We present a perturbation study of the ground-state energy of the beryllium atom by incorporating double parameters in the atom＇s Hamiltonian. The eigenvalue of the Hamiltonian is then solved with a double-fold pertu...We present a perturbation study of the ground-state energy of the beryllium atom by incorporating double parameters in the atom＇s Hamiltonian. The eigenvalue of the Hamiltonian is then solved with a double-fold perturbation scheme,where the spin-spin interaction of electrons from different shells of the atom is also considered. Calculations show that the obtained ground-state energy is in satisfactory agreement with experiment. It is found that the Coulomb repulsion of the inner-shell electrons enhances the effective nuclear charge seen by the outer-shell electrons, and the shielding effect of the outer-shell electrons to the nucleus is also notable compared with that of the inner-shell electrons.展开更多
In this paper, the electronic states of the ground states and dissociation limits of BC and BC- are correctly determined based on group theory and atomic and molecular reaction statics. The equilibrium geometries, har...In this paper, the electronic states of the ground states and dissociation limits of BC and BC- are correctly determined based on group theory and atomic and molecular reaction statics. The equilibrium geometries, harmonic frequencies and dissociation energies of the ground state of BC and BC- are calculated by using density function theory and quadratic CI method including single and double substitutions. The analytical potential energy functions of these states have been fitted with Murrell-Sorbie potential energy function from our ab initio calculation results. The spectroscopic data （αe, ωe and ωeχe） of each state is calculated via the relation between analytical potential energy function and spectroscopic data. All the calculations are in good agreement with the experimental data.展开更多
The purpose of this paper is to present a new general approach to solve ground-state energies of the double-electron systems in a uniform magnetic field, in which the basic element of evolution is the set in the solut...The purpose of this paper is to present a new general approach to solve ground-state energies of the double-electron systems in a uniform magnetic field, in which the basic element of evolution is the set in the solution space, rather than the point. The paper defines the Cell Evolutionary Algorithm, which implements such a view of the evolution mechanism. First, the optimal set in which the optimal solution may be obtained. Then this approach applies the embedded search method to get the optimal solution. We tested this approach on the atomic structure, and the results show that it can improve not only the efficiency but also the accuracy of the calculations as it relates to this specific problem.展开更多
Energies for the ground states of double electron systems in a uniform magnetic field B≤ 10 9 G are calculated by using the modified Slater basis and configuration interaction method, and the result for energy i...Energies for the ground states of double electron systems in a uniform magnetic field B≤ 10 9 G are calculated by using the modified Slater basis and configuration interaction method, and the result for energy in zero magnetic field is comparable with those obtained by different methods.展开更多
We present a global optimization method, called the real-code genetic algorithm (RGA), to the ground state energies. The proposed method does not require partial derivatives with respect to each variational parameter ...We present a global optimization method, called the real-code genetic algorithm (RGA), to the ground state energies. The proposed method does not require partial derivatives with respect to each variational parameter or solving an eigenequation, so the present method overcomes the major difficulties of the variational method. RGAs also do not require coding and encoding procedures, so the computation time and complexity are reduced. The ground state energies of hydrogenic donors in GaAs-(Ga,Al)As quantum dots have been calculated for a range of the radius of the quantum dot radii of practical interest. They are compared with those obtained by the variational method. The results obtained demonstrate the proposed method is simple, accurate, and easy implement.展开更多
There has been an increasing global and local interest in developing renewable, clean, and cheap energy towards achieving Goal number 7 of the Sustainable Development Goals (SDG). However, decisions involving suitable...There has been an increasing global and local interest in developing renewable, clean, and cheap energy towards achieving Goal number 7 of the Sustainable Development Goals (SDG). However, decisions involving suitable and sustainable locations for renewable energy projects remain an important task. This study employed Geographic Information System (GIS) and Multi-Criteria Decision Analysis (MCDA) to spatially analyze and model wind farm site suitability in Nasarawa State. The aim is to integrate the environmental, social, and economic aspects of decision-making for identifying sustainable wind farm sites. The study distinguished between two sets of decision criteria: decision constraints and decision factors. The former defined the exclusion zones while the latter were standardized based on fuzzy logic to depict varying degrees of suitability across the State. The MCDA applied the weighted linear combination method, with relative weights generated through pairwise comparisons of the analytic hierarchy process to analyze three policy scenarios: equal weights, environmental/social priority, and economic priority scenario. A combination of resulting composite maps from the constraints and the factors gave the final suitability maps. The resulting suitability index (SI) for the respective policy scenario describes the degrees of suitability: Ideal locations were denoted by one (1) and the not suitable locations by zero (0), with values in-between