Monotonicity of quantum ground state energies: Bosonic atoms and stars

TL;DR

This paper investigates how the ground state energies of bosonic quantum systems with Coulomb or Newton interactions depend on the number of particles, revealing a monotonic relationship when scaled appropriately.

Contribution

It establishes new third-order polynomial bounds demonstrating the monotonicity of the energy ratios in bosonic atoms and stars, advancing understanding of N-body quantum systems.

Findings

Energy ratios grow monotonically with N when scaled by specific polynomials.

Provides bounds for bosonic atoms and stars with Coulomb and Newton interactions.

Discusses applications of monotonicity in quantum system analysis.

Abstract

The N-dependence of the non-relativistic bosonic ground state energy is studied for quantum N-body systems with either Coulomb or Newton interactions. The Coulomb systems are "bosonic atoms," with their nucleus fixed, and the Newton systems are "bosonic stars". In either case there exists some third order polynomial in N such that the ratio of the ground state energy to the respective polynomial grows monotonically in N. Some applications of these new monotonicity results are discussed.