Based on the mean-field theory,we investigate the thermodynamic properties of the two-dimensional(2D)charged spin-1/2 Fermi gas.Lande′factor g is introduced to measure the strength of the paramagnetic effect.There is...Based on the mean-field theory,we investigate the thermodynamic properties of the two-dimensional(2D)charged spin-1/2 Fermi gas.Lande′factor g is introduced to measure the strength of the paramagnetic effect.There is a competition between diamagnetism and paramagnetism in the system.The larger the Lande′factor,the smaller the entropy and specific heat.Diamagnetism tends to increase the entropy,while paramagnetism leads to the decrease of the entropy.We find that there exists a critical value of Lande′factor for the transition point due to the competition.The entropy of the system increases with the magnetic field when g<0.58.With the growth of paramagnetism,when g>0.58,the entropy first decreases with the magnetic field,then reaches a minimum value,and finally increases again.Both the entropy and specific heat increase with the temperature,and no phase transition occurs.The specific heat tends to a constant value at the hightemperature limit,and it approaches to zero at very low temperatures,which have been proved by the analytical calculation.展开更多
We have calculated the effective g-factor for the transitions in hydrogen-like atoms and applied it to atomic cesium. We have identified that not only the g* factor in this case is an integer number g* = 1, but also t...We have calculated the effective g-factor for the transitions in hydrogen-like atoms and applied it to atomic cesium. We have identified that not only the g* factor in this case is an integer number g* = 1, but also the existence of possible entangled states related to the above tran-sitions. Furthermore we have used the above result to calculate the transition energies which are in complete agreement (within the 1% margin error). Such results can give access to the production of new laser lights from atomic cesium.展开更多
The spinning period for a free electron and the periods of spin and orbital motion of the electron in an atomic state have been calculated. We have shown that for a free electron the spinning period is: (Ts)free=1.9&#...The spinning period for a free electron and the periods of spin and orbital motion of the electron in an atomic state have been calculated. We have shown that for a free electron the spinning period is: (Ts)free=1.9×10-20s. But in the atomic case we show that, both the spin and the orbital periods depend on the quantum numbers n, ml, ms and the effective Landé-g factor, g* which is a function of the quantum number l of the atomic state given in Dirac notation. We have also calculated these periods for the ground state and some excited states—hydrogen and hydrogen-like atoms. For atomic states the approximate values of spinning period are and the related orbital periods are: (T0)atomic=(10-16-10-15)s. Therefore atto-second processes which are related to the pulse of 10-18 s will filter the orbital motion of the electron but will be long enough to detect the details of the spin motion, such as flip-flops.展开更多
We have calculated the Zeeman-fine energies of atomic Lithium (Li) by using the varying effective Landé g-factor method. We take the principle quantum number in the range;(2 ≤n ≤10 ). For this range we find 26 ...We have calculated the Zeeman-fine energies of atomic Lithium (Li) by using the varying effective Landé g-factor method. We take the principle quantum number in the range;(2 ≤n ≤10 ). For this range we find 26 different energy values and 325 wavelengths some of which are the same. The Doppler shift is found to be Δλ=±0.004λ. The Doppler shift-corrected wavelengths are in perfect agreement with the observed (NIST) values for atomic Li.展开更多
The study of magnetic field effects on the clock transition of Mg and Cd optical lattice clocks is scarce.In this work,the hyperfine-induced Landég-factors and quadratic Zeeman shift coefficients of the nsnp ^(3)...The study of magnetic field effects on the clock transition of Mg and Cd optical lattice clocks is scarce.In this work,the hyperfine-induced Landég-factors and quadratic Zeeman shift coefficients of the nsnp ^(3)P_(0)^(o) clock states for ^(111,113)Cd and ^(25)Mg were calculated by using the multi-configuration Dirac–Hartree–Fock theory.To obtain accurate values of these parameters,the impact of electron correlations and furthermore the Breit interaction and quantum electrodynamical effects on the Zeeman and hyperfine interaction matrix elements,and energy separations were investigated in detail.We also estimated the contributions from perturbing states to the Landég-factors and quadratic Zeeman shift coefficients concerned so as to truncate the summation over the perturbing states without loss of accuracy.Our calculations provide important data for estimating the first-and second-order Zeeman shifts of the clock transition for the Cd and Mg optical lattice clocks.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.11774019)the Fundamental Research Funds for the Central Universities,China(Grant No.FRF-BR-16-014A)。
