Bose-Einstein Model Research Articles

Modelling Working Memory Capacity: Is the Magical Number Four, Seven, or Does it Depend on What You Are Counting?

Limited attentional capacity is essential to working memory. How its limit should be assessed is a debated issue. Five experiments compare Cowan's 4-units and Pascual-Leone's 7-units models of limited working memory capacity, with presentation time and attention to operative schemes as potential explanations of this discrepancy. Experiments 1a-1c used the Compound Stimuli Visual Information (CSVI) task, with long versus brief presentation. Capacity was estimated with the Bose-Einstein model, assuming a different number of attending acts in each condition. Participants' k estimates in both conditions were highly correlated and the means were not different, indicating that the same capacity is assessed in both conditions. Experiments 2 and 3 used the 5000-msec CSVI, and the Visual Array Task (VAT) in two conditions (5000- vs. 120-msec presentation). Capacity in the VAT was estimated with Morey's Bayesian method. Participants' k estimates in both VAT conditions were correlated, but the mean was higher with long presentation, suggesting that the long condition benefits from recoding or chunking. The k estimate in the CSVI correlated with the short VAT and (to a lesser degree in Exp.2) with the long VAT. The mean estimate of k in the CSVI was one unit more than in the short VAT. We conclude that the CSVI and the short VAT tap the same capacity, one unit of which in the short VAT is allocated to an operative scheme; we discuss how Cowan's and Pascual-Leone's views on limited capacity can be reconciled.

Nonmonotonic temperature-dependent bandgap change of CsPbCl3 films induced by optical phonon scattering

The CsPbCl3 perovskite films are successfully grown on quartz substrates by radio frequency (RF)-magnetron sputtering method and their detailed photoluminescence properties are studied over the temperatures from 10 K to 300 K. There exists one near bandgap emission peak (∼410 nm) in the violet region with typical lifetime of few nanoseconds at room temperature. To our surprise, with temperature increasing, this band shows nonmonotonic shift, which is different to the traditional semiconductor like silicon or the same group of perovskites like MAPbI3 or CsPbBr3. The origin of this band and its temperature-dependent shift can be well described with the Bose-Einstein two-oscillator model that takes into account the interaction between electrons and phonons including acoustic phonons and optical phonons. Due to the anisotropic optical properties of the perovskite crystal, the (001)-orientated films have stronger electron phonon coupling and weaker exciton binding energy.

Temperature dependence of the infrared dielectric function and the direct bandgap of InSb from 80 to 725 K

The temperature dependence of the complex pseudodielectric function of bulk InSb (100) near the direct band gap was measured with Fourier-transform infrared ellipsometry between 30 and 500 meV at temperatures from 80 to 725 K in ultrahigh vacuum. Using the Jellison–Sales method for transparent glasses, the thickness of the native oxide was found to be 25±5 Å, assuming a high-frequency dielectric constant of about 3.8 for the native oxide. After this surface correction, the dielectric function was fitted with a Herzinger–Johs parametric semiconductor model to determine the bandgap and with a Drude term to determine the electron concentration and the mobility. We find that the bandgap decreases from 230 meV at 80 K to 185 meV at 300 K, as expected from thermal expansion and a Bose–Einstein model for electron-phonon scattering renormalization of the bandgap. Between 450 and 550 K, the bandgap remains constant near 150 meV and then increases again at even higher temperatures, presumably due to a Burstein–Moss shift resulting from thermally excited electron-hole pairs. The broadening of the direct bandgap increases steadily with temperature. The electron concentration (calculated from the Drude tail at low energies assuming parabolic bands with a constant electron mass of 0.014m0) increases from 2×1016cm−3 at 300 K to 3×1017cm−3 at 700 K, in reasonable agreement with temperature-dependent Hall measurements. The electron mobility was found to decrease from 105cm2/Vs at 450 K to 2×104cm2/Vs at 700 K, also in good agreement with Hall effect results. We describe a theoretical model that might be used to explain these experimental results.

Terahertz tyrosine modes

We have measured the terahertz spectrum of pure l-tyrosine at nineteen temperatures in the range 6K to 300K using a synchrotron as the source of radiation. By fitting the temperature dependence of the observed modes with a Bose–Einstein model, we determine unequivocal low-frequency modes of l-tyrosine at absolute zero temperature occur at 1.02 ± 0.01, 1.61 ± 0.01, 1.97 ± 0.01, and 2.19 ± 0.01THz. This determination is consistent with the more reliable of the earlier measurements. We conclude that many of the recently reported features in the terahertz spectrum of l-tyrosine are experimental artefacts.

