Daniel L. Whitenack

Resonance Lifetimes from Complex Densities

The ab initio calculation of resonance lifetimes of metastable anions challenges modern quantum chemical methods. The exact lifetime of the lowest-energy resonance is encoded into a complex “density” that can be obtained via complex-coordinate scaling. We illustrate this with one-electron examples and show how the lifetime can be extracted from the complex density in much the same way as the ground-state energy of bound systems is extracted from its ground-state density.

Stark Ionization of Atoms and Molecules within Density Functional Resonance Theory

We show that the energetics and lifetimes of resonances of finite systems under an external electric field can be captured by Kohn–Sham density functional theory (DFT) within the formalism of uniform complex scaling. Properties of resonances are calculated self-consistently in terms of complex densities, potentials, and wave functions using adapted versions of the known algorithms from DFT. We illustrate this new formalism by calculating ionization rates using the complex-scaled local density approximation and exact exchange. We consider a variety of atoms (H, He, Li, and Be) as well as the H2 molecule. Extensions are briefly discussed.

Effects of magnetic dipole-dipole interactions in atomic Bose-Einstein condensates with tunable s -wave interactions

Department of Physics,Purdue University, West Lafayette IN 47907(Dated: April 9, 2012)The s-wave interaction is usually the dominant form of interactions in atomic Bose-Einstein con-densates (BECs). Recently, Feshbach resonances have been employed to reduce the strength ofthe s-wave interaction in many atomic speicies. This opens the possibilities to study magneticdipole-dipole interactions (MDDI) in BECs, where the novel physics resulting from long-range andanisotropic dipolar interactions can be explored. Using a variational method, we study the e ect ofMDDI on the statics and dynamics of atomic BECs with tunable s-wave interactions. We bench-mark our calculation against previously observed MDDI e ects in

Density functional resonance theory: Complex density functions, convergence, orbital energies, and functionals

Aspects of density functional resonance theory (DFRT) [D. L. Whitenack and A. Wasserman, Phys. Rev. Lett. 107, 163002 (2011)], a recently developed complex-scaled version of ground-state density functional theory (DFT), are studied in detail. The asymptotic behavior of the complex density function is related to the complex resonance energy and systems threshold energy, and the functions local oscillatory behavior is connected with preferential directions of electron decay. Practical considerations for implementation of the theory are addressed including sensitivity to the complex-scaling parameter, θ. In Kohn-Sham DFRT, it is shown that almost all θ-dependence in the calculated energies and lifetimes can be extinguished via use of a proper basis set or fine grid. The highest occupied Kohn-Sham orbital energy and lifetime are related to physical affinity and width, and the threshold energy of the Kohn-Sham system is shown to be equal to the threshold energy of the interacting system shifted by a well-defined functional. Finally, various complex-scaling conditions are derived which relate the functionals of ground-state DFT to those of DFRT via proper scaling factors and a non-Hermitian coupling-constant system.