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The quantum magneto-thermoelectric effect in a two-dimensional compositional superlattice under the influence of an electromagnetic wave (EMW) in two cases is investigated. Two cases of the electron scattering mechanism are considered: the electron-acoustic phonon scattering and electron-optical phonon scattering. Analytical expressions for the quantum Ettingshausen coefficient (EC), the thermopower tensor, the thermoelectric tensor and the kinetic tensor are obtained by using a quantum kinetic equation. These expressions are numerically solved for the two-dimensional compositional superlattice GaAs/AlGaAs and the results are discussed. The results show that in the case of electron-acoustic phonon scattering, the Shubnikov-de Haas oscillations appear when we examine the dependences of the quantum EC, the thermopower tensor and the thermoelectric tensor on the magnetic field. In the case of electron-optical phonon scattering, resonance peaks that satisfy the condition of the inter-subband magneto-phonon resonance appear. In the two cases, the superlattice period (a parameter specific to the material) strongly affects the quantum magneto-thermoelectric effect. When the superlattice period is small, quantum EC oscillations (in the case of electron-acoustic phonon interaction) and quantum EC resonance peaks (in the case of electron-optical phonon interaction) appear. However, when the superlattice period is large, these oscillations and resonance peaks are not observed. Especially, the influence of electromagnetic waves on the quantum magneto-thermoelectric effect is also clarified. The quantum theory of the magneto-thermoelectric effect has been studied from low temperature to high temperature. This overcomes the limitations of the Boltzmann kinetic equation which was studied at high temperature. The results are new and can serve as a basis for further development of the theory of quantum magneto-thermoelectric effects in low-dimensional semiconductor systems.

This paper analyses the transference from spatial to non-spatial meanings of below as a preposition, an adverb, and a particle within the 2017 Corpus of Contemporary American English, genre: fiction. In light of the Multimodal Image Theory and Extended Conceptual Metaphor Theory, the data analysis shows that the prototypical meaning of below has two variants in its Visual space, and two non-spatial meanings namely Less and Inferior. The mechanism of meaning transference is mappings in which salient aspects of absence of contact, force, and occlusion between the Trajector (TR) and Landmark (LM) are retained in construing the non-spatial scenes associated with the word.

The Quantum photo-stimulated Peltier effect has been theoretically studied under the influence of confined acoustic phonon in a cylindrical quantum wires with an infinite potential by using the quantum kinetic equation method. In this work, we assume that the confined electrons-confined acoustic phonons scattering is essential. Moreover, the presence of a strong electromagnetic wave (EMW) is also taken into account to determine the influence of confined phonons on the aforementioned effects. We have defined the analytical expressions for the kinetic tensors and the Peltier coefficients (PC). In detailed consideration, the quantum number m1, m2 were changed in order to characterize the influence of confined acoustic phonon (confined AP). As the radius of the wire increases to infinity, we obtained the results that corresponded to the case of bulk phonons (unconfined AP). The theoretical results have been numerically evaluated and discussed for the GaAs/AlGaAs cylindrical quantum wires (CQW). The change of PC in two cases unconfined AP and confined AP have been found according to augment of EMW frequency. The value of resonant peaks has altered under the effect of confined AP. The difference of PC also has been discovered when investigating its dependence on the cyclotron frequency. Furthermore, the PC reduced suddenly when considering the dependence of PC on the radius of wire and PC on the low temperature. All numerical showed that the magnitude of PC diverse significantly in comparison with unconfined AP case and doped two - dimensional semiconductor superlattice. This means that the confinement of the phonon affects the Peltier effect quantitatively and qualitatively. These results are new and provide to completing the theory of the Peltier effect in low-dimensional semiconductor systems.

This paper summarizes different approaches to the meaning extension of the English preposition over and proposes a multimodal approach comprising three spatial image theories and one mental space theory in reference to an image-based view. It is concluded that the author’s proposal is a combination of Deane’s 2005 multimodal spatial representations and 2017 Kövecses’s model, in which there is an emphasis that treating the spatial configurations of a spatial marker requires different frames and when the marker denotes a non-spatial sense, there exists an activation of a metaphor layered from its frame in certain context with a specific communicative purpose to the domain of which the frame is a part and finally the activation will reach the image schema that supports the frame.

The effect of confined optical phonons and laser radiation are taken into account to study the Hall effect in a compositional semiconductor superlattice (CSSL). The new theoretical expressions of the Hall conductivity, the Hall coefficient and the magnetoresistance are obtained as functions of the external fields (the magnetic field B , the laser frequency Ω and amplitude E ), the CSSL parameters (the well length d I , the barrier length d II and height U ) and the quantum number m characterizing the phonon confinement effect. The magneto-confined phonon resonance condition in a CSSL is also carried out to explain the numerical evaluation results for the GaAs / Al x Ga 1 − x As CSSL. When optical phonons are confined, the Hall conductivity has more resonance peaks in comparison with that for bulk phonons. In addition, these sub-peaks are more separate from the main peaks as the CSSL layers thickness decreases. The tighter CSSL period is, the more forcefully the phonon confinement makes. When the CSSL period d is smaller than 30 nm , the contribution of confined optical phonons is significant and could not be neglected. The magnetophonon resonance for bulk semiconductor could be achieved in the limit the CSSL period goes to infinity. Furthermore, the Hall conductivity increases and the Hall coefficient, the magnetoresistance decrease due to the laser radiation and the effect of confined optical phonons. Especially, the near-linear dependence of the magnetoresistance on temperature is in good agreement with the experimental result.