depicting varying degrees of wind farm site suitability. Based on the SI, priority locations indicating areas with good prospects, in addition to the most suitable parcels of land, were identified and delineated. The composite decision constraint revealed that wind farm projects would not be viable in more than half (57.58%) of the State. Wind speed was the major constraint and accounted for the exclusion of 46.25%, with a mean fuzzy membership value of 0.2008 indicating low suitability across the State. Also, the average acceptable wind farm location for the three-policy scenario was 33.33% of the entire study area. Lafia, Obi, Keana, Awe, Nasarawa-Eggon, Wamba and Kokona LGAs were the identified priority Local Government Areas (LGAs). However, only Lafia, Obi, and Nasarawa-Eggon were consistent with changes in the policy objectives. All the priority LGAs have one or more of the most suitable parcels within their administrative boundaries except for Wamba. Despite the severe limitations of wind speed, substantial parts of Nasarawa State still provide great development potentials for wind energy. The “most suitable” locations in Lafia, Nasarawa-Eggon, and Obi LGAs should have first consideration for the development of wind energy in the State.展开更多
The properties of large bipolarons in two and three dimensions are investigated by averaging over therelative wavefunction of the two electrons and using the Lee-Low-Pines-Huybrechts variational method.The ground-stat...The properties of large bipolarons in two and three dimensions are investigated by averaging over therelative wavefunction of the two electrons and using the Lee-Low-Pines-Huybrechts variational method.The ground-state(GS)and excited-state energies of the Frhlich bipolaron for the whole range of electron-phonon coupling constantscan be obtained.The energies of the first relaxed excited state(RES)and Franck-Condon(FC)excited state of thebipolaron are also calculated.It is found that the first RES energy is lower than the FC state energy.The comparisonof our GS and RES energies with those in literature is also given.展开更多
In <span style="font-family:;" "="">the </span><span style="font-family:;" "="">framework of the variational Monte Carlo method, the ground states of...In <span style="font-family:;" "="">the </span><span style="font-family:;" "="">framework of the variational Monte Carlo method, the ground states of the lithium atom and l</span><span style="font-family:;" "="">ithium like ions up to <i>Z</i> = 10 in an external strong magnetic field are evaluated. Furthermore, the two low-lying excited states <img src="Edit_d92f9e9d-e574-4fa3-91fb-a153db020509.png" alt="" /></span><span style="font-family:;" "="">, <span style="font-size:10.0pt;font-family:;" "=""><span></span></span><span style="font-size:10.0pt;font-family:;" "=""><span></span></span><span style="font-size:10.0pt;font-family:;" "=""><span></span></span><span style="font-size:10.0pt;font-family:;" "=""><span></span></span><span style="font-size:10.0pt;font-family:;" "=""><span></span></span><img src="data:image/png;base64,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" alt="" /> <img src="Edit_5bf0039b-89f7-4346-a3cb-178f5df359cf.png" width="0" height="0" alt="" /><img src="data:image/png;base64,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" alt="" /><img src="Edit_41f9b122-3fdc-4f01-9470-542944413516.png" alt="" /></span><span style="font-family:;" "="">and <img src="data:image/png;base64,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" alt="" /><span></span></span><span style="font-family:;" "=""><span> <img src="Edit_79f5e8c8-0b24-4dfd-8b9e-080183cc967f.png" alt="" /></span>of the lithium atom in strong magnetic field are also investigated</span><span style="font-family:;" "="">. </span><span style="font-family:;" "="">Simple trial wave functions for lithium are used.</span>展开更多
We study the ground-state information of one-dimensional Heisenberg chain with alternating D-term. Given the ground-state phase diagram, the ground-state energy and the entanglement entropy are obtained by tensor-net ...We study the ground-state information of one-dimensional Heisenberg chain with alternating D-term. Given the ground-state phase diagram, the ground-state energy and the entanglement entropy are obtained by tensor-net work algorithm. The phase transition points are shown in the entanglement entropy figure. The results are agreed with the phase diagram.展开更多
The influence of the electric field on the properties of the bound magnetopolaron in an infinite-depth GaAs semiconductor quantum well is investigated using the linear-combination operator and the unitary transformati...The influence of the electric field on the properties of the bound magnetopolaron in an infinite-depth GaAs semiconductor quantum well is investigated using the linear-combination operator and the unitary transformation method. The relationships between the polaron＇s ground state energy and the Coulomb bound potential, electric field, magnetic field, and well-width are derived and discussed. Our numerical results show that the absolute value of the polaron＇s ground state energy increases as the electric field and the Coulomb bound potential increase, and decreases as the well-width and the magnetic field strength increase. When the well-width is small,the quantum size effect is significant.展开更多
The properties of a bound polaron in a parabolic quantum dot with weak electron-LO-phonon coupling under a Coulomb field are studied. The ground state energy of the bound polaron is derived by using a linear combinati...The properties of a bound polaron in a parabolic quantum dot with weak electron-LO-phonon coupling under a Coulomb field are studied. The ground state energy of the bound polaron is derived by using a linear combination operator and the perturbation method. The influence of the interaction between phonons with different wave vectors in the recoil process on the ground state energy of the bound polaron is discussed. Numerical calculations are performed,and the results show that the ground state energy increases significantly as the effective confinement length of the quantum dot decreases,considering of the interaction between phonons. When l0〉1.0, the influence of the interaction between phonons on the ground state energy cannot be ignored.展开更多