Tailoring the Electron-Phonon Interaction in Au25(SR)18 Nanoclusters via Ligand Engineering and Insight into Luminescence.

Understanding the electron-phonon interaction in Au nanoclusters (NCs) is essential for enhancing and tuning their photoluminescence (PL) properties. Among all the methods, ligand engineering is the most straightforward and facile one to design Au NCs with the desired PL properties. However, a systematic understanding of the ligand effects toward electron-phonon interactions in Au NCs is still missing. Herein, we synthesized four Au25(SR)18- NCs protected by different -SR ligands and carefully examined their temperature-dependent band-gap renormalization behavior. Data analysis by a Bose-Einstein two-oscillator model revealed a suppression of high-frequency optical phonons in aromatic-ligand-protected Au25 NCs. Meanwhile, a low-frequency breathing mode and a quadrupolar mode are attributed as the main contributors to the phonon-assisted nonradiative relaxation pathway in aromatic-ligand-protected Au25 NCs, which is in contrast with non-aromatic-ligand-protected Au25 NCs, in which tangential and radial modes play the key roles. The PL measurements of the four Au25 NCs showed that the suppression of optical phonons led to higher quantum yields in aromatic-ligand-protected Au25 NCs. Cryogenic PL measurements provide insights into the nonradiative energy relaxation, which should be further investigated for a full understanding of the PL mechanism in Au25 NCs.

High-quality, temperature-dependent terahertz spectroscopy of single crystalline L-alanine: Experiment and density-functional theory.

For the first time, the terahertz transmittance spectra of l-alanine have been measured using a single crystal. Measurements were obtained over a large temperature range (12-300K) and revealed 18 absorptions between 20 and 250 cm-1. These modes were sharp and symmetric, a feature of single crystals and low temperatures. The spectra were directly compared to those of a powdered pellet sample. Raman spectroscopy and x-ray diffraction were used to confirm the sample's structure and purity. With increasing temperature, all modes exhibit spectral redshift, well described by a Bose-Einstein model, indicating the phonon origin of the absorptions. The exceptions are the 91 and 128 cm-1 modes. The former blueshifts. The latter initially blueshifts but transitions to redshifting. Both behaviors are anomalous. Density-functional theory modeling helped assign all the observed modes.

Network edge entropy decomposition with spin statistics

In a previous study, we have explored how to decompose the global entropy of a network into edge components using a graph-spectral decomposition technique. Here, we develop this work in more depth to understand the role of edge entropy as an efficient and effective tool in analysing network structure. We use the edge entropy distribution as a network feature or characterisation and combine it with linear discriminant analysis to distinguish different types of network model and structure. Interpreting the normalised Laplacian matrix as the network Hamiltonian (or energy) operator, the network is assumed to be in thermodynamic equilibrium with a heat bath where the energy states correspond to the normalised Laplacian eigenvalues. To model the way in which particles occupy the energy states, we explore the use of three different spin-dependent statistical models to determine the thermodynamic entropy of the network. These are a) the classical spinless Maxwell-Boltzmann distribution, and two models based on quantum mechanical spin-statistics, namely b) the Bose-Einstein model for particles with integer spin, and c) the Fermi-Dirac model for particles with half-integer spin. By using the spectral decomposition of the Laplacian, we illustrate how to project out the edge-entropy components from the global network entropy. In this way, the detailed distribution of entropy across the edges of a network can be constructed. Compared to our previous study of the von Neumann edge entropy, where the edge entropy just depends on the degrees of the nodes forming an edge, in the case of the new statistical mechanical model, there is a more subtle dependence of the edge entropy on the structure of a network. We illustrate how this new edge entropy distribution can be used to more effectively identify variations in network structure, in particular for edges incorporating nodes of large degree. Numerical experiments on synthetic and real-world data-sets are presented to evaluate the qualitative and quantitative differences in performance.

Temperature-dependent terahertz spectroscopy of l-phenylalanine

Undiluted l-phenylalanine has been cooled to 6K and its transmission spectrum obtained under terahertz radiation from a synchrotron source. Three distinct absorption bands are evident: at 1.37, 2.14, and 2.32THz. Each of these tracks to lower frequency (“redshifts”) as the temperature is increased from 6 to 250K. The observed shifts are in the range of 0.1–0.2THz. The form of the temperature dependence is well accounted for by a Bose–Einstein model, from which the zero-temperature frequency of each mode and the characteristic temperature of the associated phonon bath may be estimated. At 6K a fourth band is evident, at 2.65THz. However, the depth of this, touching the noise floor, coupled with the increasing opacity of the sample with temperature for frequencies beyond 2.5THz, makes it difficult to track. The frequencies of all four modes are in good accord with and thus confirm a previous calculation.

