# The excitation spectrum of Bose gases interacting through singular potentials

## TL;DR

This paper rigorously confirms Bogoliubov theory for the excitation spectrum of large Bose gases with singular, scaled interactions, providing precise energy and spectrum estimates in the large particle limit.

## Contribution

It proves the validity of Bogoliubov theory for a range of interaction scalings in Bose gases, including singular potentials, with explicit energy and spectrum results.

## Key findings

- Ground state energy matches Bogoliubov predictions
- Low-lying excitation spectrum is accurately described
- Results hold for small coupling constants and large particle number

## Abstract

We consider systems of $N$ bosons in a box with volume one, interacting through a repulsive two-body potential of the form $\kappa N^{3\beta-1} V(N^\beta x)$. For all $0 < \beta < 1$, and for sufficiently small coupling constant $\kappa > 0$, we establish the validity of Bogoliubov theory, identifying the ground state energy and the low-lying excitation spectrum up to errors that vanish in the limit of large $N$.