The electric field in the crystal planar channels is studied by the Thomas Fermi method. The Thomas-Fermi equation and the corresponding boundary conditions are derived for the crystal planar channels. The numericalso...The electric field in the crystal planar channels is studied by the Thomas Fermi method. The Thomas-Fermi equation and the corresponding boundary conditions are derived for the crystal planar channels. The numericalsolution for the electric field in the channels between (110) planes of the single crystal silicon and the critical angles ofchannelling protons in them are shown. Reasonable agreements with the experimental data are obtained. The resultsshow that the Thomas-Fermi method for the crystal works well in this study, and a microscopic research of the channelelectric field with the contribution of all atoms and the atomic ionization being taken into account is practical.展开更多
Electron spectrum in doped n-Si quantum wires is calculated by the Thomas-Fermi (TF) method under finite temperatures. The many-body exchange corrections are taken into account. The doping profile is arbitrary. At the...Electron spectrum in doped n-Si quantum wires is calculated by the Thomas-Fermi (TF) method under finite temperatures. The many-body exchange corrections are taken into account. The doping profile is arbitrary. At the first stage, the electron potential energy is calculated from a simple two-dimensional equation. The effective iteration scheme is proposed there that is valid for multidimensional problems. Then the energy levels and wave functions of this quantum well are simulated from the Schrödinger equations. The expansion by the full set of eigenfunctions of the linear harmonic oscillator is used. The quantum mechanical perturbation theory can be utilized to compute the energy levels. Generally, the perturbation theory for degenerate energy levels should be used.展开更多
The damping and frequency-shift in Landau mechanism of a quadrupole mode in a disc-shaped rubidium Bose-Einstein condensate are investigated by using the Hartree-Fock-Bogoliubov approximation. The practical relaxation...The damping and frequency-shift in Landau mechanism of a quadrupole mode in a disc-shaped rubidium Bose-Einstein condensate are investigated by using the Hartree-Fock-Bogoliubov approximation. The practical relaxations of the elementary excitations and the orthometric relation among them are taken into account to obtain advisable calculation formula for damping as well as frequency-shift. The first approximation of Gaussian distribution function is employed for the ground-state wavefunction to suitably eliminate the divergence of the analytic three-mode coupling matrix elements. According to these methods, both Landau damping rate and frequency-shift of the quadrupole mode are analytically calculated. In addition, all the theoretical results agree with the experimental ones.展开更多
In the present investigations,the fusion crosssections for the formation of 200Pb compound nucleus(CN)using 16O+184 W,30Si+170Er,and 40Ar+160Gd nuclear reactions at energies above the Coulomb barrier were calculated t...In the present investigations,the fusion crosssections for the formation of 200Pb compound nucleus(CN)using 16O+184 W,30Si+170Er,and 40Ar+160Gd nuclear reactions at energies above the Coulomb barrier were calculated to understand the effect of entrance channel mass asymmetry(α)on the fusion reactions;the Skyrme energy density formalism(SEDF)was used for this calculation.The SEDF uses the Hartree-Fock-Bogolyubov(HFB)computational program with Skyrme forces such as SkM*,SLy4,and SLy5 to obtain the nucleus-nucleus potential parameters for the above reactions.Using the SEDF model with SkM*,SLy4,and SLy5 interaction forces,the theoretical fusion cross-sections were determined above the barrier energy and compared with the available experimental fusion cross-sections.The results show a close agreement between the theoretical and experimental values for all selected systems at energies well above the barrier.However,near the barrier energies,the theoretical values were observed to be higher than the experimental values.展开更多
Electromagnetic screening is studied from the perspective of fluid mechanics by generalizing the Drude theory, which unifies three known results： Thomas–Fermi screening of the longitudinal field in both metals and s...Electromagnetic screening is studied from the perspective of fluid mechanics by generalizing the Drude theory, which unifies three known results： Thomas–Fermi screening of the longitudinal field in both metals and superconductors, the skin effect of the transverse field in metals, and the Meissner effect in superconductors. In the special case of superfluid electrons, we slightly generalize the London equations to incorporate the longitudinal electric fields. Moreover, regarding the experiments, our study points out that the dynamical measurement may overestimate the superfluid density.展开更多
Thomas-Fermi theory is an approximate method, which is widely used to describe the properties of matter at various hierarchical levels (atomic nucleus, atom, molecule, solid, etc.). Special development is achieved usi...Thomas-Fermi theory is an approximate method, which is widely used to describe the properties of matter at various hierarchical levels (atomic nucleus, atom, molecule, solid, etc.). Special development is achieved using Thomas-Fermi theory to the theory of extreme states of matter appearing under high pressures, high temperatures or strong external fields. Relevant sections of physics and related sciences (astrophysics, quantum chemistry, a number of applied sciences) determine the scope of Thomas-Fermi theory. Popularity Thomas-Fermi theory is related to its relative simplicity, clarity and versatility. The latter means that the result of the calculation by Thomas-Fermi theory applies immediately to all chemical elements: the transition from element to element is as simple scale transformation. These features make it to be a highly convenient tool for qualitative and, in many cases, and quantitative analysis.展开更多