Combining the first-principles calculations and structural enumeration with recognition,the delithiation process of LiNiO_(2)is investigated,where various supercell shapes are considered in order to obtain the formati...Combining the first-principles calculations and structural enumeration with recognition,the delithiation process of LiNiO_(2)is investigated,where various supercell shapes are considered in order to obtain the formation energy of Li_(x)NiO_(2).Meanwhile,the voltage profile is simulated and the ordered phases of lithium vacancies corresponding to concentrations of 1/4,2/5,3/7,1/2,2/3,3/4,5/6,and 6/7 are predicted.To understand the capacity decay in the experiment during the charge/discharge cycles,deoxygenation and Li/Ni antisite defects are calculated,revealing that the chains of oxygen vacancies will be energetically preferrable.It can be inferred that in the absence of oxygen atom in high delithiate state,the diffusion of Ni atoms is facilitated and the formation of Li/Ni antisite is induced.展开更多
By a combination method of Lee-Low-Pines unitary transformation method and Pekar-type variational method,the ground state energy(GSE)of the bound polaron is studied in the asymmetrical Gaussian potential quantum well ...By a combination method of Lee-Low-Pines unitary transformation method and Pekar-type variational method,the ground state energy(GSE)of the bound polaron is studied in the asymmetrical Gaussian potential quantum well considering the temperature and electromagneticfield.The impacts of the temperature and asymmetrical Gaussian potential,electromagnetic field and phonon-electron coupling upon the GSE are obtained.The results show that the GSE of the bound polaron not only oscillates as the temperature changes regardless of the electromagneticfield and asymmetrical Gaussian potential and Coulomb impurity potential(CIP)and electron-phonon coupling but also has different rules with the electromagnetic field and asymmetrical Gaussian potential and CIP and electron-phonon coupling at different temperature zones.展开更多
The equilibrium geometries, electronic structures and electronic properties including adiabatic electron affinity（AEA）, vertical detachment energy（VDE）, simulated photoelectron spectroscopy, HOMO-LUMO gap, charge ...The equilibrium geometries, electronic structures and electronic properties including adiabatic electron affinity（AEA）, vertical detachment energy（VDE）, simulated photoelectron spectroscopy, HOMO-LUMO gap, charge transfer, and magnetic moment for DySi_n（n = 3~10） clusters and their anions were systematically investigated by using the ABCluster global search technique combined with the B3 LYP and B2 PLYP density functional methods. The results showed that the lowest energy structure of neutral DySi_n（n = 3~10） can be regarded as substituting a Si atom of the ground state structure of Si_（n＋1） with a Dy atom. For anions, the extra electron effect on the structure is significant. Starting from n = 6, the lowest energy structures of DySi_n~？（n = 3~10） differ from those of neutral. The ground state is quintuplet electronic state for DySi_n（n = 3~10） excluding DySi_4 and DySi_9, which is a septet electronic state. For anions, the ground state is a sextuplet electronic state. The reliable AEA and VDE of DySi_n（n = 3~10） are reported. Analyses of HOMO-LUMO gaps indicated that doping Dy atom to silicon clusters can improve significantly their photochemical reactivity, especially for DySi_9. Analyses of NPA revealed that the 4 f electrons of Dy in DySi_4, DySi_9, and DySi_n~？ with n = 4 and 6~10 participate in bonding. That is, DySi_nbelongs to the AB type. The 4 f electrons of Dy atom provide substantially the total magnetic moments for DySi_n and their anions. The dissociation energies of Ln（Ln = Pr, Sm, Eu, Gd, Ho, and Dy） fromLn Sin and their anions were evaluated to examine the relative stabilities.展开更多
Magnetic field and temperature dependence of the properties of the ground state of the strong-coupling bound magnetopolaron in quantum rods （QRs） with hydrogenic impurity is studied by means of the Huybrechts- Lee-L...Magnetic field and temperature dependence of the properties of the ground state of the strong-coupling bound magnetopolaron in quantum rods （QRs） with hydrogenic impurity is studied by means of the Huybrechts- Lee-Low-Pines transformation method and the quantum statistical theory. The expressions for the ground-state energy and the mean number ofphonons of the magnetopolaron are derived. Results of the numerical calculations show that the bound state of the magnetopolaron cannot be formed when the value of the aspect ratio of the QR, the dielectric constant ratio, the electron-phonon coupling strength or the temperature parameter is small. The larger the deviation of the value of aspect ratio e′ from 1 is, the more it is unfavorable to the stability of the ground state of the magnetopolaron. When the magnetopolaron is in the bound state, the absolute value of its ground-state energy and its mean number ofphonons increase with an increase of the dielectric constant ratio and confinement strength of QRs, but decrease with an increase in the cyclotron frequency of the external magnetic field and the temperature. The absolute value of the ground-state energy and the mean number of phonons of the magnetopolaron decrease with decreasing e′ when e′ 〈 1, but decrease with increasing e′ when e′ 〉 1. They get the maximum value at e′=1.展开更多
