In the study, the motion of a charged spin-1/2 fermion is found out. It is assumed, in the system, that the free fermion is subjected to a linearly space-dependent magnetic field which can be supposed to be a focusing magnetic field of a quadrupole magnet in beam dynamics in the accelerator physics. In such an examination, two-component Dirac equation is solved via perturbation approximation of the Asymptotic Iteration Method, which has been widely used for the last decades. The results show that the fermion is bounded to the magnetic field for a certain condition of the strength of the field. For such a system, the analytical form of the energy eigenvalues are obtained. Moreover, to see whether this analytical expression works properly, the numerical eigenvalues are compared with the ones obtained by direct use of the AIM. We have an inspiration that the studies on beam dynamics and magnet design in particle accelerator physics may gain from this work.
{"title":"Analytical Energy Eigenvalues of a Dirac Particle in Focusing Field of a Quadrupole Magnet","authors":"H. F. Kisoglu","doi":"10.1139/cjp-2022-0286","DOIUrl":"https://doi.org/10.1139/cjp-2022-0286","url":null,"abstract":"In the study, the motion of a charged spin-1/2 fermion is found out. It is assumed, in the system, that the free fermion is subjected to a linearly space-dependent magnetic field which can be supposed to be a focusing magnetic field of a quadrupole magnet in beam dynamics in the accelerator physics. In such an examination, two-component Dirac equation is solved via perturbation approximation of the Asymptotic Iteration Method, which has been widely used for the last decades. The results show that the fermion is bounded to the magnetic field for a certain condition of the strength of the field. For such a system, the analytical form of the energy eigenvalues are obtained. Moreover, to see whether this analytical expression works properly, the numerical eigenvalues are compared with the ones obtained by direct use of the AIM. We have an inspiration that the studies on beam dynamics and magnet design in particle accelerator physics may gain from this work.","PeriodicalId":9413,"journal":{"name":"Canadian Journal of Physics","volume":"36 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76074646","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This note revisits the semi-classical theory of quantum oscillations in hybridization-gap insulators, and argues that the physical origin of the oscillations, at T=0 K, is a sudden change in the diamagnetic moment of each Landau level as it crosses the hybridized region of the valence band.
{"title":"de Haas van Alphen oscillations in hybridization-gap insulators as a sudden change in the diamagnetic moment of Landau levels","authors":"S. Julian","doi":"10.1139/cjp-2022-0340","DOIUrl":"https://doi.org/10.1139/cjp-2022-0340","url":null,"abstract":"This note revisits the semi-classical theory of quantum oscillations in hybridization-gap insulators, and argues that the physical origin of the oscillations, at T=0 K, is a sudden change in the diamagnetic moment of each Landau level as it crosses the hybridized region of the valence band.","PeriodicalId":9413,"journal":{"name":"Canadian Journal of Physics","volume":"18 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78714505","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
R. Horchani, A. Ikot, I. Okon, U. Okorie, L. Obagboye, A. Ahmadov, H.Y. Abdullah, K. W. Qadir, A. Abdel‐Aty
In this study, we obtained exact solutions of the Feinberg–Horodecki equation for the time-dependent Wei-Hua potential, which is constructed by the temporal counterpart of the spatial form of this potential. We have obtained the quantized momentum eigenvalues and the corresponding wave functions. We obtain the partition function for the system and study other thermodynamic properties which include vibrational mean momentum (U), vibrational specific heat capacity (C), vibrational entropy (s) and vibrational free momentum (F) as a signature in the momentum space.
{"title":"Quantized momentum Eigenstates and thermodynamic properties of the Feinberg-Horodecki equation for the Time-Dependent Wei-Hua Oscillator","authors":"R. Horchani, A. Ikot, I. Okon, U. Okorie, L. Obagboye, A. Ahmadov, H.Y. Abdullah, K. W. Qadir, A. Abdel‐Aty","doi":"10.1139/cjp-2022-0223","DOIUrl":"https://doi.org/10.1139/cjp-2022-0223","url":null,"abstract":"In this study, we obtained exact solutions of the Feinberg–Horodecki equation for the time-dependent Wei-Hua potential, which is constructed by the temporal counterpart of the spatial form of this potential. We have obtained the quantized momentum eigenvalues and the corresponding wave functions. We obtain the partition function for the system and study other thermodynamic properties which include vibrational mean momentum (U), vibrational specific heat capacity (C), vibrational entropy (s) and vibrational free momentum (F) as a signature in the momentum space.","PeriodicalId":9413,"journal":{"name":"Canadian Journal of Physics","volume":"6 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82012856","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The characteristic dependence of the Hall mobility upon the temperature of a degenerate ensemble of two-dimensional electrons in a well of heterostructure has been calculated in some broad details, for the ohmic field region, at the low temperatures. Apart from the electronic interactions with the remote ionized impurities and the surface roughness, the study also duly considers some factors which are often ignored for mathematical simplicity. These include, the inelasticity of the electron-phonon collisions and the true phonon distribution. The results thus obtained for heterostructures like AlGaAs/GaAs, AlGaN/GaN and AlInSb/InSb, show that the consideration of the above details significantly changes the overall characteristics, and makes them agree quite well with the experimental data.
