Geometry of wave functions

Yu. A. Aminov

Samuel L. Braunstein, Carlton M. Caves

Kuyukov

Gravity and geometry the phase space of the wave function

Bogdan Mielnik

Jincheng Zhang

This paper explores the potential of non-linear geometry, leveraging the concept of wave function collapse, to generate complex geometries from simple perturbations. The core claim is to extend this established theory beyond conventional geometric applications, demonstrating the emergence of intricate structures through the manipulation of wave function dynamics. We propose a modified collapse theory that allows for the formation of non-linear geometric properties, opening new avenues for understanding and potentially creating novel geometries. This work builds upon established quantum mechanics principles, aiming to provide a fundamentally different approach to geometric analysis.

Yuri Alexandre Aoto, Márcio Fabiano da Silva

The set of all electronic states that can be expressed as a single Slater determinant forms a submanifold, isomorphic to the Grassmannian, of the projective Hilbert space of wave functions. We explored this fact by using tools of Riemannian geometry of Grassmannians as described by [Absil et al., Acta Appl. Math. 80, 199 (2004)] to propose an algorithm that converges to a Slater determinant that is a critical point of the overlap function with a correlated wave function. This algorithm can be applied to quantify the entanglement or correlation of a wave function. We show that this algorithm is equivalent to the Newton method using the standard parametrization of Slater determinants by orbital rotations, but it can be more efficiently implemented because the orbital basis used to express the correlated wave function is kept fixed throughout the iterations. We present the equations of this method for a general configuration interaction wave function and for a wave function with up to double excitations over a reference determinant. Applications of this algorithm to selected electronic systems are also presented and discussed.