The Hyperspherical Four-Fermion Problem

TL;DR

This paper reviews recent theoretical advances in understanding four interacting fermions using hyperspherical coordinates, emphasizing the universality regime and its implications for phenomena like the BCS-BEC crossover.

Contribution

It introduces a hyperspherical coordinate approach to four-fermion problems, providing detailed formulas and insights into the universality regime and few-body processes.

Findings

Insights into the hyperspherical method for four-fermion systems

Formulas for calculating recombination processes

Implications for the BCS-BEC crossover

Abstract

The problem of a few interacting fermions in quantum physics has sparked intense interest, particularly in recent years owing to connections with the behavior of superconductors, fermionic superfluids, and finite nuclei. This review addresses recent developments in the theoretical description of four fermions having finite-range interactions, stressing insights that have emerged from a hyperspherical coordinate perspective. The subject is complicated, so we have included many detailed formulas that will hopefully make these methods accessible to others interested in using them. The universality regime, where the dominant length scale in the problem is the two-body scattering length, is particularly stressed, including its implications for the famous BCS-BEC crossover problem Derivations and relevant formulas are also included for the calculation of challenging few-body processes such as recombination.