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Analytical diagonalisation of the Hamiltonian of the quantum Rabi model in the Coulomb gauge 库仑规范中量子拉比模型哈密顿量的解析对角化
Pub Date : 2022-01-27 DOI: 10.33581/2520-2243-2022-1-44-51
A. Leonau, I. Feranchuk
In the present paper we investigate the approximate analytical diagonalisation of the Hamiltonian of the quantum Rabi model written in the Coulomb gauge and taking into account the gauge invariance of the system. It is shown that the Hamiltonian of the model can be diagonalised with high accuracy on the basis of a unitary operator of the gauge transformation utilising a simple basis set of state vectors. It is essential that the obtained approximate expressions do not depend on the variational parameters and are valid within the whole range of the parameter values. The zeroth-order approximation and uniformly available approximation are derived for the eigenstates of the system, and their comparison with the results of the numerical simulation is elaborated. The second-order correction to the zeroth-order approximation is deduced and its contribution to the energy of the system is estimated. The obtained results could be useful for description of the evolution of the quantum Rabi model as well as for investigation of systems of two-level atoms in the resonant quantum field.
在考虑系统规范不变性的情况下,研究了用库仑规范表示的量子拉比模型哈密顿量的近似解析对角化。利用一个简单的状态向量基集,在规范变换的酉算子的基础上,可以高精度地对角化模型的哈密顿量。重要的是,所得到的近似表达式不依赖于变分参数,并且在参数值的整个范围内有效。推导了系统特征态的零阶近似和一致可用近似,并与数值模拟结果进行了比较。推导了零阶近似的二阶修正,并估计了其对系统能量的贡献。所得结果可用于描述量子Rabi模型的演化以及共振量子场中二能级原子系统的研究。
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引用次数: 0
Electroluminescence of SiO2 films grown on Si by thermal oxidation and plasma-enhanced chemical vapor deposition 用热氧化和等离子体增强化学气相沉积在Si上生长SiO2薄膜的电致发光
Pub Date : 2021-10-20 DOI: 10.33581/2520-2243-2021-3-26-31
I. Romanov, N. Kovalchuk, L. Vlasukova, I. Parkhomenko, V. Saladukha, U. Pilipenka, D. V. Shestovski, S. Demidovich
Emission of the silicon oxide films grown on Si by wet thermal oxidation at 900 °С and by plasma-enhanced chemical vapor deposition from the SiH4 + N2O mixture at 350 °С has been compared using electroluminescence. The electroluminescence spectra were recorded in electrolyte – insulator – semiconductor system. The intense band in the red range with a maximum at 1.9 eV dominates the electroluminescence spectrum of the thermal oxide film. It was concluded that this band is related with the existence of silanol groups (Si — OH) in the oxide matrix. Multiband emission in the UV range is observed in the electroluminescence spectrum of the oxide film formed by plasma-enhanced chemical vapor deposition. Additional investigations using IR and RS spectroscopy revealed that observed spectrum modulation is of an oscillatory nature and is not the result of interference. Presumably, the luminescence in the UV region is due to the presence of oxygen deficiency centers containing bonds with hydrogen atoms.