The 62Sm, 64Gd, 66Dy, 70Yb, 72Hf and 74W nuclei are classified as deformed nuclei. Low-lying bands are one of the most fundamental excitation modes in the energy spectra of deformed nuclei. In this paper a theoretical...The 62Sm, 64Gd, 66Dy, 70Yb, 72Hf and 74W nuclei are classified as deformed nuclei. Low-lying bands are one of the most fundamental excitation modes in the energy spectra of deformed nuclei. In this paper a theoretical analysis of the experimental data within the phenomenological model is presented. The energy spectra of ground states are calculated. It is found that the low-lying spectra of ground band states are in good agreement with the experimental data.展开更多
We study the energy level crossing and the thermal fidelity in a two-qubit system with the presence of a transverse inhomogeneous magnetic field.With the help of contour plots,we clearly identify the ground states of ...We study the energy level crossing and the thermal fidelity in a two-qubit system with the presence of a transverse inhomogeneous magnetic field.With the help of contour plots,we clearly identify the ground states of the system in different regions of parameter space,and discuss the corresponding energy level crossing.The fidelity between the ground state of the system and the state of the system at temperature T is calculated.The result shows that the fidelity is very sensitive to the magnetic field anisotropic factor,indicating that this factor may be used as a controller of the fidelity.The influence of the Yangian transition operators on the fidelity of the system is discussed.We find that the Yangian operators can change the fidelity dramatically and give rise to sudden birth and sudden death phenomena of the thermal fidelity.This makes the corresponding Yangian operators possible candidates for switchers to turn the fidelity on and off.展开更多
We report results on electronic, transport, and bulk properties of rock-salt magnesium selenide (MgSe), from density functional theory (DFT) calculations. We utilized a local density approximation (LDA) potential and ...We report results on electronic, transport, and bulk properties of rock-salt magnesium selenide (MgSe), from density functional theory (DFT) calculations. We utilized a local density approximation (LDA) potential and the linear combination of atomic orbitals formalism (LCAO). We followed the Bagayoko, Zhao, and Williams (BZW) method, as enhanced by Ekuma and Franklin (BZW-EF), to perform a generalized minimization of the energy, down to the actual ground state of the material. We describe the successive, self-consistent calculations, with augmented basis sets, that are needed for this generalized minimization. Due to the generalized minimization, our results have the full, physical content of DFT, as per the second DFT theorem [AIP Advances, 4, 127104 (2014)]. Our calculated, indirect bandgap of 2.49 eV, for a room temperature lattice constant of 5.460 <span style="white-space:nowrap;">Å</span>, agrees with experimental findings. We present the ground-state band structure, the related total and partial densities of states, DOS and PDOS, respectively, and electron and hole effective masses for the material. Our calculated bulk modulus of 63.1 GPa is in excellent agreement with the experimental value of 62.8 ± 1.6 GPa. Our predicted equilibrium lattice constant, at zero temperature, is 5.424 <span style="white-space:nowrap;">Å</span>, with a corresponding indirect bandgap of 2.51 eV. We discuss the reasons for the agreements between our findings and available, corresponding, experimental ones, particularly for the band gap, unlike the previous DFT results obtained with ab-initio LDA or GGA potentials.展开更多
We study the two-dimensional weak-coupling Frohlich polaron in a completely anisotropic quantum dot in a perpendicular magnetic field. By performing a unitary transformation, we first transform the Hamiltonian into a ...We study the two-dimensional weak-coupling Frohlich polaron in a completely anisotropic quantum dot in a perpendicular magnetic field. By performing a unitary transformation, we first transform the Hamiltonian into a new one which describes an anisotropic harmonic oscillator with new mass and trapping frequencies interacting with the same phonon bath but with different interaction form and strength. Then employing the second-order Rayleigh–Schrodinger perturbation theory, we obtain the polaron correction to the ground-state energy. The magnetic field and anisotropic effects on the polaron correction to the ground-state energy are discussed.展开更多
Laser pulse nonlinear transmission measurements through saturable absorbers of known absorption parameters allow the measurement of their energy density. On the other hand, nonlinear transmission measurements of laser...Laser pulse nonlinear transmission measurements through saturable absorbers of known absorption parameters allow the measurement of their energy density. On the other hand, nonlinear transmission measurements of laser pulses of known energy density through absorbing media allow their absorption parameter determination. The peak energy density w0P of second harmonic pulses of a mode-locked titanium sapphire laser at wavelength λP = 400 nm is determined by nonlinear energy transmission measurement TE through the dye ADS084BE (1,4-bis(9-ethyl-3-car-bazovinylene)-2-methoxy-5-(2’-ethyl-hexyloxy)-benzene) in tetrahydrofuran. TE(w0P) calibration curves are calculated for laser pulse peak energy density reading w0P from measured pulse energy transmissions TE. The ground-state absorption cross-section σP and the excited-state absorption cross-section σex at λP, and the number density N0 of the retinal Schiff base isoform RetA in pH 7.4 buffer of the blue-light adapted recombinant rhodopsin fragment of the histidine kinase rhodopsin HKR1 from Chlamydomonas reinhardtii were determined by picosecond titanium sapphire second harmonic laser pulse energy transmission measurement TE through RetA as a function of laser input peak energy density w0P. The complete absorption cross-section spectrum展开更多
基金Project supported by the National Natural Science Foundation of China(Grant No.11647071)the Natural Science Foundation of Jiangsu Province,China(Grant No.BK20160435)