Temperature dependence of the optical absorption edge of doped gallium arsenide

The temperature dependences of the optical absorption edges of Zn doped GaAs semiconductor crystals have been measured from 300 to 560 K. The temperature dependence of the optical absorption in the Urbach edges is adequately reproduced by a Bose-Einstein model. Analysis of experimental results gave us the opportunity to offer an explicit function of two arguments (photon energy and temperature) for the absorption coefficient of doped crystals in the Urbach edge region.

Photoluminescence investigation of the properties of GaAsSb in the dilute Sb regime

GaAsSb epitaxial layers are grown using liquid-phase epitaxy (LPE) technique over oriented GaAs substrates. The layers contain up to 1.84% Sb, as estimated from high-resolution X-ray diffraction (HRXRD) measurements. Detailed photoluminescence (PL) studies are made on the as-grown and high-temperature-annealed layers to reveal various electronic transitions in the materials. Excitation power-dependent PL measurements are done to investigate the origin of each of the transitions. The bandgap energy, obtained from PL, shows a reduction of approximately 17 meV per at% increase in Sb content, which agrees well with the bandgap reduction, calculated with the band anticrossing (BAC) model. Analysis of the temperature-dependent PL data, using Bose–Einstein model, indicates that both the electron–phonon interaction and the average phonon temperatures strongly depend on the Sb content in GaAsSb.

Investigation of temperature dependence of Raman and photoluminescence analysis of YBa2Cu3O7 (YBCO) doped with SiO2 nanoparticles

We report the effect of SiO2 nanoparticles (12 nm) in YBa2Cu3O7 (YBCO) matrix. The samples YBCO and SiO2+YBCO are fabricated by a conventional solid-state reaction method, in ambiance conditions. We analyze these samples using X-ray diffraction (XRD), resonant Raman, environmental scanning electron microscopy (ESEM), and Photoluminescence (PL) as a function of temperature in the range from 77 to 837 K. The XRD confirm that the doped YBCO still displays a perovskite structure with the orthorhombic Pmmm phase. The Rietveld refinement confirms that SiO2 nanoparticles induce not only a strong effect on the oxygen?s O(5) and O(8) positions but also an elongation of the unit cell along the c-axis. The PL intensity of pure YBCO is more intense than the doped one that is mainly composed of two bands located at 2.4 eV and 1.88 eV. We simulate the PL intensity with temperature using the Bose-Einstein model with two activation energies corresponding to some specific vibration mode energies. The simulation reveals that the exchange energy between different levels in pure and doped YBCO is conducted by only two vibrations modes that are strongly linked to the oxygen and copper atoms in the YBCO matrix. We determine the evolution of Raman mode frequencies at 340 and 500 cm?1 with temperature using the Lorentzian function at q = 0 of the Balkanski model.

Near-infrared refractive index of synthetic single crystal and polycrystalline diamonds at high temperatures

We measured the refractive index n(T) and thermo-optical coefficient β(T) = (1/n)(dn/dT) of high quality synthetic diamonds from room temperature to high temperatures, up to 1520 K, in near-infrared spectral range at wavelength 1.56 μm, using a low-coherence interferometry. A type IIa single crystal diamond produced by high pressure–high temperature technique and a transparent polycrystalline diamond grown by chemical vapor deposition were tested and revealed a very close n(T) behavior, with n = 2.384 ± 0.001 at T = 300 K, monotonically increasing to 2.428 at 1520 K. The n(T) data corrected to thermal expansion of diamond are well fitted with 3rd order polynomials, and alternatively, with the Bose-Einstein model with an effective oscillator frequency of 970 cm−1. Almost linear n(T) dependence is observed above 800 K. The thermo-optical coefficient is found to increase monotonically from (0.6 ± 0.1) × 10−5 K−1 (300 K) to (2.0 ± 0.1) × 10−5 K−1 (1300 K) with a tendency to saturation at >1200 K. These β(T) values are an order of magnitude lower than those known for Si, GaAs, and InP. The obtained results significantly extend the temperature range, where the refractive index of diamond was previously measured.