用电致发光法比较了900°С温度下湿式热氧化法和350°С温度下等离子体增强化学气相沉积法在Si表面生长的氧化硅薄膜的发射特性。记录了电解液-绝缘体-半导体体系的电致发光光谱。热氧化膜的电致发光光谱以1.9 eV为最大值的红色强带为主。结果表明,该条带与氧化基质中硅烷醇基团(Si - OH)的存在有关。在等离子体增强化学气相沉积形成的氧化膜的电致发光光谱中观察到紫外范围内的多波段发射。利用红外光谱和RS光谱的进一步研究表明,观察到的光谱调制具有振荡性质,而不是干扰的结果。据推测,紫外区的发光是由于含有氢原子键的缺氧中心的存在。
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引用次数: 0
Formation of epitaxial InSb films on semi-insulating GaAs(100) by explosive thermal evaporation: their structure and electrical properties 半绝缘GaAs(100)外延InSb薄膜的爆炸热蒸发制备及其结构和电学性能
Pub Date : 2021-10-20 DOI: 10.33581/2520-2243-2021-3-20-25
E. Kolesnikova, V. Uglov, A. K. Kuleshov, D. P. Rusalsky
In the present work, the influence of the deposition temperature of InSb films on semi-insulating GaAs(100) on their phase composition, crystal perfection and electrical properties was investigated. The InSb films of various extent of crystal perfection are formed by means of explosive thermal deposition of InSb on semi-insulating GaAs(100) substrates in the temperature range of 375–460 °C. X-ray diffraction analysis established that the films are heteroepitaxial. It is shown that an increase in the deposition temperature of InSb films from 375 to 460 °C leads to a change in the film surface roughness (Ra) from 3.4 to 19.1 nm. The Hall voltage sensitivity to the magnetic field of InSb films varies in the range of 500–1500 mV/T. The electron concentration (n) and mobility (μ) changes in the range of 2 ⋅ 1016 – 6 ⋅ 1016 cm–3, 10 ⋅ 103 – 21 ⋅ 103 cm2/(V ⋅ s). The formed InSb films on semi-insulating GaAs(100) substrate are of practical interest for the manufacture of highly sensitive miniature Hall devices.
本文研究了半绝缘GaAs(100)上InSb薄膜沉积温度对其相组成、晶体完善度和电学性能的影响。在375 ~ 460℃的温度范围内,用爆炸热沉积法在半绝缘的GaAs(100)衬底上沉积InSb,形成了不同晶体完美程度的InSb薄膜。x射线衍射分析证实薄膜是异质外延的。结果表明,当InSb薄膜的沉积温度从375℃升高到460℃时,薄膜表面粗糙度(Ra)从3.4 nm升高到19.1 nm。InSb薄膜对磁场的霍尔电压灵敏度在500 ~ 1500mv /T范围内变化。电子浓度(n)和迁移率(μ)分别在2⋅1016 ~ 6⋅1016 cm - 3,10⋅103 ~ 21⋅103 cm2/(V·s)范围内变化。在半绝缘GaAs(100)衬底上形成的InSb薄膜对制备高灵敏度微型霍尔器件具有实际意义。
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引用次数: 0
Fractional differential model of the spread of COVID-19 COVID-19传播的分数阶差分模型
Pub Date : 2021-10-13 DOI: 10.33581/2520-2243-2021-3-40-48
T. A. Efimova, I. Timoshchenko, N. Abrashina-Zhadaeva
This paper studies a mathematical model of the spread of the COVID-19 pandemic based on ordinary differential equations with a time-fractional derivative. The model takes into account the susceptibility of the population to infection, the incubation period, the number of contacts between healthy and sick people, number of infected, recovered and deceased people in a certain period. To test the model a comparison was made with models obtained with a time derivative of integer orders, with known data for the Italian region of Lombardy. The results suggest that the use of a mathematical model based on a time-fractional derivative with the help of data such as susceptibility of the population to infection, incubation period, number of infected, recovered and deceased people in a certain period, ultimately can help health authorities to develop effective measures against the pandemic. This is especially possible if we expand the model and consider partial differential equations describing the convection-diffusion process, taking into account the prediction of the geographical distribution of the most important medical resources.
