0.771}{\mathrm{Al}}_{0.229}$ alloy. It is also theoretically shown that the fine structure of the low-energy absorption features originates from the extra spin ordering due to the appearance of the so-called antistructure Ni atoms and their clusters in the ${\mathrm{Ni}}_{0.771}{\mathrm{Al}}_{0.229}$ alloy, and it is experimentally shown that this fine structure persists up to room temperature. The temperature dependencies of the optical and magneto-optical properties of ${\mathrm{Ni}}_{0.771}{\mathrm{Al}}_{0.229}$ alloy can be ascribed to the presence of magnetic inhomogeneity in the sample. The existence of magnetic inhomogeneity in the alloy is further confirmed by the ac magnetic-susceptibility measurements in which the susceptibility curve exhibits two magnetic transitions, one at 87.5 K and the other at 252 K. The spin ordering (paramagnetic-to-ferromagnetic transition) and Ni enrichment play a key role for the physical properties.

Vibrationally Mediated Photodissociation of Jet-Cooled CH3CF2Cl: A Probe of Energy Flow and Bond Breaking Dynamics

A double resonance scheme was employed to photodissociate jet-cooled CH3CF2Cl in a time-of-flight mass spectrometer. First, the molecule was promoted to the second (3νCH) or third (4νCH) methyl overtone by direct IR excitation. Subsequently, a UV laser beam at ∼235 nm was used to both dissociate the molecule and tag the Cl 2P3/2 [Cl] and Cl 2P1/2 [Cl*] photofragments by (2 + 1) resonantly enhanced multiphoton ionization. The photofragment action spectra revealed multiple peak structures in both overtone regions, attributed to couplings of the C−H stretches and to methyl stretch−deformation Fermi resonances. The cooling of the samples afforded narrowing of the peaks, relative to room temperature photoacoustic spectra, due to the reduced rotational and vibrational congestion, and enabled observation of a new splitting in the high frequency peak of the second overtone. This splitting apparently resulted from a local resonance of the mixed stretch−deformation state with a close lying dark state. The time scales for vibrational energy redistribution in the local resonance and between the mixed stretch−deformations were evaluated. These time scales and the measured Cl*/Cl branching ratios were compared to those of other hydrohalocarbon compounds. The Cl*/Cl ratio was also compared to that of the nearly isoenergetic vibrationless ground state 193 nm photodissociation and found to be different, demonstrating the effect of vibrational pre-excitation on the photodissociation dynamics.

Raman scattering in carbon nanotubes revisited

We explain the origin of the high-energy mode in the first-order Raman spectra of single-walled carbon nanotubes by double-resonant scattering. Following this interpretation, we calculate the multiple-peak structure as found in Raman experiments. The highest peak is above the graphite $\ensuremath{\Gamma}$-point frequency; its amplitude is larger than that of the second peak. We derive positive and negative frequency shifts as a function of excitation energy, which we observe experimentally as well. We predict a difference in frequency and shape of the high-energy mode in Stokes and anti-Stokes scattering.

Multiple-peak structures in energy-loss spectra of swift ions

Generally valid expressions have been developed for the energy-loss spectrum of ions penetrating matter, separated into contributions with different numbers of charge-changing events. The theoretical procedure is based on series expansion of the generalized Bothe–Landau formula in terms of the probability for charge exchange and is particularly suited for analysis of multiple-peak structures. Numerical results are given for 32 MeV He ions penetrating carbon, a system studied experimentally by Ogawa and coworkers. Accurate analytical expressions for the partial spectra of swift ions are found based upon a modification of the Landau approach.

Extrapolation-Directed Crossover Considering Sampling Bias in Real-coded Genetic Algorithm

We propose a new Real-coded GA(RCGA) using the combination of two crossovers, UNDX-m and EDX. The search region of UNDX-m is biased to the inside area that the population of the RCGA covers. Because of this search bias, the GA using UNDX-m causes stagnation of its search if the cost function has a kind of structure, so called, a ridge structure or a multiple-peak structure. In order to overcome this stagnation, we propose a new crossover EDX, whose search is biased toward extrapolative one. Experimental results show that RCGA with EDX can deal with both ridge-structure function whose dimension reaches more than hundreds and multiple-peak function whose optimum resides at the corner of the search area.

Specific heat of the periodic Anderson model: From weak to strong coupling

We study the temperature dependence of the specific heat in the periodic Anderson model as function of the on-site Coulomb interaction, hybridization, and position of the f-electrons energy level. At strong coupling (U=infinity) we use slave bosons, whereas at weak coupling we use a simple Hartree-Fock decomposition. We find that both in the strong and weak coupling limits the specific heat of the system presents a multiple peak structure in a mean field treatment. We believe these features to be related to band-shape effects. The temperature evolution of the low-temperature peak position on the model parameters for the non-half filled non-symmetric case is discussed.

Nonresonant microwave absorption in Bi2212 single crystal: Second peak and microwave power dependence

Nonresonant microwave absorption (NMA) measurements were carried out at liquid-nitrogen temperature on a high quality Bi2212 single crystal, as a function of microwave power in three mutual orientations of crystal ab plane, dc field (Hdc), and microwave magnetic field (Hw). NMA line shapes in Bi2212 crystal are complicated with a narrow peak (P1 peak) located near zero field, followed by a much broader second peak (P2 peak) in the particular orientations. More excitingly, we show that the P2 peak qualitatively evolves as a function of microwave power in the orientation of Hdc ⊥ ab plane, $$H_W | {ab}.$$ plane, and Hdc ⊥ Hw. In this configuration, as the microwave power is progressively increased, the broad P2 peak first gets smeared off and then a multiple peak structure appears, which develops into another narrower second peak (Ps-peak) at high enough microwave powers. In the orientation of $$H_{dc} | {ab}.$$ plane, Hw ⊥ ab plane, and Hdc ⊥ Hw, we report for the first time the appearance and disappearance of a new second peak (P2-like peak) as a function of microwave power.

Large-scale synthesis of ultrafine Si nanoparticles by ball milling

Si nanoparticles have been synthesized by ball-milling of graphite and SiO 2 powders. The solid-phase reaction, C(graphite)+SiO 2→Si+CO 2, was found to be a novel technique for fabrication of ultrafine Si particles. The reduced Si in the powder assembled as nanoparticles with a wide range of diameters. Multiple-peak structures were observed in the photoluminescence spectra of the Si nanoparticles at room temperature. The peak energies were found to coincide with the PL peak pinning energies previously reported in porous Si. Thus, the fine structures of luminescence spectra could be attributed to the size quantization of the Si nanoparticles formed via solid-phase reaction during ball-milling.