{"title":"On some comprehensive study of the Hall mobility of an ohmic ensemble of two-dimensional electrons confined in a quantum well of a heterostructure at low lattice temperatures","authors":"B. Roy, S. Bhattacharyya, D. Bhattacharya","doi":"10.1139/cjp-2022-0144","DOIUrl":"https://doi.org/10.1139/cjp-2022-0144","url":null,"abstract":"The characteristic dependence of the Hall mobility upon the temperature of a degenerate ensemble of two-dimensional electrons in a well of heterostructure has been calculated in some broad details, for the ohmic field region, at the low temperatures. Apart from the electronic interactions with the remote ionized impurities and the surface roughness, the study also duly considers some factors which are often ignored for mathematical simplicity. These include, the inelasticity of the electron-phonon collisions and the true phonon distribution. The results thus obtained for heterostructures like AlGaAs/GaAs, AlGaN/GaN and AlInSb/InSb, show that the consideration of the above details significantly changes the overall characteristics, and makes them agree quite well with the experimental data.","PeriodicalId":9413,"journal":{"name":"Canadian Journal of Physics","volume":"299 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78530117","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
G. Estevez-Delgado, J. Estevez-Delgado, M. P. Duran, A. Cleary-Balderas
Starting from the solution of the Einstein field equations in a static and spherically symmetric spacetime which contains an isotropic fluid, we construct a model to represent the interior of compact objects with compactness rate u=GM/(c2R )<0.23577. The solution is obtained by imposing the isotropy condition for the radial and tangential pressures, this generates an ordinary differential equation of second order for the temporal gtt and radial grr metric potentials, which can be solved for a specific function of gtt. The graphic analysis of the solution shows that it is physically acceptable, that is to say, the density, pressure and speed of sound are positive, regular and monotonically decreasing functions, also, the solution is stable due to meeting the criteria of the adiabatic index. When taking the data of mass M=1.44+0.15-0.14M⊙ and radius R=13.02+1.24-1.06 km which corresponds to the estimations of the star PSR J0030+045 we obtain values of central density ρc=7.5125x1017 kg/m3 for the maximum compactness u=0.19628 and of ρc=2.8411x1017 kg/m3 for the minimum compactness u=0.13460, which are consistent with those expected for this type of stars.
{"title":"A regular interior solution of Einstein field equations.","authors":"G. Estevez-Delgado, J. Estevez-Delgado, M. P. Duran, A. Cleary-Balderas","doi":"10.1139/cjp-2023-0126","DOIUrl":"https://doi.org/10.1139/cjp-2023-0126","url":null,"abstract":"Starting from the solution of the Einstein field equations in a static and spherically symmetric spacetime which contains an isotropic fluid, we construct a model to represent the interior of compact objects with compactness rate u=GM/(c<sup>2</sup>R )<0.23577. The solution is obtained by imposing the isotropy condition for the radial and tangential pressures, this generates an ordinary differential equation of second order for the temporal g<sub>tt</sub> and radial g<sub>rr</sub> metric potentials, which can be solved for a specific function of g<sub>tt</sub>. The graphic analysis of the solution shows that it is physically acceptable, that is to say, the density, pressure and speed of sound are positive, regular and monotonically decreasing functions, also, the solution is stable due to meeting the criteria of the adiabatic index. When taking the data of mass M=1.44<sup>+0.15</sup><sub>-0.14</sub>M</sub>⊙</sub> and radius R=13.02<sup>+1.24</sup><sub>-1.06</sub> km which corresponds to the estimations of the star PSR J0030+045 we obtain values of central density ρ<sub>c</sub>=7.5125x10<sup>17</sup> kg/m<sup>3</sup> for the maximum compactness u=0.19628 and of ρ<sub>c</sub>=2.8411x10<sup>17</sup> kg/m<sup>3</sup> for the minimum compactness u=0.13460, which are consistent with those expected for this type of stars.","PeriodicalId":9413,"journal":{"name":"Canadian Journal of Physics","volume":"22 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2022-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90728066","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we study a spatially homogeneous and anisotropic Bianchi type II space-time in the presence of matter and modified holographic Ricci dark energy in Barber’s second self-creation theory of gravitation. We obtain exact solution of the field equations by assuming (i) a special law of variation of the mean Hubble parameter and (ii) the component σ1 1 of the shear tensor σi i is proportional to the expansion scalar in the model. Some physical and dynamical parameter are determined and their significant roles are discussed in respect of cosmic evolution of the universe. We observe that the model is consistent with modern cosmological observational data.