本文研究了基于时间分数阶微分方程的新冠肺炎大流行传播数学模型。该模型考虑了人群对感染的易感性、潜伏期、健康人与病人之间的接触次数、一定时期内感染、康复和死亡人数。为了验证该模型,我们将其与意大利伦巴第地区已知数据与整数阶时间导数得到的模型进行了比较。结果表明,利用基于时间分数导数的数学模型,结合人群对感染的易感性、潜伏期、一定时期内感染、康复和死亡人数等数据,最终可以帮助卫生部门制定有效的应对措施。如果我们扩展模型并考虑描述对流扩散过程的偏微分方程,并考虑到最重要医疗资源的地理分布预测,这尤其可能。
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引用次数: 1
PWO based electromagnetic calorimetry to operate at a low temperature 基于ppo的电磁量热法在低温下工作
Pub Date : 2021-10-13 DOI: 10.33581/2520-2243-2021-3-67-73
P. Orsich, K. Brinkmann, V. Dormenev, M. Korzhik, V. Mechinsky, D. Kozlov, H. Zaunick
The degradation of the optical transmittance under ionising radiation of the scintillation crystal in the scintillation spectral range leads to the losses of the light output, which results in the deterioration of the energy resolution and limits the operation time of the calorimeter made of the scintillator. This effect is especially prominent for calorimeters operating at a low temperature. The use of a lead tungstate scintillation crystal PbWO4 in calorimetry at a low temperature in the range from –20 to –45 °C provides a threefold increase in its scintillation yield, which causes a significant improvement in the energy resolution in the range up to 10 MeV. Keep on this feature is critically important for hadron spectroscopy. However, as the temperature of the PbWO4 crystal is lowered, the rate of spontaneous relaxation of colour centers created under ionising radiation significantly slows down, which shifts the dynamic level of the induced absorption towards a higher value under long-term irradiation of high-energy physics experiments. A comparison is made of the spontaneous relaxation of induced absorption in the spectral region of scintillations with stimulated relaxation upon irradiation of samples by infrared photons of different wavelengths. It is shown that the relaxation of colour centers can be accelerated up to one thousand times. Thus, recovery stimulation allows fast and efficient in situ recovery of the crystal optical transmittance either at beam-off periods or online at data acquisition. The application can substantially improve or extend the running period of the PWO based calorimeters at low temperatures by keeping the radiation damage at a tolerable level.
在闪烁光谱范围内,闪烁晶体在电离辐射下的透光率下降,导致光输出的损失,从而导致能量分辨率的下降,限制了由闪烁体制成的量热计的工作时间。这种效应对于在低温下工作的量热计尤其突出。使用钨酸铅闪烁晶体PbWO4在-20至-45°C的低温量热法中,其闪烁产额增加了三倍,这使得能量分辨率显著提高,最高可达10 MeV。保持这一特征对强子光谱学至关重要。然而,随着PbWO4晶体温度的降低,电离辐射下产生的色心自发弛豫速率明显减慢,这使得高能物理实验长期辐照下诱导吸收的动态水平向更高的值移动。用不同波长的红外光子照射样品,比较了闪烁光谱区诱导吸收的自发弛豫和受激弛豫。结果表明,色心的松弛可以加速一千倍。因此,恢复刺激允许在波束关闭期间或在线数据采集时快速有效地原位恢复晶体光学透射率。该应用程序可以通过将辐射损伤保持在可容忍的水平,大大改善或延长基于ppo的量热计在低温下的运行周期。
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引用次数: 0
Outlook for nuclear physics research in Belarus 白俄罗斯核物理研究展望
Pub Date : 2021-10-11 DOI: 10.33581/2520-2243-2021-3-62-66
M. Korzhik
The future nuclear physics research capabilities for scientists from Belarus are discussed. The following branches for the activity: megascience class research platforms created in Russia and the European Union, a new generation of ionizing radiation sources, use of the world nuclear science network for short-term research and, monitoring of nuclear power plants are debated. The purposes of nuclear physics research are suggested to be a balanced combining of the further penetration deep into the matter, to clarify its status and time evolution and, the routine activity associated with clarifying the details of the world, for which sufficiently well-developed models have already been created. Further, the goals of nuclear physics research are specified. They include preventing the loss of knowledge in the field of nuclear physics; conservation of the acceptable qualification and its reproducibility, maintaining the appropriate level of the engineering corps for the perception of the latest knowledge. This article is based on the author’s personal experience in participating in projects of high scientific significance. The route of considering the areas of application of nuclear physics scientists’ efforts is formed according to the principle of maximum return from the highly qualified personnel (PhDs and doctors of science). Ain importance of training undergraduates and graduate students for a scientific career is underlined. Finally, a need to maintain a high level of knowledge in the branch for the expertise upon the request of the government to secure and develop the country is pointed out.