Temperature-dependent optical spectra of single-crystal (CH3NH3)PbBr3 cleaved in ultrahigh vacuum

We measure temperature-dependent one-photon and two-photon induced photoluminescence from (${\mathrm{CH}}_{3}{\mathrm{NH}}_{3}$)${\mathrm{PbBr}}_{3}$ single crystals cleaved in ultrahigh vacuum. An approach is presented to extract absorption spectra from a comparison of both measurements. Cleaved crystals exhibit broad photoluminescence spectra. We identify the direct optical band gap of 2.31 eV. Below 200 K, the band gap increases with temperature, and it decreases at elevated temperature, as described by the Bose-Einstein model. An excitonic transition is found 22 meV below the band gap at temperatures $<200$ K. Defect emission occurs at photon energies $<2.16$ eV. In addition, we observe a transition at 2.25 eV (2.22 eV) in the orthorhombic (tetragonal and cubic) phase. Below 200 K, the associated exciton binding energy is also 22 meV, and the transition redshifts at higher temperature. The binding energy of the exciton related to the direct band gap, in contrast, decreases in the cubic phase. High-energy emission from free carriers is observed with higher intensity than reported in earlier studies. It disappears after exposing the crystals to air.

Growth and coalescence control of inclined c-axis polar and semipolar GaN multilayer structures grown on Si(111), Si(112), and Si(115) by metalorganic vapor phase epitaxy

Herein, silicon substrates in alternative orientations from the commonly used Si(111) were used to enable the growth of polar and semipolar GaN-based structures by the metalorganic vapor phase epitaxy method. Specifically, Si(112) and Si(115) substrates were used for the epitaxial growth of nitride multilayer structures, while the same layer schemes were also deposited on Si(111) for comparison purposes. Multiple approaches were studied to examine the influence of the seed layers and the growth process conditions upon the final properties of the GaN/Si(11x) templates. Scanning electron microscope images were acquired to examine the topography of the deposited samples. It was observed that the substrate orientation and the process conditions allow control to produce an isolated GaN block growth or a coalesced layer growth, resulting in inclined c-axis GaN structures under various forms. The angles of the GaN c-axis inclination were determined by x-ray diffraction measurements and compared with the results obtained from the analysis of the atomic force microscope (AFM) images. The AFM image analysis method to determine the structure tilt was found to be a viable method to estimate the c-axis inclination angles of the isolated blocks and the not-fully coalesced layers. The quality of the grown samples was characterized by the photoluminescence method conducted at a wide range of temperatures from 77 to 297 K, and was correlated with the sample degree of coalescence. Using the free-excitation peak positions plotted as a function of temperature, analytical Bose-Einstein model parameters were fitted to obtain further information about the grown structures.

Experimental and modelling study of InGaBiAs/InP alloys with up to 5.8% Bi, and with Δso > Eg

Temperature dependent photo-modulated reflectance is used to measure the band gap Eg and spin–orbit splitting energy Δso in dilute-Bi In0.53Ga0.47As1-xBix/InP for 1.2% ≤ x ≤ 5.8%. At room temperature, Eg decreases with increasing Bi from 0.65 to 0.47 eV (∼2.6 μm), while Δso increases from 0.42 to 0.62 eV, leading to a crossover between Eg and Δso around 3.8% Bi. The 5.8% Bi sample is the first example of this alloy where Δso > Eg has been confirmed at all temperatures. The condition Δso > Eg is important for suppressing hot-hole-producing non-radiative Auger recombination and inter-valence band absorption losses and so holds promise for the development of mid-infra-red devices based on this material system. The measured variations of Eg and Δso as a function of Bi content at 300 K are compared to those calculated using a 12-band k.p Hamiltonian which includes valence band anti-crossing effects. The Eg results as a function of temperature are fitted with the Bose–Einstein model. We also look for evidence to support the prediction that Eg in dilute bismides may show a reduced temperature sensitivity, but find no clear indication of that.

Temperature dependence of the optical properties of Ba0.75Sr0.25TiO3 thin films

Optical properties of Ba0.75Sr0.25TiO3 (BST(75/25)) ferroelectric thin film have been investigated by spectroscopic ellipsometry in a broad temperature interval from 10 to 300K. The polycrystalline perovskite-phase BST films were prepared by pulsed laser deposition technique. The complex dielectric functions and optical parameters of the films were determined in the 1.5–5.5eV spectral range. The spectra can be divided into two distinctive regions according to the magnitude of absorption coefficient separated by a band gap. An apparent reduction of the band gap was observed on increasing temperature. This can be ascribed to the renormalization of electronic band structure due to the electron–phonon interaction, which follows the Bose–Einstein model.

