Adiabatic Decoupling and Time-Dependent Born–Oppenheimer Theory

Adiabatic Decoupling and Time-Dependent Born-Oppenheimer Theory

We reconsider the time-dependent Born-Oppenheimer theory with the goal to carefully separate between the adiabatic decoupling of a given group of energy bands from their orthogonal subspace and the semiclassics within the energy bands. Band crossings are allowed and our results are local in the sense that they hold up to the first time when a band crossing is encountered. The adiabatic decoupli...

Adiabatic approximation in nonperturbative time-dependent density-functional theory.

We construct the exact exchange-correlation potential of time-dependent density-functional theory and the approximation to it that is adiabatic but exact otherwise. For the strong-field double ionization of the Helium atom these two potentials are virtually identical. Thus, memory effects play a negligible role in this paradigm process of nonlinear, nonperturbative electron dynamics. We identif...

Adiabatic approximation of time-dependent density matrix functional response theory.

Time-dependent density matrix functional theory can be formulated in terms of coupled-perturbed response equations, in which a coupling matrix K(omega) features, analogous to the well-known time-dependent density functional theory (TDDFT) case. An adiabatic approximation is needed to solve these equations, but the adiabatic approximation is much more critical since there is not a good "zero ord...

An adiabatic mode time-dependent parabolic equation

An adiabatic mode time-dependent parabolic equation for the 3D problems of underwater acoustic propagation problem is derived by the multiple-scale method. The Cauchy problem for this equation is considered.

Time-Dependent One-Body Reduced Density Matrix Functional Theory Adiabatic Approximations and Beyond