{"title":"Bianchi type-II modified holographic Ricci dark energy model in Barber's self-creation theory of gravitation","authors":"S. Ram, M. K. Verma, S. Chandel","doi":"10.1139/cjp-2022-0007","DOIUrl":"https://doi.org/10.1139/cjp-2022-0007","url":null,"abstract":"In this paper, we study a spatially homogeneous and anisotropic Bianchi type II space-time in the presence of matter and modified holographic Ricci dark energy in Barber’s second self-creation theory of gravitation. We obtain exact solution of the field equations by assuming (i) a special law of variation of the mean Hubble parameter and (ii) the component σ1 1 of the shear tensor σi i is proportional to the expansion scalar in the model. Some physical and dynamical parameter are determined and their significant roles are discussed in respect of cosmic evolution of the universe. We observe that the model is consistent with modern cosmological observational data.","PeriodicalId":9413,"journal":{"name":"Canadian Journal of Physics","volume":"5 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2022-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87927235","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A method to construct the boundary shape function (BSF) and then two novel methods are developed to obtain the solutions of fourth-order singularly perturbed beam equation and nonlinear boundary value problem (BVP). In the first type algorithm, the free function is a series of complete basis functions while the corresponding BSFs are new bases. The trial functions with fractional powers exponential are suitable for the singularly perturbed beam equation under fixed-end and simply-supported boundary conditions. With the aid of the BSF, we can improve the asymptotic and uniform approximations to exactly satisfy the prescribed boundary conditions. In the second type algorithm, the solution of nonlinear BVP is viewed as a boundary shape function while the free function is regarded as a new variable. With this means, the fourth-order nonlinear BVP is exactly converted to an initial value problem with new variable, the terminal value of which are unknown, when the initial conditions are given. The computed order of convergence and an error estimation are given. Numerical illustrations, including the singularly perturbed examples, show that the present methods, based on the new idea of the BSF, are highly effective, accurate and convergent fast.
{"title":"Solving the fourth-order nonlinear boundary value problem by a boundary shape functions method","authors":"Chein-Shan Liu, Botong Li","doi":"10.1139/cjp-2021-0224","DOIUrl":"https://doi.org/10.1139/cjp-2021-0224","url":null,"abstract":"A method to construct the boundary shape function (BSF) and then two novel methods are developed to obtain the solutions of fourth-order singularly perturbed beam equation and nonlinear boundary value problem (BVP). In the first type algorithm, the free function is a series of complete basis functions while the corresponding BSFs are new bases. The trial functions with fractional powers exponential are suitable for the singularly perturbed beam equation under fixed-end and simply-supported boundary conditions. With the aid of the BSF, we can improve the asymptotic and uniform approximations to exactly satisfy the prescribed boundary conditions. In the second type algorithm, the solution of nonlinear BVP is viewed as a boundary shape function while the free function is regarded as a new variable. With this means, the fourth-order nonlinear BVP is exactly converted to an initial value problem with new variable, the terminal value of which are unknown, when the initial conditions are given. The computed order of convergence and an error estimation are given. Numerical illustrations, including the singularly perturbed examples, show that the present methods, based on the new idea of the BSF, are highly effective, accurate and convergent fast.","PeriodicalId":9413,"journal":{"name":"Canadian Journal of Physics","volume":"18 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2022-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74504739","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
One can use the generalized uncertainty principle (GUP) to incorporate the minimum measurable length in quantum gravity. It may be interesting to have a minimal time interval as well as the minimal length in the relativistic version of quantum mechanics in the presence of the gravitational effects. In this paper, we consider a covariant version of the generalized uncertainty principle to investigate the effects of both the minimal time and the minimal length. Using the covariant GUP, the energy-momentum dispersion relation is modified. Starting with the modified dispersion relation, the corrections to the wave function are obtained and the problems of the particle in a box and the Hydrogen atom are revisited. Considering the minimal time may be an interesting new topic which is not widely studied before. It may lead to new results which can open a new window into quantum gravity.