In the 1970s,scientists began experimenting with powerful laser beams to compress and heat the hydrogen isotopes to the point of fusion,a technique called ICF(Inertial Confinement Fusion).In the“direct drive”approac...In the 1970s,scientists began experimenting with powerful laser beams to compress and heat the hydrogen isotopes to the point of fusion,a technique called ICF(Inertial Confinement Fusion).In the“direct drive”approach to ICF,powerful beams of laser light are focused on a small spherical pellet containing micrograms of deuterium and tritium.The rapid heating caused by the laser“driver”makes the outer layer of the target explode.In keeping with Isaac Newton’s Third Law“For every action,there is an equal and opposite reaction”,the remaining portion of the target is driven inwards in a rocket-like implosion,causing compression of the fuel inside the capsule and the formation of a shock wave,which further heats the fuel in the very center and results in a self-sustaining burn.The fusion burn propagates outward through the cooler,outer regions of the capsule much more rapidly than the capsule can expand.Instead of magnetic fields,the plasma is confined by the inertia of its own mass—hence the term inertial confinement fusion.A similar process can be observed on an astrophysical scale in stars and the terrestrial uber world,that have exhausted their nuclear fuel,hence inertially or gravitationally collapsing and generating a supernova explosion,where the results can easily be converted to induction of energy in control forms for a peaceful purpose(i.e.,inertial fusion reaction)by means of thermal physics and statistical mechanics behavior of an ideal Fermi gas,utilizing Fermi-Degeneracy and Thomas-Fermi theory.The fundamental understanding of thermal physics and statistical mechanics enables us to have a better understanding of Fermi-Degeneracy as well as Thomas-Fermi theory of ideal gas,which results in laser compressing matter to a super high density for purpose of producing thermonuclear energy in way of controlled form for peaceful shape and form i.e.CTR(Controlled Thermonuclear Reaction).In this short review,we have concentrated on Fundamental of State Equations by driving them as it was evaluated in book Statistical Mechanics written by Mayer,J.and Mayer,M.in this article.展开更多
In this paper, a hybrid method based on the collocation and Newton-Kantorovich methods is used for solving the nonlinear singular Thomas-Fermi equation. At first, by using the Newton-Kantorovich method, the nonlinear ...In this paper, a hybrid method based on the collocation and Newton-Kantorovich methods is used for solving the nonlinear singular Thomas-Fermi equation. At first, by using the Newton-Kantorovich method, the nonlinear problem is converted to a sequence of linear differential equations, and then, the fractional order of rational Legendre functions are introduced and used for solving linear differential equations at each iteration based on the collocation method. Moreover, the boundary conditions of the problem by using Ritz method without domain truncation method are satisfied. In the end, the obtained results compare with other published in the literature to show the performance of the method, and the amounts of residual error are very small, which indicates the convergence of the method.展开更多
基金The project supported by National Natural Science Foundation of China under Grant No. 10075004 and the Chinese High Performance Computing Center (Beijing)
文摘The electric field in the crystal planar channels is studied by the Thomas Fermi method. The Thomas-Fermi equation and the corresponding boundary conditions are derived for the crystal planar channels. The numericalsolution for the electric field in the channels between (110) planes of the single crystal silicon and the critical angles ofchannelling protons in them are shown. Reasonable agreements with the experimental data are obtained. The resultsshow that the Thomas-Fermi method for the crystal works well in this study, and a microscopic research of the channelelectric field with the contribution of all atoms and the atomic ionization being taken into account is practical.
文摘Electron spectrum in doped n-Si quantum wires is calculated by the Thomas-Fermi (TF) method under finite temperatures. The many-body exchange corrections are taken into account. The doping profile is arbitrary. At the first stage, the electron potential energy is calculated from a simple two-dimensional equation. The effective iteration scheme is proposed there that is valid for multidimensional problems. Then the energy levels and wave functions of this quantum well are simulated from the Schrödinger equations. The expansion by the full set of eigenfunctions of the linear harmonic oscillator is used. The quantum mechanical perturbation theory can be utilized to compute the energy levels. Generally, the perturbation theory for degenerate energy levels should be used.
基金supported by the National Natural Science Foundation of China(Grant No.11264039)the Key Discipline of Theoretical Physics of Xinjiang,China(Grant Nos.LLWLY201202 and LLWLY201203)the Postgraduate Scientific and Theoretical Innovation Project of Xinjiang Normal University,China(Grant No.20131234)
文摘The damping and frequency-shift in Landau mechanism of a quadrupole mode in a disc-shaped rubidium Bose-Einstein condensate are investigated by using the Hartree-Fock-Bogoliubov approximation. The practical relaxations of the elementary excitations and the orthometric relation among them are taken into account to obtain advisable calculation formula for damping as well as frequency-shift. The first approximation of Gaussian distribution function is employed for the ground-state wavefunction to suitably eliminate the divergence of the analytic three-mode coupling matrix elements. According to these methods, both Landau damping rate and frequency-shift of the quadrupole mode are analytically calculated. In addition, all the theoretical results agree with the experimental ones.