讨论了白俄罗斯科学家未来的核物理研究能力。讨论的内容包括:在俄罗斯和欧盟建立的超级科学级研究平台、新一代电离辐射源、利用世界核科学网络进行短期研究以及监测核电站。建议核物理学研究的目的是进一步深入物质,澄清其状态和时间演变,以及与澄清世界细节有关的日常活动的平衡结合,为此已经创建了足够完善的模型。进一步,明确了核物理学研究的目标。它们包括防止核物理领域知识的流失;保持可接受的资格及其可重复性,保持工程队的适当水平,以感知最新的知识。这篇文章是基于作者参与高科学意义项目的个人经验。考虑核物理科学家努力的应用领域的路线是根据高素质人才(博士和科学博士)最大回报的原则形成的。强调了培养本科生和研究生从事科学事业的重要性。最后,根据国家安全与发展的要求,指出了在该部门保持高水平的专业知识的必要性。
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引用次数: 1
Peculiarity of the low temperature magnetoresistive effect in the Corbino disk with magnetic ordering 具有磁有序的科比诺盘低温磁阻效应的特性
Pub Date : 2021-10-08 DOI: 10.33581/2520-2243-2021-3-12-19
V. I. Halauchuk, Michail G. Lukashevich
The transverse magnetoresistance (MR) hysteresis loops of a magnetically ordered Corbino disk have been studied in the temperature range 300–2 K in an external magnetic field with induction up to 1 T oriented in the plane of the disk (ϕ = 0°) and perpendicularly to its plane (ϕ = 90°). The Corbino disk is made of a thin permalloy film obtained on an insulating sitall substrate by ion-beam sputtering. Independently of the temperature and measurement geometry, the field dependences of MR in the range of weak magnetic fields up to the magnetisation saturation exhibit sharp peaks of the negative MR caused by the domain walls motion during the magnetisation reversal of the sample. The position of the peak in the magnetic field (Bp) is determined by the temperature as well as the angle between magnetic field direction and the disk plane. It was found that a temperature change in the range of T = 300–2 K leads to a change in its position in the range of 0.2–6.0 mT and 8–22 mT at ϕ = 0° and ϕ = 90°, respectively. The magnetic field direction reorientation from in-plane to out-of-pane at T = 2 K leads to the Bp change from 6 to 22 mT. In the range of strong magnetic fields above the magnetization saturation field at ϕ = 0° the positive MR component decreases with induction and has a linear non-saturable dependence down to T ≈ 40–50 K due to the magnon MR component dominance. The complete freezing of magnons at T = 2 K leads to the absence of high-field magnetoresistive effect. At ϕ = 90° in weak fields, the MR changes its sign from positive to negative due to the anisotropic MR component dominance because of the disk magnetisation reorientation perpendicular to the current lines. In a strong field it changes the slope due to the saturation of negative anisotropic MR component, as well as possible additional contribution of the positive geometric Lorentzian MR.
