Concavity Theorems for Energy Surfaces

TL;DR

This paper investigates the concavity properties of energy surfaces in constrained energy minimizations, identifies the contradiction caused by fluctuations of collective coordinates, and proposes a solution to mitigate these fluctuations.

Contribution

It introduces a novel approach to address fluctuations in collective coordinates, improving the understanding of energy surface concavity in constrained minimizations.

Findings

Concavity properties limit the complexity of energy landscapes.

Fluctuations of collective coordinates cause contradictions in energy surface analysis.

A proposed solution reduces the impact of these fluctuations.

Abstract

Concavity properties prevent the existence of significant landscapes in energy surfaces obtained by strict constrained energy minimizations. The inherent contradiction is due to fluctuations of collective coordinates. A solution to those fluctuations is given.