We present an improved Born-Oppenheimer method for the treatment of molecules. Our development is based on taking into account a portion of the kinetic energy which was inadvertently omitted by Born and Oppenheimer. O...We present an improved Born-Oppenheimer method for the treatment of molecules. Our development is based on taking into account a portion of the kinetic energy which was inadvertently omitted by Born and Oppenheimer. Our theory replaces the set of standard atom-atom potentials by an evolution operator. In particular, in contrast to the traditional Born-Oppenheimer method our amended basis describes the so-called Wannier phenomenon which deforms potential surfaces, and traps one or more threshold electrons into an unstable equilibrium. Within our framework that trapping manifests itself as a Fresnel distribution. Finally we discover a π/2 phase jump in the evolution operator caused by the diffraction of a two-electron wave from a potential ridge.展开更多
We apply the second-order Born-Oppenheimer （BO） approximation to investigate the dynamics of the Rabi model, which describes the interaction between a two-level system and a single bosonic mode beyond the rotating w...We apply the second-order Born-Oppenheimer （BO） approximation to investigate the dynamics of the Rabi model, which describes the interaction between a two-level system and a single bosonic mode beyond the rotating wave approxi- mation. By comparing with the numerical results, we find that our approach works well when the frequency of the two-level system is much smaller than that of the bosonic mode.展开更多
The Tolman-Oppenheimer-Volkov (TOV) equation is solved with a new ansatz: the external boundary condition with mass M<sub>0</sub> and radius R<sub>1</sub> is dual to the internal boundary condi...The Tolman-Oppenheimer-Volkov (TOV) equation is solved with a new ansatz: the external boundary condition with mass M<sub>0</sub> and radius R<sub>1</sub> is dual to the internal boundary condition with density ρ<sub>bc</sub> and inner radius r<sub>i</sub>, and the two boundary conditions yield the same result. The inner boundary condition is imposed with a density ρ<sub>bc</sub> and an inner radius r<sub>i</sub>, which is zero for the compact neutron stars, but non-zero for the shell-stars: stellar shell-star and galactic (supermassive) shell-star. Parametric solutions are calculated for neutron stars, stellar shell-stars, and galactic shell-stars. From the results, an M-R-relation and mass limits for these star models can be extracted. A new method is found for solving the Einstein equations for Kerr space-time with matter (extended Kerr space-time), i.e. rotating matter distribution in its own gravitational field. Then numerical solutions are calculated for several astrophysical models: white dwarf, neutron star, stellar shell-star, and galactic shell-star. The results are that shell-star star models closely resemble the behaviour of abstract black holes, including the Bekenstein-Hawking entropy, but have finite redshifts and escape velocity v c and no singularity.展开更多
文摘We present an improved Born-Oppenheimer method for the treatment of molecules. Our development is based on taking into account a portion of the kinetic energy which was inadvertently omitted by Born and Oppenheimer. Our theory replaces the set of standard atom-atom potentials by an evolution operator. In particular, in contrast to the traditional Born-Oppenheimer method our amended basis describes the so-called Wannier phenomenon which deforms potential surfaces, and traps one or more threshold electrons into an unstable equilibrium. Within our framework that trapping manifests itself as a Fresnel distribution. Finally we discover a π/2 phase jump in the evolution operator caused by the diffraction of a two-electron wave from a potential ridge.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.10975181 and 11175247)the National Basic Research Program of China(Grant No.2012CB922104)
文摘We apply the second-order Born-Oppenheimer （BO） approximation to investigate the dynamics of the Rabi model, which describes the interaction between a two-level system and a single bosonic mode beyond the rotating wave approxi- mation. By comparing with the numerical results, we find that our approach works well when the frequency of the two-level system is much smaller than that of the bosonic mode.
文摘The Tolman-Oppenheimer-Volkov (TOV) equation is solved with a new ansatz: the external boundary condition with mass M<sub>0</sub> and radius R<sub>1</sub> is dual to the internal boundary condition with density ρ<sub>bc</sub> and inner radius r<sub>i</sub>, and the two boundary conditions yield the same result. The inner boundary condition is imposed with a density ρ<sub>bc</sub> and an inner radius r<sub>i</sub>, which is zero for the compact neutron stars, but non-zero for the shell-stars: stellar shell-star and galactic (supermassive) shell-star. Parametric solutions are calculated for neutron stars, stellar shell-stars, and galactic shell-stars. From the results, an M-R-relation and mass limits for these star models can be extracted. A new method is found for solving the Einstein equations for Kerr space-time with matter (extended Kerr space-time), i.e. rotating matter distribution in its own gravitational field. Then numerical solutions are calculated for several astrophysical models: white dwarf, neutron star, stellar shell-star, and galactic shell-star. The results are that shell-star star models closely resemble the behaviour of abstract black holes, including the Bekenstein-Hawking entropy, but have finite redshifts and escape velocity v c and no singularity.
基金Supported by the Science Foundation of Fujian Educational Department (JA03159) the Science ResearchFoundation of Putian University(2004Q003 2004Q002)