The influence of confined optical phonons on the Hall Coefficient (HC) in a Cylindrycal Quantum Wire (CQW) with an infinite potential (for electron – confined optical phonons scattering). Consider a case where CQW is placed in a perpendicular magnetic field , a constant - electric field and an intense electromagnetic wave . By using the quantum kinetic equation for electrons interacting with Confined Optical Phonon (COP), we obtain analytical expressions for (HC), which are different from in comparison to those obtained for the HC in the case of normal bulk semiconductor and in the case of cylindrycal quantum wire with electron – unconfined phonons scattering mechanism. Numerical calculations are also applied for AlGaAs/GaAs/AlGaAs cylindrycal quantum wire, we see the HC depends on magnetic field B, temperature T, frequency Ω and amplitude E0 of laser radiation and especially quantum index m1 and m2 characterizing the phonon confinement. This influence is due to the quantum index m1 and m2, which makes an increase of Hall coefficient by 2,3 times in comparition with the case of unconfined phonons. When the quantum number m1 and m2 goes to zero, the result is the same as in the case of unconfined phonons.

Based on the quantum kinetic equation method, the Hall effect in doped semiconductor superlattices (DSSL) has been theoretically studied under the influence of confined LO-phonons and the laser radiation. The analytical expression of the Hall conductivity tensor, the magnetoresistance and the Hall coefficient of a GaAs:Si/GaAs:Be DSSL is obtained in terms of the external fields, lattice period and doping concentration. The quantum numbers N, n, m were varied in order to characterize the effect of electron and LO-phonon confinement. Numerical evaluations showed that LO-phonon confinement enhanced the probability of electron scattering, thus increasing the number of resonance peaks in the Hall conductivity tensor and decreasing the magnitude of the magnetoresistance as well as the Hall coefficient when compared to the case of bulk phonons. The nearly linear increase of the magnetoresistance with temperature was found to be in good agreement with experiment.

Vyvyan EvansOxford University Press, 2009, pp. xv+377

Based on the quantum kinetic equation method, the influence of confined optical phonons and laser radiation on the Radioelectric effect in a cylindrical semiconductor quantum wire with parabolic potential subjected to a dc electric field and a linearly polarized electromagnetic wave has been theoretically studied. The obtained analytical expression of the Radioelectric field (REF) depends on frequencies and amplitudes of the external electromagnetic waves, the quantum wire parameters, the temperature of the system, and especially the quantum numbers (n and m) which characterize the phonon confinement. Numerical calculations for the GaAs/GaAsAl quantum wire show the strongly impact of the confined optical phonons as well as the laser radiation on the REF magnitude and posture. The REF also has more resonance peaks in comparison with that in case of bulk phonon.

The magnetoresistance is one of the important properties of semiconductors. Starting from the hamiltonian for the electron-acoustic phonon system, we obtained the expression for the electron distribution function and especially the expression for the magnetoresistance in quantum wells with parabolic potential (QWPP) under the influence of electromagnetic wave (EMW) in the presence of magnetic field. We estimated numerical values and graphed for a GaAs/GaAsAl quantum well to see the nonlinear dependence of the magnetoresistance on the temperature of the system T, the amplitude E0 and the frequency Ω of the electromagnetic waves, the magnetic field B, the parameters of the quantum well and the momentum relaxation time τ clearly.

The radioelectric effect (REE) in the Rectangular quantum wires (RQW) with an infinite potential under the influences of confined phonons and a linearly polarized electromagnetic wave (EMW) is theoretically studied by using quantum kinetic equations method. The obtained analytical expression of the Radioelectric field (REF) depends on frequencies of EMW (ω) and the laser (Ω), the size L of wire, the temperature T, and also especially the quantum numbers (m and j) characterizing confined phonons. Numerical calculation for a GaAs/GaAsAl RQW which shows that confined phonons and a linearly EMW impact strongly on the REE. There are differences in values and postures of the REF from the two dismensional systems which caused by differences potentials. The results also show that REF is much greater than that in case of unconfined phonons.

The influence of confined optical phonons on the Hall effect in a quantum well under the present of a perpendicular magnetic field and an in-plane intense electromagnetic wave, has been theoretical studied. The analytical expression of the Hall coefficient for electron — confined optical phonon interaction is obtained base on the quantum kinetic equation method. It is found that the Hall coefficient depends on the frequency and amplitude of the electromagnetic wave, the magnetic induction, the quantum well width, the temperature of the system and especially the quantum number m characterizing the phonon confinement. Numerical calculations are also applied for AlGaAs/GaAs/AlGaAs quantum well to show the nonlinear dependence of the Hall coefficient on the electromagnetic wave amplitude and the remarkable contribution of confined optical phonons on the magnitude of the Hall coefficient as well as the magneto-phonon resonance condition. All results are compared with that in case of unconfined phonons to see differences.

The influence of confined acoustic phonons on the Radioelectric field in a quantum well has been studied in the presence of a linearly polarized electromagnetic wave and a laser radiation. By using the quantum kinetic equation for electrons with confined electrons - confined acoustic phonons interaction, the analytical expression for the Radio electric field is obtained. The formula of the Radio electric field contains the quantum number m characterizing the phonons confinement and comes back to the case of unconfined phonons when m reaches to zero. The dependence of the Radio electric field on the frequency of the laser radiation, in case of confined acoustic phonons, is also achieved by numerical method for a specific quantum well AlGaAs/GaAs/AlGaAs. Results show that the Radio electric field has a peak and reaches saturation as the frequency of the laser radiation increases.