Joseph Dillon

Research Interests

Spent a decade as a theoretical chemist developing methods to model energy and charge transfer processes in molecular systems. For the past few years I’ve been investigating connections between this work and research in other areas of physics and mathematics.

Fig. 3 - Graph of |ζ|²(1/2,t) / |ζ’|²(1/2,t)[Green], 16/j(t)²[Blue] and the
difference between 16/j(t)² and 4/Log²(t/2π)[Dashed Red] where
j(t)=2 log(π)-ψ(1/4-it/2)-ψ(1/4+it/2), ψ(s) denotes the digamma
function and j(t)~-2 Log(t/2π) for sufficiently large t.

Fig. 1 - Graph of non-adiabatic potential energy function for (CH)₂N₃.

Fig. 4 - Graph of |Υ|²(t,σ)=|ζ|²(1/2-t,σ) / |ζ|²(1/2+t,σ) for 7≤σ≤100 and
|t|< 1/2. Note that (σ,t,Y)∊ℝ³ such that |Υ|²(t,σ)=1 are marked
in Red and that t=0 corresponds with the critical line.

Fig. 2 - Graph of non-adiabatic potential energy function for H₃O.

Table 1 - Transformation properties of graphs of well-known transcendental f(z)=ℜ+i ℑ, ℜ, ℑ and their set of zeros and poles R U γ, where z ∈ ℂ.