Grafos como modelos dinâmicos e estáticos em mecânica quântica.

Abstract

The graph formalism allows its approach to different areas of knowledge in which concepts by ele ments and the relationship between them are possible to model. In this work, we show how graphs can be used as models in quantum mechanics through of two models, one envolving dynamics in a system and other, involving quantum information, which is a static model. With the scatter ing in quantum graphs using a Green’s function formulation, the probability of transmission of a quantum particle through a structure defined by a graph was studied in a efficient way by using its adjacency matrix. It allowed us to bring a new approach, using these scattering probabilities, to define a scaterring entropy based in the Shannon entropy. In the static case, with the graph states, which can be used as resource in quantum information, they were modeled by the incidence ma trix, allowing a good numerical efficiency. Thus, entanglement measurements in cases with noisy quantum gates that entangle the system were reproduced.