Applying the improved Rayleigh SchrSdinger perturbation theory based on an integral equation to helium-like ions in ground states and treating electron correlations as perturbations, we obtain the second-order correct...Applying the improved Rayleigh SchrSdinger perturbation theory based on an integral equation to helium-like ions in ground states and treating electron correlations as perturbations, we obtain the second-order corrections to wavefunctions consisting of a few terms and the third-order corrections to energicity. It is demonstrated that the corrected wavefunctions are bounded and quadratically integrable, and the corresponding perturbation series is convergent. The results clear off the previous distrust for the convergence in the quantum perturbation theory and show a reciprocal development on the quantum perturbation problem of the ground state helium-like systems.展开更多
A universal relation between the leading correction to the entropy and extremality was proposed in the work of Goon and Penco.In this paper,we extend this work to massive gravity and investigate thermodynamic extremal...A universal relation between the leading correction to the entropy and extremality was proposed in the work of Goon and Penco.In this paper,we extend this work to massive gravity and investigate thermodynamic extremality relations in a topologically higher-dimensional black hole.A rescaled cosmological constant is added to the action of the massive gravity as a perturbative correction.This correction modifies the extremality bound of the black hole and leads to shifts in the mass,entropy,etc.Regarding the cosmological constant as a variable related to pressure,we obtain the thermodynamic extremality relations between the mass and entropy,pressure,charge,and parameters ci by accurate calculations.Finally,these relations are verified by a triple product identity,which shows that the universal relation exists in black holes.展开更多
基金supported by the National Natural Science Foundation of China (Grant No 10575034)the Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics of China (Grant No T152504)
文摘Applying the improved Rayleigh SchrSdinger perturbation theory based on an integral equation to helium-like ions in ground states and treating electron correlations as perturbations, we obtain the second-order corrections to wavefunctions consisting of a few terms and the third-order corrections to energicity. It is demonstrated that the corrected wavefunctions are bounded and quadratically integrable, and the corresponding perturbation series is convergent. The results clear off the previous distrust for the convergence in the quantum perturbation theory and show a reciprocal development on the quantum perturbation problem of the ground state helium-like systems.
基金Supported by NSF C(11875196,11375121,11205125,11005016)Xihua University Talent Project(Z201021)。
文摘A universal relation between the leading correction to the entropy and extremality was proposed in the work of Goon and Penco.In this paper,we extend this work to massive gravity and investigate thermodynamic extremality relations in a topologically higher-dimensional black hole.A rescaled cosmological constant is added to the action of the massive gravity as a perturbative correction.This correction modifies the extremality bound of the black hole and leads to shifts in the mass,entropy,etc.Regarding the cosmological constant as a variable related to pressure,we obtain the thermodynamic extremality relations between the mass and entropy,pressure,charge,and parameters ci by accurate calculations.Finally,these relations are verified by a triple product identity,which shows that the universal relation exists in black holes.