文摘We present a perturbation study of the ground-state energy of the beryllium atom by incorporating double parameters in the atom＇s Hamiltonian. The eigenvalue of the Hamiltonian is then solved with a double-fold perturbation scheme,where the spin-spin interaction of electrons from different shells of the atom is also considered. Calculations show that the obtained ground-state energy is in satisfactory agreement with experiment. It is found that the Coulomb repulsion of the inner-shell electrons enhances the effective nuclear charge seen by the outer-shell electrons, and the shielding effect of the outer-shell electrons to the nucleus is also notable compared with that of the inner-shell electrons.
文摘In this paper, the electronic states of the ground states and dissociation limits of BC and BC- are correctly determined based on group theory and atomic and molecular reaction statics. The equilibrium geometries, harmonic frequencies and dissociation energies of the ground state of BC and BC- are calculated by using density function theory and quadratic CI method including single and double substitutions. The analytical potential energy functions of these states have been fitted with Murrell-Sorbie potential energy function from our ab initio calculation results. The spectroscopic data （αe, ωe and ωeχe） of each state is calculated via the relation between analytical potential energy function and spectroscopic data. All the calculations are in good agreement with the experimental data.
基金Supported by the opening Foundation of state key Laboratory of Magnetic Resonance and Atomic and Molecularphysics, Wuhan Insti
文摘The purpose of this paper is to present a new general approach to solve ground-state energies of the double-electron systems in a uniform magnetic field, in which the basic element of evolution is the set in the solution space, rather than the point. The paper defines the Cell Evolutionary Algorithm, which implements such a view of the evolution mechanism. First, the optimal set in which the optimal solution may be obtained. Then this approach applies the embedded search method to get the optimal solution. We tested this approach on the atomic structure, and the results show that it can improve not only the efficiency but also the accuracy of the calculations as it relates to this specific problem.
文摘Energies for the ground states of double electron systems in a uniform magnetic field B≤ 10 9 G are calculated by using the modified Slater basis and configuration interaction method, and the result for energy in zero magnetic field is comparable with those obtained by different methods.
文摘We present a global optimization method, called the real-code genetic algorithm (RGA), to the ground state energies. The proposed method does not require partial derivatives with respect to each variational parameter or solving an eigenequation, so the present method overcomes the major difficulties of the variational method. RGAs also do not require coding and encoding procedures, so the computation time and complexity are reduced. The ground state energies of hydrogenic donors in GaAs-(Ga,Al)As quantum dots have been calculated for a range of the radius of the quantum dot radii of practical interest. They are compared with those obtained by the variational method. The results obtained demonstrate the proposed method is simple, accurate, and easy implement.
文摘There has been an increasing global and local interest in developing renewable, clean, and cheap energy towards achieving Goal number 7 of the Sustainable Development Goals (SDG). However, decisions involving suitable and sustainable locations for renewable energy projects remain an important task. This study employed Geographic Information System (GIS) and Multi-Criteria Decision Analysis (MCDA) to spatially analyze and model wind farm site suitability in Nasarawa State. The aim is to integrate the environmental, social, and economic aspects of decision-making for identifying sustainable wind farm sites. The study distinguished between two sets of decision criteria: decision constraints and decision factors. The former defined the exclusion zones while the latter were standardized based on fuzzy logic to depict varying degrees of suitability across the State. The MCDA applied the weighted linear combination method, with relative weights generated through pairwise comparisons of the analytic hierarchy process to analyze three policy scenarios: equal weights, environmental/social priority, and economic priority scenario. A combination of resulting composite maps from the constraints and the factors gave the final suitability maps. The resulting suitability index (SI) for the respective policy scenario describes the degrees of suitability: Ideal locations were denoted by one (1) and the not suitable locations by zero (0), with values in-between depicting varying degrees of wind farm site suitability. Based on the SI, priority locations indicating areas with good prospects, in addition to the most suitable parcels of land, were identified and delineated. The composite decision constraint revealed that wind farm projects would not be viable in more than half (57.58%) of the State. Wind speed was the major constraint and accounted for the exclusion of 46.25%, with a mean fuzzy membership value of 0.2008 indicating low suitability across the State. Also, the average acceptable wind farm location for the three-policy scenario was 33.33% of the entire study area. Lafia, Obi, Keana, Awe, Nasarawa-Eggon, Wamba and Kokona LGAs were the identified priority Local Government Areas (LGAs). However, only Lafia, Obi, and Nasarawa-Eggon were consistent with changes in the policy objectives. All the priority LGAs have one or more of the most suitable parcels within their administrative boundaries except for Wamba. Despite the severe limitations of wind speed, substantial parts of Nasarawa State still provide great development potentials for wind energy. The “most suitable” locations in Lafia, Nasarawa-Eggon, and Obi LGAs should have first consideration for the development of wind energy in the State.
