Geometric double‐perturbation expansion of the coupled Hartree‐Fock second‐order energy

1974 ◽  
Vol 61 (9) ◽  
pp. 3737-3741 ◽  
Author(s):  
H. Nakatsuji ◽  
J. I. Musher
Keyword(s):  
Perturbation Expansion ◽  
Second Order ◽  
Hartree Fock ◽  
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.

Non-linear transverse waves in a Vlasov plasma

1969 ◽  
Vol 3 (4) ◽  
pp. 577-592 ◽  
Author(s):  
S. Peter Gary
Keyword(s):  
Perturbation Expansion ◽  
Second Order ◽  
Electron Cyclotron ◽  
Wave Number ◽  
Linear Dispersion ◽  
Transverse Waves ◽  
Non Linear ◽  
Long Time ◽  
Linear Damping ◽  
Electron Cyclotron Waves

Non-linear transverse waves in a classical non-relativistic collisionless, Maxwellian electron gas with external magnetic field B0 are considered. There is assumed a small, sinusoidal variation in the initial electric and magnetic fields, corresponding to excitation of a discrete wave-number mode. The non-linear Vlasov equation is solved to second order in the long time limit via the Montgomery—Gorman perturbation expansion, and the time-independent, spatially homogeneous part of the second-order distribution function is used to modify the linear dispersion relation. For frequencies near the electron cyclotron frequency a non-linear damping decrement results such that, for many values of the parameters, the damping is less than the linear rate. Thus at sufficiently long times, the rate of damping of transverse electron cyclotron waves should decrease, a result similar to that for non-linear damping of longitudinal electron plasma waves.

Sign in / Sign up

Export Citation Format

Share Document