Nonadiabatic dynamics in multidimensional complex potential energy surfaces

Despite the continuous development of methods for describing nonadiabatic dynamics, there is a lack of multidimensional approaches for processes where the wave function norm is not conserved. A new surface hopping variant closes this knowledge gap.

Identification of Fully Measurable Grand Lebesgue Spaces

We consider the Banach function spaces, called fully measurable grand Lebesgue spaces, associated with the function norm ρ(f)=ess supx∈X⁡δ(x)ρp(x)(f), where ρp(x) denotes the norm of the Lebesgue space of exponent p(x), and p(·) and δ(·) are measurable functions over a measure space (X,ν), p(x)∈[1,∞], and δ(x)∈(0,1] almost everywhere. We prove that every such space can be expressed equivalently replacing p(·) and δ(·) with functions defined everywhere on the interval (0,1), decreasing and increasing, respectively (hence the full measurability assumption in the definition does not give an effective generalization with respect to the pointwise monotone assumption and the essential supremum can be replaced with the simple supremum). In particular, we show that, in the case of bounded p(·), the class of fully measurable Lebesgue spaces coincides with the class of generalized grand Lebesgue spaces introduced by Capone, Formica, and Giova.

Integral means on radially weighted spaces of analytic functions

Hilbert spaces of analytic functions generated by rotationally symmetric measures on disks and annuli are studied. A domination relation between function norm and weighted sums of integral means on circles is developed. The function norm and the weighted sum take the same value for a specified class of polynomials. This class can be varied according to two parameters. Parts of the construction carry over to other Banach spaces of analytic of harmonic functions. Counterexamples illuminating properties of the complex method of interpolation appear as a byproduct.