基金the Natural Science Foundation of the Education Bureau of Zhejiang Province under Grant No.200601309partially by National Natural Science Foundation of China under Grant No.10274067
文摘The properties of large bipolarons in two and three dimensions are investigated by averaging over therelative wavefunction of the two electrons and using the Lee-Low-Pines-Huybrechts variational method.The ground-state(GS)and excited-state energies of the Frhlich bipolaron for the whole range of electron-phonon coupling constantscan be obtained.The energies of the first relaxed excited state(RES)and Franck-Condon(FC)excited state of thebipolaron are also calculated.It is found that the first RES energy is lower than the FC state energy.The comparisonof our GS and RES energies with those in literature is also given.
文摘In <span style="font-family:;" "="">the </span><span style="font-family:;" "="">framework of the variational Monte Carlo method, the ground states of the lithium atom and l</span><span style="font-family:;" "="">ithium like ions up to <i>Z</i> = 10 in an external strong magnetic field are evaluated. Furthermore, the two low-lying excited states <img src="Edit_d92f9e9d-e574-4fa3-91fb-a153db020509.png" alt="" /></span><span style="font-family:;" "="">, <span style="font-size:10.0pt;font-family:;" "=""><span></span></span><span style="font-size:10.0pt;font-family:;" "=""><span></span></span><span style="font-size:10.0pt;font-family:;" "=""><span></span></span><span style="font-size:10.0pt;font-family:;" "=""><span></span></span><span style="font-size:10.0pt;font-family:;" "=""><span></span></span><img src="data:image/png;base64,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" alt="" /> <img src="Edit_5bf0039b-89f7-4346-a3cb-178f5df359cf.png" width="0" height="0" alt="" /><img src="data:image/png;base64,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" alt="" /><img src="Edit_41f9b122-3fdc-4f01-9470-542944413516.png" alt="" /></span><span style="font-family:;" "="">and <img src="data:image/png;base64,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" alt="" /><span></span></span><span style="font-family:;" "=""><span> <img src="Edit_79f5e8c8-0b24-4dfd-8b9e-080183cc967f.png" alt="" /></span>of the lithium atom in strong magnetic field are also investigated</span><span style="font-family:;" "="">. </span><span style="font-family:;" "="">Simple trial wave functions for lithium are used.</span>
文摘We study the ground-state information of one-dimensional Heisenberg chain with alternating D-term. Given the ground-state phase diagram, the ground-state energy and the entanglement entropy are obtained by tensor-net work algorithm. The phase transition points are shown in the entanglement entropy figure. The results are agreed with the phase diagram.
文摘The influence of the electric field on the properties of the bound magnetopolaron in an infinite-depth GaAs semiconductor quantum well is investigated using the linear-combination operator and the unitary transformation method. The relationships between the polaron＇s ground state energy and the Coulomb bound potential, electric field, magnetic field, and well-width are derived and discussed. Our numerical results show that the absolute value of the polaron＇s ground state energy increases as the electric field and the Coulomb bound potential increase, and decreases as the well-width and the magnetic field strength increase. When the well-width is small,the quantum size effect is significant.
文摘The properties of a bound polaron in a parabolic quantum dot with weak electron-LO-phonon coupling under a Coulomb field are studied. The ground state energy of the bound polaron is derived by using a linear combination operator and the perturbation method. The influence of the interaction between phonons with different wave vectors in the recoil process on the ground state energy of the bound polaron is discussed. Numerical calculations are performed,and the results show that the ground state energy increases significantly as the effective confinement length of the quantum dot decreases,considering of the interaction between phonons. When l0〉1.0, the influence of the interaction between phonons on the ground state energy cannot be ignored.