在300-2 K的温度范围内,研究了磁有序Corbino磁盘的横向磁阻(MR)磁滞回线,其感应强度高达1 T,取向于磁盘平面(ϕ = 0°)并垂直于其平面(ϕ = 90°)。Corbino盘是由离子束溅射在绝缘基板上获得的薄坡莫合金薄膜制成的。独立于温度和测量几何形状,在弱磁场范围内,直到磁化饱和,磁流变率的场依赖性表现出由样品磁化反转期间畴壁运动引起的负磁流变率的尖锐峰值。峰值在磁场中的位置(Bp)由温度以及磁场方向与磁盘平面的夹角决定。在φ = 0°和φ = 90°处,温度在T = 300-2 K范围内的变化导致其位置分别在0.2-6.0 mT和8-22 mT范围内发生变化。在T = 2 K处,磁场方向从面内转向面外,导致Bp从6 mT变化到22 mT。在φ = 0°磁化饱和场以上的强磁场范围内,由于磁振子MR分量占主导地位,正MR分量随感应而减小,并且线性不饱和依赖于T≈40-50 K。在T = 2k时,磁振子完全冻结,导致没有高场磁阻效应。在弱场中ϕ = 90°时,由于磁盘磁化重新定向垂直于电流线,磁振子的各向异性磁振子分量占主导地位,磁振子的符号从正变为负。在强磁场中,由于负各向异性磁流变分量的饱和,以及正几何洛伦兹磁流变分量可能的额外贡献,使得斜率发生变化。
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引用次数: 0
Formation of holographic diffraction gratings in thin films of chalcogenide glassy semiconductors 硫系玻璃半导体薄膜全息衍射光栅的形成
Pub Date : 2021-10-05 DOI: 10.33581/2520-2243-2021-3-4-11
Andrian M. Nastas, Mikhail S. Iovu, I. Agishev, Ilya V. Gavrusenok, E. Melnikova, I. Stashkevitch, A. Tolstik
The paper presents a study of the formation of holographic diffraction gratings in thin films of chalcogenide glassy semiconductors. The recording process of holographic gratings at the argon-laser radiation wave length 488 nm and the process of chemical etching that enables the formation of а relief holographic grating are analysed. The optimum conditions for the formation of diffraction gratings in films of arsenic sulfide As2S3 are defined. It is shown that at the 488 nm wave length of an argon laser the optimum exposure comes to ∼5–8 J/cm2. At the recording stage a quasi-phase (relief-phase) grating is formed, with the diffraction efficiency on the order of a few per cent. Etching of the exposed sample with a solution of NaOH alkali in deionised water and isopropanol makes it possible to increase considerably the relief depth and to improve the diffraction efficiency of a thin diffraction grating approximately up to 20 % for the red spectral region, and to approach the maximal value ∼34 % for the near infra-red region. The results of the study considered look promising for the creation of relief holographic gratings which are essential in present-day optical instrument building (production of spectral devices, holographic sights, and the like).
本文研究了硫系玻璃半导体薄膜中全息衍射光栅的形成。分析了氩激光辐射波长488nm全息光栅的记录过程和形成浮雕全息光栅的化学刻蚀过程。确定了在硫化砷As2S3薄膜中形成衍射光栅的最佳条件。结果表明,在488 nm波长下,氩激光的最佳曝光量为~ 5-8 J/cm2。在录音阶段quasi-phase(救援阶段)光栅形成,与衍射效率的几个百分点。蚀刻的暴露与氢氧化钠碱溶液样品在去离子水和异丙醇可以大大增加救援深度和提高一层薄薄的衍射光栅的衍射效率约20%红色光谱区,和接近最大价值∼34%近红外区。该研究的结果被认为对浮雕全息光栅的创造很有希望,这在当今的光学仪器制造(光谱设备、全息瞄准具等的生产)中是必不可少的。
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引用次数: 0
Improving the efficiency of an industrial silicon solar cell by doping with nickel 用镍掺杂提高工业硅太阳能电池的效率
Pub Date : 2021-09-29 DOI: 10.33581/2520-2243-2021-3-4-12
M. Bakhadirkhanov, Z. Kenzhaev, B. Ismaylov, V. Odzhaev, U. Prasalovich, Yu.N. Yankovski
The possibility of adjusting the operational parameters of industrial solar cells produced by the company Suniva based on monocrystalline silicon by means of additional diffusion doping with nickel in the temperature range 700–1200 °C has been investigated. It is shown that the optimal temperature of nickel diffusion is Tdiff = 800–850 °C. In this case the value of the maximum power Pmax increases by 20–28 % in relation to the parameters of the original industrial photocell. At diffusion temperatures Tdiff > 1000 °C, a sharp decrease in Pmax occurs, which is associated with an increase in the depth of the p–n-junction due to the distillation of phosphorus atoms during high-temperature diffusion of nickel. The positive effect of diffusion alloying with nickel on the electrophysical parameters of photocells is greatest in the case when the nickel impurity clusters are in the region of the p–n-junction, i. e. with diffusion alloying to the front side of the plate. The action of electrically neutral nickel clusters is less pronounced when they are located in the region of the isotypic p–p+ transition; in case of diffusion alloying with nickel in the opposite side of the plate.