Fabrication and temperature-dependent band gap shrinkage of α-phase Bi2O3thin films grown by atomic layer deposition method

α-Bi 2 O 3 thin films were deposited on different substrates by atomic layer deposition method. The results of X-ray diffraction, high-resolution transmission electron microscopy and X-ray photoelectron spectroscope correspond to α-Bi 2 O 3 . The Fourier transform infrared spectroscopy analyses indicate that the reaction is rather complete during the deposition. Optical properties of the films have been investigated using ultraviolet-infrared transmittance spectra in the temperature range of 8–300 K. It is found that the band gap E g decreases from 3.12 to 3.03 eV with the temperature. The parameters α B and Θ B of the Bose-Einstein model are 69.3 meV and 293.9 K, respectively. The band narrowing coefficient d E g /d T is −0.435 meV/K at room temperature. The present results can be considerable for future application of Bi 2 O 3 -based electro-optic and wide temperature range optoelectronic devices.

The Size of the Largest Part of Random Weighted Partitions of Large Integers

We consider partitions of the positive integernwhose parts satisfy the following condition. For a given sequence of non-negative numbers {bk}k≥1, a part of sizekappears in exactlybkpossible types. Assuming that a weighted partition is selected uniformly at random from the set of all such partitions, we study the asymptotic behaviour of the largest partXn. LetD(s)=∑k=1∞bkk−s,s=σ+iy, be the Dirichlet generating series of the weightsbk. Under certain fairly general assumptions, Meinardus (1954) obtained the asymptotic of the total number of such partitions asn→∞. Using the Meinardus scheme of conditions, we prove thatXn, appropriately normalized, converges weakly to a random variable having Gumbel distribution (i.e., its distribution function equalse−e−t, −∞<t<∞). This limit theorem extends some known results on particular types of partitions and on the Bose–Einstein model of ideal gas.

Nanostructured CdSe Films in Low Size-Quantization Regime: Temperature Dependence of the Band Gap Energy and Sub-Band Gap Absorption Tails

Temperature dependence of the band gap energy and sub-band gap absorption tails in 3D assemblies of close packed weakly quantized CdSe quantum dots deposited as thin films was studied. The range from cryogenic temperatures (∼10 K) up to 340 K was covered. Excitonic absorption peaks were not observed even at temperatures as low as 11 K, which was attributed to the finite particle size distribution and interdot electronic coupling effects. The temperature coefficient of the band gap energy of the nanostructured films of 9.4 × 10–4 eV K–1 is higher by a factor of 1.35 than the corresponding value for the bulk CdSe specimen. As compared to the case of films constituted of strongly quantized ZnSe QDs, where the factor αnanocrystal/αbulk was found to be 1.82 (Pejova, B.; Abay, B.; Bineva, I. J. Phys. Chem. C 2011, 115, 37), the present findings imply that this ratio increases upon enhancement of size quantization effects in semiconductor nanocrystals. Analysis of the temperature-dependent optical absorption data within the Bose-Einstein model implies that no phonon confinement effects influence the phonon spectrum in the presently studied material due to the very small size-quantization effects. This situation is opposite to what we have recently found in the case of 3D arrays of strongly quantized ZnSe films. The characteristic Einstein temperature of the presently studied material corresponds to phonon frequency of about 220 cm–1, in excellent agreement with the LO mode frequency of bulk CdSe (210–214 cm–1). It is demonstrated that the Urbach rule is valid in the presently studied nanostructured material in low size-quantization regime. Urbach energies are several times higher than the values characteristic for macrocrystalline materials, due to the relatively high degree of inherent structural disorder in the studied QD solids. At the same time, however, these values are approximately three times smaller than those reported for strongly quantized ZnSe films in our previous study. The dynamical (temperature-dependent) term accounts for only about 22% of the overall Urbach energy values, though this value is higher than the corresponding ratio in the case of strongly quantized ZnSe films.

A study of energy band gap versus temperature for Cu 2ZnSnS 4 thin films

The temperature dependent band gap energy of Cu 2ZnSnS 4 thin film was studied in the temperature range of 77–410 K. Various relevant parameters, which explain the temperature variation of the fundamental band gap, have been calculated using empirical and semi-empirical models. Amongst the models evaluated, the Varshni and Pässler models show the best agreement with experimental data in the middle temperature range. However, the Bose–Einstein model fits reasonably well over the entire temperature range evaluated. The calculated fitting parameters are in good agreement with the estimated value of the Debye temperature calculated using the Madelung–Einstein approximation and the Hailing method.