基金Project supported by the Science Fund of the Guangdong Major Project of Basic and Applied Basic Research,China(Grant No.2019B030302011)the Fund of the Science and Technology Program of Guangzhou,China(Grant No.202201010090)。
文摘Combining the first-principles calculations and structural enumeration with recognition,the delithiation process of LiNiO_(2)is investigated,where various supercell shapes are considered in order to obtain the formation energy of Li_(x)NiO_(2).Meanwhile,the voltage profile is simulated and the ordered phases of lithium vacancies corresponding to concentrations of 1/4,2/5,3/7,1/2,2/3,3/4,5/6,and 6/7 are predicted.To understand the capacity decay in the experiment during the charge/discharge cycles,deoxygenation and Li/Ni antisite defects are calculated,revealing that the chains of oxygen vacancies will be energetically preferrable.It can be inferred that in the absence of oxygen atom in high delithiate state,the diffusion of Ni atoms is facilitated and the formation of Li/Ni antisite is induced.
基金supported by the National Natural Science Foundation of China under Grant No.11975011。
文摘By a combination method of Lee-Low-Pines unitary transformation method and Pekar-type variational method,the ground state energy(GSE)of the bound polaron is studied in the asymmetrical Gaussian potential quantum well considering the temperature and electromagneticfield.The impacts of the temperature and asymmetrical Gaussian potential,electromagnetic field and phonon-electron coupling upon the GSE are obtained.The results show that the GSE of the bound polaron not only oscillates as the temperature changes regardless of the electromagneticfield and asymmetrical Gaussian potential and Coulomb impurity potential(CIP)and electron-phonon coupling but also has different rules with the electromagnetic field and asymmetrical Gaussian potential and CIP and electron-phonon coupling at different temperature zones.
基金Supported by the National Natural Science Foundation of China(21263010)Program for Innovative Research Team in Universities of Inner Mongolia Autonomous Region(NMGIRT-A1603)Inner Mongolia Natural Science Foundation(2015MS0216)
文摘The equilibrium geometries, electronic structures and electronic properties including adiabatic electron affinity（AEA）, vertical detachment energy（VDE）, simulated photoelectron spectroscopy, HOMO-LUMO gap, charge transfer, and magnetic moment for DySi_n（n = 3~10） clusters and their anions were systematically investigated by using the ABCluster global search technique combined with the B3 LYP and B2 PLYP density functional methods. The results showed that the lowest energy structure of neutral DySi_n（n = 3~10） can be regarded as substituting a Si atom of the ground state structure of Si_（n＋1） with a Dy atom. For anions, the extra electron effect on the structure is significant. Starting from n = 6, the lowest energy structures of DySi_n~？（n = 3~10） differ from those of neutral. The ground state is quintuplet electronic state for DySi_n（n = 3~10） excluding DySi_4 and DySi_9, which is a septet electronic state. For anions, the ground state is a sextuplet electronic state. The reliable AEA and VDE of DySi_n（n = 3~10） are reported. Analyses of HOMO-LUMO gaps indicated that doping Dy atom to silicon clusters can improve significantly their photochemical reactivity, especially for DySi_9. Analyses of NPA revealed that the 4 f electrons of Dy in DySi_4, DySi_9, and DySi_n~？ with n = 4 and 6~10 participate in bonding. That is, DySi_nbelongs to the AB type. The 4 f electrons of Dy atom provide substantially the total magnetic moments for DySi_n and their anions. The dissociation energies of Ln（Ln = Pr, Sm, Eu, Gd, Ho, and Dy） fromLn Sin and their anions were evaluated to examine the relative stabilities.
基金supported by the Natural Science Foundation of Hebei Province(No.A2008000463)the Science and Technology Research and Development Plan of Qinhuangdao(No.201101A027)
文摘Magnetic field and temperature dependence of the properties of the ground state of the strong-coupling bound magnetopolaron in quantum rods （QRs） with hydrogenic impurity is studied by means of the Huybrechts- Lee-Low-Pines transformation method and the quantum statistical theory. The expressions for the ground-state energy and the mean number ofphonons of the magnetopolaron are derived. Results of the numerical calculations show that the bound state of the magnetopolaron cannot be formed when the value of the aspect ratio of the QR, the dielectric constant ratio, the electron-phonon coupling strength or the temperature parameter is small. The larger the deviation of the value of aspect ratio e′ from 1 is, the more it is unfavorable to the stability of the ground state of the magnetopolaron. When the magnetopolaron is in the bound state, the absolute value of its ground-state energy and its mean number ofphonons increase with an increase of the dielectric constant ratio and confinement strength of QRs, but decrease with an increase in the cyclotron frequency of the external magnetic field and the temperature. The absolute value of the ground-state energy and the mean number of phonons of the magnetopolaron decrease with decreasing e′ when e′ 〈 1, but decrease with increasing e′ when e′ 〉 1. They get the maximum value at e′=1.
