Excitation spectrum for the Lee-Huang-Yang model for the bose gas in a periodic box

TL;DR

This paper derives a new formula for excited states of the Lee-Huang-Yang model of a weakly interacting Bose gas in a periodic box, using a non-Hermitian transform to analyze pair excitations.

Contribution

It introduces a novel formula for many-body excited states of the Lee-Huang-Yang Hamiltonian, extending Wu's ground state analysis to excited states.

Findings

New formula for excited eigenstates derived

Non-Hermitian transform isolates pair excitation processes

Provides insights into the excitation spectrum of the Bose gas

Abstract

We derive a new formula for excited many-body eigenstates of the approximate Hamiltonian of Lee, Huang, and Yang, which describes the weakly interacting bose gas in a periodic box. Our formula utilizes a non-Hermitian transform to isolate a process of pair excitation in all excited states. This program is inspired by the description of Wu for the many-body ground state of the Lee-Huang-Yang Hamiltonian, as well as similar descriptions for the ground state of quadratic Hamiltonians in generic trapping potentials.