文摘Based on the mean-field theory,we investigate the thermodynamic properties of the two-dimensional(2D)charged spin-1/2 Fermi gas.Lande′factor g is introduced to measure the strength of the paramagnetic effect.There is a competition between diamagnetism and paramagnetism in the system.The larger the Lande′factor,the smaller the entropy and specific heat.Diamagnetism tends to increase the entropy,while paramagnetism leads to the decrease of the entropy.We find that there exists a critical value of Lande′factor for the transition point due to the competition.The entropy of the system increases with the magnetic field when g<0.58.With the growth of paramagnetism,when g>0.58,the entropy first decreases with the magnetic field,then reaches a minimum value,and finally increases again.Both the entropy and specific heat increase with the temperature,and no phase transition occurs.The specific heat tends to a constant value at the hightemperature limit,and it approaches to zero at very low temperatures,which have been proved by the analytical calculation.
文摘We have calculated the effective g-factor for the transitions in hydrogen-like atoms and applied it to atomic cesium. We have identified that not only the g* factor in this case is an integer number g* = 1, but also the existence of possible entangled states related to the above tran-sitions. Furthermore we have used the above result to calculate the transition energies which are in complete agreement (within the 1% margin error). Such results can give access to the production of new laser lights from atomic cesium.
文摘The spinning period for a free electron and the periods of spin and orbital motion of the electron in an atomic state have been calculated. We have shown that for a free electron the spinning period is: (Ts)free=1.9×10-20s. But in the atomic case we show that, both the spin and the orbital periods depend on the quantum numbers n, ml, ms and the effective Landé-g factor, g* which is a function of the quantum number l of the atomic state given in Dirac notation. We have also calculated these periods for the ground state and some excited states—hydrogen and hydrogen-like atoms. For atomic states the approximate values of spinning period are and the related orbital periods are: (T0)atomic=(10-16-10-15)s. Therefore atto-second processes which are related to the pulse of 10-18 s will filter the orbital motion of the electron but will be long enough to detect the details of the spin motion, such as flip-flops.
文摘We have calculated the Zeeman-fine energies of atomic Lithium (Li) by using the varying effective Landé g-factor method. We take the principle quantum number in the range;(2 ≤n ≤10 ). For this range we find 26 different energy values and 325 wavelengths some of which are the same. The Doppler shift is found to be Δλ=±0.004λ. The Doppler shift-corrected wavelengths are in perfect agreement with the observed (NIST) values for atomic Li.
基金Project supported by the National Natural Science Foundation of China (Grant No.61775220)the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No.XDB21030100)the Key Research Project of Frontier Science of the Chinese Academy of Sciences (Grant No.QYZDB-SSW-JSC004)。
文摘The study of magnetic field effects on the clock transition of Mg and Cd optical lattice clocks is scarce.In this work,the hyperfine-induced Landég-factors and quadratic Zeeman shift coefficients of the nsnp ^(3)P_(0)^(o) clock states for ^(111,113)Cd and ^(25)Mg were calculated by using the multi-configuration Dirac–Hartree–Fock theory.To obtain accurate values of these parameters,the impact of electron correlations and furthermore the Breit interaction and quantum electrodynamical effects on the Zeeman and hyperfine interaction matrix elements,and energy separations were investigated in detail.We also estimated the contributions from perturbing states to the Landég-factors and quadratic Zeeman shift coefficients concerned so as to truncate the summation over the perturbing states without loss of accuracy.Our calculations provide important data for estimating the first-and second-order Zeeman shifts of the clock transition for the Cd and Mg optical lattice clocks.