本文研究了在700 ~ 1200℃温度范围内,通过扩散掺杂镍的方法来调整Suniva公司生产的单晶硅工业太阳能电池工作参数的可能性。结果表明,镍的最佳扩散温度为Tdiff = 800 ~ 850℃。在这种情况下,与原始工业光电池的参数相比,最大功率Pmax的值增加了20 - 28%。在扩散温度Tdiff > 1000℃时,Pmax急剧下降,这与镍在高温扩散过程中磷原子的蒸馏导致p - n结深度增加有关。当镍杂质团簇位于p - n结区域,即扩散合金化到板的正面时,镍扩散合金化对光电池电物理参数的积极影响最大。当电中性镍团簇位于p-p +同型跃迁区域时,其作用不明显;如果扩散合金与镍在板的另一边。
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引用次数: 0
Variation of the silicon optical parameters after rapid heat treatment 快速热处理后硅光学参数的变化
Pub Date : 2021-09-29 DOI: 10.33581/2520-2243-2021-3-81-85
V. Anishchik, V. A. Harushka, U. Pilipenka, V. Ponariadov, V. Saladukha, A. Omelchenko
The results of the effect of rapid heat treatment on the optical characteristics of a silicon wafer surface in the region of the G-point in the Brillouin zone are presented for different types of silicon wafers conductivity, their doping level, the covalent radii of dopants and the crystallographic orientation of the wafer surface. The absorption coefficient and refractive index of the initial 100 mm diameter samples KDB-12 <100>, KDB-10 <111>, KDB-0.005 <100> and KES-0.015 <100>, underwent standard chemical-mechanical polishing, was measured on a Uvisel 2 ellipsometer (Horiba Scientific, France) in the spectral range 0.6–6.0 eV (200–2100 nm) before and after rapid heat treatment. The incidence angle of the light beam was 70° relative to the sample plane. It is shown that the changes in the optical characteristics of the silicon surface in the spectral region of the location of the G-point in the Brillouin zone after rapid heat treatment is due to a decrease in the surface deformation potential due to solid-phase recrystallisation of the mechanically damaged layer. It has been established that carrying out the rapid heat treatment of silicon samples with a high boron concentration leads to a more significant decrease in the refractive index and absorption compared with silicon with a low boron concentration, due to an increase in the depletion of the silicon surface with boron as a result of diffusion processes at the silicon – silicon dioxide interface.
本文给出了快速热处理对不同类型硅片电导率、掺杂水平、掺杂共价半径和硅片表面晶体取向在布里渊区g点区域的光学特性的影响。采用Uvisel 2型椭偏仪(Horiba Scientific, France)在光谱范围0.6 ~ 6.0 eV (200 ~ 2100 nm)上测量了经过标准化学机械抛光的初始100mm直径样品KDB-12、KDB-10、KDB-0.005和KES-0.015的吸收系数和折射率。光束的入射角相对于样品平面为70°。结果表明,快速热处理后硅表面在布里渊区g点位置光谱区域光学特性的变化是由于机械损伤层固相再结晶导致表面变形势降低所致。已经确定,与低硼浓度的硅相比,对高硼浓度的硅样品进行快速热处理会导致折射率和吸收率的显著下降,这是由于硅-二氧化硅界面处的扩散过程导致硅表面被硼耗尽的增加。
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引用次数: 0
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Journal of the Belarusian State University. Physics
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