Variational approach to $N$-body interactions in finite volume

TL;DR

This paper develops a variational framework for solving finite-volume N-body problems with periodic interactions, enabling efficient numerical computation of energy spectra in lattice systems.

Contribution

It introduces a general variational formalism for N-body finite-volume problems that leverages infinite-volume solutions for practical numerical analysis.

Findings

Derivation of N-body secular equations in finite volume.

Connection between finite-volume solutions and infinite-volume wave functions.

Potential for numerical computation of energy spectra in lattice models.

Abstract

We explore variational approach to the finite-volume $N$-body problem. The general formalism for N non-relativistic spinless particles interacting with periodic pair-wise potentials yields N-body secular equations. The solutions depend on the infinite-volume N-body wave functions. Given that the infinite-volume N-body dynamics may be solved by the standard Faddeev approach, the variational N-body formalism can provide a convenient numerical framework for finding discrete energy spectra in periodic lattice structures.