分野別セミナー

Abstract: In this talk we explore relevant mathematical concepts, namely, Green’s function, graphs and topological
quantifiers to describe (as relatively good approximations) certain materials and/or processes. We argue that in
many instances, the simplicity of these mathematical constructions allows to employ ideas from machine learning to
look for the best parameters and configurations useful in applications. We start with the usual definition of Green’s
functions and then address how they can be used to optimize wave-guides geometries to probe optical-electric
properties of materials. Then, we very briefly review common ideas in graph theory and show that a discrete Green’s
function can be connected to the spanning tree constant STC (a kind of topological index), which by its turn can be
associated to the critical temperature Tc of the Ising model, a prototype system to describe ferromagnetic materials. Using machine learning techniques we then explore how Tc changes as we modify the structure of the different
lattices. For so, the STC is the “correlation-bridge”. As a last example, we consider transport properties in 2D
systems, nowadays among the most promising types of materials for different applications, as sensors and green
energy (solar cells). We show that quantum walks, a quantum mechanics dynamics on general graphs, can
surprisingly accurately mimic the band structures of so important structures like graphene, germanene and silicene,
with a minimal of computational efforts. Such an approach, e.g., could be used to select candidate 2D materials for
applications, without a high computational cost. Thus, only after selecting the most promises ones, we could use ab
initio methods to better characterize their chemical-physical properties. An illustration in this direction is given in
the context of lattice thermal conductivity.

Links to pertinent references:

https://doi.org/10.1016/j.aop.2018.07.026

https://doi.org/10.1088/1751-8121/ac0e52

https://doi.org/10.1088/1742-5468/ac8742

https://doi.org/10.1039/d3cp02896h

https://doi.org/10.1103/PhysRevB.108.094303

https://doi.org/10.1103/PhysRevE.109.025303


Short biography

Marcos G. E. da Luz is a Bachelor in Physics from UFPR (1990) and PhD in Physics from Unicamp (1995). From 1995 to 1997 he was a post-doc at the Physics Department – Harvard University. Since 1998 he has been at the Physics
Department-UFPR-Brazil, becoming a full professor in 2017. He has been a visitor professor and researcher in many
institutions, in countries like France, Germany, Mexico, Spain and USA. He has published about 150 papers in
scientific journals, in areas like quantum mechanics, statistical physics, material sciences, biological-related
systems and complexity theory. Presently he is the leader of the multidisciplinary lab MADComplex (Modeling and
Analysis of Data in Complexity) at UFPR.