基金Supported by IIUM University Research Grant Type B(EDW B13-034-0919)MOHE Fundamental Research Grant Scheme(FRGS13-074-0315)
文摘The 62Sm, 64Gd, 66Dy, 70Yb, 72Hf and 74W nuclei are classified as deformed nuclei. Low-lying bands are one of the most fundamental excitation modes in the energy spectra of deformed nuclei. In this paper a theoretical analysis of the experimental data within the phenomenological model is presented. The energy spectra of ground states are calculated. It is found that the low-lying spectra of ground band states are in good agreement with the experimental data.
基金Project supported by the National Natural Science Foundation of China(Grant No.11075101)the Science & Technology Committee of Shanghai Municipality,China(Grant Nos.08dj1400202 and 09PJ1404700)+1 种基金the Training Fund of NENU's Scientific Innvovation Project,China(Grant No.NENU-STC08018)the Ph.D.Program Foundation of Ministry of Education of China (Grant No.20093108110004)
文摘We study the energy level crossing and the thermal fidelity in a two-qubit system with the presence of a transverse inhomogeneous magnetic field.With the help of contour plots,we clearly identify the ground states of the system in different regions of parameter space,and discuss the corresponding energy level crossing.The fidelity between the ground state of the system and the state of the system at temperature T is calculated.The result shows that the fidelity is very sensitive to the magnetic field anisotropic factor,indicating that this factor may be used as a controller of the fidelity.The influence of the Yangian transition operators on the fidelity of the system is discussed.We find that the Yangian operators can change the fidelity dramatically and give rise to sudden birth and sudden death phenomena of the thermal fidelity.This makes the corresponding Yangian operators possible candidates for switchers to turn the fidelity on and off.
文摘We report results on electronic, transport, and bulk properties of rock-salt magnesium selenide (MgSe), from density functional theory (DFT) calculations. We utilized a local density approximation (LDA) potential and the linear combination of atomic orbitals formalism (LCAO). We followed the Bagayoko, Zhao, and Williams (BZW) method, as enhanced by Ekuma and Franklin (BZW-EF), to perform a generalized minimization of the energy, down to the actual ground state of the material. We describe the successive, self-consistent calculations, with augmented basis sets, that are needed for this generalized minimization. Due to the generalized minimization, our results have the full, physical content of DFT, as per the second DFT theorem [AIP Advances, 4, 127104 (2014)]. Our calculated, indirect bandgap of 2.49 eV, for a room temperature lattice constant of 5.460 <span style="white-space:nowrap;">Å</span>, agrees with experimental findings. We present the ground-state band structure, the related total and partial densities of states, DOS and PDOS, respectively, and electron and hole effective masses for the material. Our calculated bulk modulus of 63.1 GPa is in excellent agreement with the experimental value of 62.8 ± 1.6 GPa. Our predicted equilibrium lattice constant, at zero temperature, is 5.424 <span style="white-space:nowrap;">Å</span>, with a corresponding indirect bandgap of 2.51 eV. We discuss the reasons for the agreements between our findings and available, corresponding, experimental ones, particularly for the band gap, unlike the previous DFT results obtained with ab-initio LDA or GGA potentials.
基金Project supported by the National Natural Science Foundation of China(Grant No.11375090)the K.C.Wong Magna Foundation in Ningbo University,China
文摘We study the two-dimensional weak-coupling Frohlich polaron in a completely anisotropic quantum dot in a perpendicular magnetic field. By performing a unitary transformation, we first transform the Hamiltonian into a new one which describes an anisotropic harmonic oscillator with new mass and trapping frequencies interacting with the same phonon bath but with different interaction form and strength. Then employing the second-order Rayleigh–Schrodinger perturbation theory, we obtain the polaron correction to the ground-state energy. The magnetic field and anisotropic effects on the polaron correction to the ground-state energy are discussed.
文摘Laser pulse nonlinear transmission measurements through saturable absorbers of known absorption parameters allow the measurement of their energy density. On the other hand, nonlinear transmission measurements of laser pulses of known energy density through absorbing media allow their absorption parameter determination. The peak energy density w0P of second harmonic pulses of a mode-locked titanium sapphire laser at wavelength λP = 400 nm is determined by nonlinear energy transmission measurement TE through the dye ADS084BE (1,4-bis(9-ethyl-3-car-bazovinylene)-2-methoxy-5-(2’-ethyl-hexyloxy)-benzene) in tetrahydrofuran. TE(w0P) calibration curves are calculated for laser pulse peak energy density reading w0P from measured pulse energy transmissions TE. The ground-state absorption cross-section σP and the excited-state absorption cross-section σex at λP, and the number density N0 of the retinal Schiff base isoform RetA in pH 7.4 buffer of the blue-light adapted recombinant rhodopsin fragment of the histidine kinase rhodopsin HKR1 from Chlamydomonas reinhardtii were determined by picosecond titanium sapphire second harmonic laser pulse energy transmission measurement TE through RetA as a function of laser input peak energy density w0P. The complete absorption cross-section spectrum