基金the National Natural Science Foundation of China (No. 2003E103)the National High-Tech Research and Development Program of China (No. 2002AA331050)the Doctorate Foundation of North-western Polytechnical University (No. CX200507).
文摘In the present investigations,the fusion crosssections for the formation of 200Pb compound nucleus(CN)using 16O+184 W,30Si+170Er,and 40Ar+160Gd nuclear reactions at energies above the Coulomb barrier were calculated to understand the effect of entrance channel mass asymmetry(α)on the fusion reactions;the Skyrme energy density formalism(SEDF)was used for this calculation.The SEDF uses the Hartree-Fock-Bogolyubov(HFB)computational program with Skyrme forces such as SkM*,SLy4,and SLy5 to obtain the nucleus-nucleus potential parameters for the above reactions.Using the SEDF model with SkM*,SLy4,and SLy5 interaction forces,the theoretical fusion cross-sections were determined above the barrier energy and compared with the available experimental fusion cross-sections.The results show a close agreement between the theoretical and experimental values for all selected systems at energies well above the barrier.However,near the barrier energies,the theoretical values were observed to be higher than the experimental values.
基金Project supported by the National Natural Science Foundation of China(Grant No.11504164)
文摘Electromagnetic screening is studied from the perspective of fluid mechanics by generalizing the Drude theory, which unifies three known results： Thomas–Fermi screening of the longitudinal field in both metals and superconductors, the skin effect of the transverse field in metals, and the Meissner effect in superconductors. In the special case of superfluid electrons, we slightly generalize the London equations to incorporate the longitudinal electric fields. Moreover, regarding the experiments, our study points out that the dynamical measurement may overestimate the superfluid density.
文摘Thomas-Fermi theory is an approximate method, which is widely used to describe the properties of matter at various hierarchical levels (atomic nucleus, atom, molecule, solid, etc.). Special development is achieved using Thomas-Fermi theory to the theory of extreme states of matter appearing under high pressures, high temperatures or strong external fields. Relevant sections of physics and related sciences (astrophysics, quantum chemistry, a number of applied sciences) determine the scope of Thomas-Fermi theory. Popularity Thomas-Fermi theory is related to its relative simplicity, clarity and versatility. The latter means that the result of the calculation by Thomas-Fermi theory applies immediately to all chemical elements: the transition from element to element is as simple scale transformation. These features make it to be a highly convenient tool for qualitative and, in many cases, and quantitative analysis.
文摘In the 1970s,scientists began experimenting with powerful laser beams to compress and heat the hydrogen isotopes to the point of fusion,a technique called ICF(Inertial Confinement Fusion).In the“direct drive”approach to ICF,powerful beams of laser light are focused on a small spherical pellet containing micrograms of deuterium and tritium.The rapid heating caused by the laser“driver”makes the outer layer of the target explode.In keeping with Isaac Newton’s Third Law“For every action,there is an equal and opposite reaction”,the remaining portion of the target is driven inwards in a rocket-like implosion,causing compression of the fuel inside the capsule and the formation of a shock wave,which further heats the fuel in the very center and results in a self-sustaining burn.The fusion burn propagates outward through the cooler,outer regions of the capsule much more rapidly than the capsule can expand.Instead of magnetic fields,the plasma is confined by the inertia of its own mass—hence the term inertial confinement fusion.A similar process can be observed on an astrophysical scale in stars and the terrestrial uber world,that have exhausted their nuclear fuel,hence inertially or gravitationally collapsing and generating a supernova explosion,where the results can easily be converted to induction of energy in control forms for a peaceful purpose(i.e.,inertial fusion reaction)by means of thermal physics and statistical mechanics behavior of an ideal Fermi gas,utilizing Fermi-Degeneracy and Thomas-Fermi theory.The fundamental understanding of thermal physics and statistical mechanics enables us to have a better understanding of Fermi-Degeneracy as well as Thomas-Fermi theory of ideal gas,which results in laser compressing matter to a super high density for purpose of producing thermonuclear energy in way of controlled form for peaceful shape and form i.e.CTR(Controlled Thermonuclear Reaction).In this short review,we have concentrated on Fundamental of State Equations by driving them as it was evaluated in book Statistical Mechanics written by Mayer,J.and Mayer,M.in this article.
文摘In this paper, a hybrid method based on the collocation and Newton-Kantorovich methods is used for solving the nonlinear singular Thomas-Fermi equation. At first, by using the Newton-Kantorovich method, the nonlinear problem is converted to a sequence of linear differential equations, and then, the fractional order of rational Legendre functions are introduced and used for solving linear differential equations at each iteration based on the collocation method. Moreover, the boundary conditions of the problem by using Ritz method without domain truncation method are satisfied. In the end, the obtained results compare with other published in the literature to show the performance of the method, and the amounts of residual error are very small, which indicates the convergence of the method.