{"title":"The effects of the covariant generalized uncertainty principle on quantum mechanics","authors":"Mohaddeseh Seifi, A. Sefiedgar","doi":"10.1139/cjp-2022-0217","DOIUrl":"https://doi.org/10.1139/cjp-2022-0217","url":null,"abstract":"One can use the generalized uncertainty principle (GUP) to incorporate the minimum measurable length in quantum gravity. It may be interesting to have a minimal time interval as well as the minimal length in the relativistic version of quantum mechanics in the presence of the gravitational effects. In this paper, we consider a covariant version of the generalized uncertainty principle to investigate the effects of both the minimal time and the minimal length. Using the covariant GUP, the energy-momentum dispersion relation is modified. Starting with the modified dispersion relation, the corrections to the wave function are obtained and the problems of the particle in a box and the Hydrogen atom are revisited. Considering the minimal time may be an interesting new topic which is not widely studied before. It may lead to new results which can open a new window into quantum gravity.","PeriodicalId":9413,"journal":{"name":"Canadian Journal of Physics","volume":"35 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2022-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86566310","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This article is designed to inspect the thermal effects of an unsteady compressible flow of a viscous fluid through a symmetric channel. Combined effects of convective heat transfer, magnetic field and radiation are also given special attention in this article. Basic laws of mass, momentum and energy for compressible flow are employed in the modeling of the current problem. In addition, slip boundary conditions are also implemented in the analysis of the above thermal flow problem. Coupled non-linear differential equations are solved numerically using explicit finite difference technique. Finally, the influence of different sundry parameters on the axial velocity, flow rate and heat transfer are visualized through graphs. Time variant behavior of flow rate is calculated. Outcomes of the results reveal that the increment of the flow rate is related to the increase of compressibility parameters. Enhancement in the temperature profiles in the presence of radiation number is also reported. This model is most general version of peristalsis of compressible flow in view of natural convection and radiation impact with extensive applications in aircraft industry, geophysics and other industrial situations (cooling of electronic equipment, heat exchangers and so forth).
{"title":"Unsteady Radiative-Convective Flow of a Compressible Fluid: A Numerical Approach","authors":"R. Rafaqat, A. Khan, A. Zaman","doi":"10.1139/cjp-2022-0154","DOIUrl":"https://doi.org/10.1139/cjp-2022-0154","url":null,"abstract":"This article is designed to inspect the thermal effects of an unsteady compressible flow of a viscous fluid through a symmetric channel. Combined effects of convective heat transfer, magnetic field and radiation are also given special attention in this article. Basic laws of mass, momentum and energy for compressible flow are employed in the modeling of the current problem. In addition, slip boundary conditions are also implemented in the analysis of the above thermal flow problem. Coupled non-linear differential equations are solved numerically using explicit finite difference technique. Finally, the influence of different sundry parameters on the axial velocity, flow rate and heat transfer are visualized through graphs. Time variant behavior of flow rate is calculated. Outcomes of the results reveal that the increment of the flow rate is related to the increase of compressibility parameters. Enhancement in the temperature profiles in the presence of radiation number is also reported. This model is most general version of peristalsis of compressible flow in view of natural convection and radiation impact with extensive applications in aircraft industry, geophysics and other industrial situations (cooling of electronic equipment, heat exchangers and so forth).","PeriodicalId":9413,"journal":{"name":"Canadian Journal of Physics","volume":"56 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2022-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86035325","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this article, we study the effects of minimal length corrections on the cyclotron acceleration and radiation of a charged particle moving in a magnetic monopole field. Using the modified Hamiltonian describing the dynamics of a charged particle moving in a magnetic monopole field we derive the modified cyclotron frequency and modified acceleration. Also, we derive the modified power for the cyclotron radiation using the modified acceleration. We find that all modified quantities are dependent of the deformation parameter α . In addition, we find that, the modified electromagnetic angular momentum and magnetic charges are not quantized as an integer multiple, thus we establish the modified Dirac quantization condition and the usual Dirac quantization condition is just the term of zero order in α . The modified Dirac quantization condition allows fractional charges which arise from vacuum fluctuations. In the Born approximation, we derive the modified scattering cross section and then we estimate the upper bound on the minimal length.
{"title":"On magnetic monopole and Dirac quantization condition in the minimal length formalism","authors":"F. Twagirayezu","doi":"10.1139/cjp-2022-0028","DOIUrl":"https://doi.org/10.1139/cjp-2022-0028","url":null,"abstract":"In this article, we study the effects of minimal length corrections on the cyclotron acceleration and radiation of a charged particle moving in a magnetic monopole field. Using the modified Hamiltonian describing the dynamics of a charged particle moving in a magnetic monopole field we derive the modified cyclotron frequency and modified acceleration. Also, we derive the modified power for the cyclotron radiation using the modified acceleration. We find that all modified quantities are dependent of the deformation parameter α . In addition, we find that, the modified electromagnetic angular momentum and magnetic charges are not quantized as an integer multiple, thus we establish the modified Dirac quantization condition and the usual Dirac quantization condition is just the term of zero order in α . The modified Dirac quantization condition allows fractional charges which arise from vacuum fluctuations. In the Born approximation, we derive the modified scattering cross section and then we estimate the upper bound on the minimal length.","PeriodicalId":9413,"journal":{"name":"Canadian Journal of Physics","volume":"19 2 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2022-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75723477","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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