A Second Order Energy Dissipative Scheme for Time Fractional L$$^{2}$$ Gradient Flows using SAV Approach

2021 ◽  
Vol 90 (1) ◽  
Author(s):  
Dianming Hou ◽  
Chuanju Xu
Keyword(s):  
Second Order ◽  
Gradient Flows ◽  
Order Energy

Adiabatic second-order energy derivatives in quantum mechanics

1958 ◽  
Vol 54 (2) ◽  
pp. 251-257 ◽  
Author(s):  
W. Byers Brown ◽  
H. C. Longuet Higgins
Keyword(s):  
Quantum Mechanics ◽  
General Equation ◽  
Canonical Ensemble ◽  
Second Order ◽  
Order Derivative ◽  
Interacting Particles ◽  
Energy Derivatives ◽  
Order Energy ◽  
Classical Analogue ◽  
Image Position

ABSTRACTThe general equation for the adiabatic second-order derivative of the energy En of an eigenstate with respect to parameters λ and λ′ occurring in the Hamiltonian ℋ isThe applications of this equation to molecules (λ, λ′ = nuclear position coordinates) and to enclosed assemblies of interacting particles (λ = λ′ = volume) are discussed, and the classical analogue of the equation for a micro-canonical ensemble is derived.

scholarly journals Near-infrared quantum cutting in Ho3+, Yb3+-codoped BaGdF5 nanoparticles via first- and second-order energy transfers

2012 ◽  
Vol 7 (1) ◽  
pp. 636 ◽  
Author(s):  
Linna Guo ◽  
Yuhua Wang ◽  
Jia Zhang ◽  
Yanzhao Wang ◽  
Pengyu Dong
Keyword(s):  
Near Infrared ◽  
Second Order ◽  
Order Energy ◽  
Energy Transfers ◽  
Quantum Cutting
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