ON-LINE QLunch: Tommaso Guaita

Speaker: Tommaso Guaita, The Max Planck Institute of Quantum Optics

Title: A Geometric Perspective on Variational Methods in Quantum Mechanics

Abstract: In this talk I will discuss the use of variational manifolds, embedded in many-body Hilbert space, to approximate real time evolution of quantum systems. I will show how this can be understood from the point of view of a geometric framework. While typical variational methods require the variational family to be a Kähler manifold, I will tackle the more general non-Kähler case. Here, there exists a range of non-equivalent approaches whose properties will be analysed. I will show how the geometric perspective is particularly suited to understanding these differences.
To better illustrate the different types of manifolds one can encounter, I will introduce some relevant examples built through the Gilmore-Perelemov construction.

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