Stopping power beyond the adiabatic approximation

Appearance of Gauge Fields and Forces beyond the adiabatic approximation

Stopping Stochastic Approximation

The practical application of stochastic approximation methods require a reliable means to stop the iterative process when the estimate is close to the optimal value or when further improvement of the estimate is doubtful. Conventional ideas on stopping stochastic algorithms employ probabilistic criteria based on the asymptotic distribution of the stochastic approximation process, often with the...

Two-magnon scattering and the spin-phonon interaction beyond the adiabatic approximation.

We consider a model of Raman scattering for a two–dimensional S = 1/2 Heisenberg Anti-Ferromagnet which includes a dynamical spin–phonon interaction. We observe a broadening of the line shape due to increased coupling with excited high–energy spin states. Our results are close to a model of random, static exchange interactions, first introduced in this context by Haas et al. [J. Appl. Phys. 75,...

Ionization of the hydrogen atom in strong magnetic fields Beyond the adiabatic approximation

High magnetic fields in neutron stars, B ∼ 1011 − 1013 G, substantially modify the properties of atoms and their interaction with radiation. In particular, the photoionization cross section becomes anisotropic and polarization dependent, being strongly reduced when the radiation is polarized perpendicular to the field. In a number of previous works based on the adiabatic approximation the concl...

Excitation energies from time-dependent density-functional theory beyond the adiabatic approximation.

Time-dependent density-functional theory in the adiabatic approximation has been very successful for calculating excitation energies in molecular systems. This paper studies nonadiabatic effects for excitation energies, using the current-density functional of Vignale and Kohn [Phys. Rev. Lett. 77, 2037 (1996)]. We derive a general analytic expression for nonadiabatic corrections to excitation e...