From few to many body degrees of freedom

TL;DR

This paper discusses microscopic few-body techniques for simplifying and directly tackling many-body problems in one-dimensional quantum gases, highlighting their theoretical foundations and applications.

Contribution

It introduces non-perturbative direct methods for studying one-dimensional fermionic and bosonic gases using few-body information.

Findings

Effective pseudopotentials reproduce collisional and binding energies.

Simplified theories facilitate many-body problem analysis.

Non-perturbative methods are effective in 1D systems.

Abstract

Here, I focus on the use of microscopic, few-body techniques that are relevant in the many-body problem. These methods can be divided into indirect and direct. In particular, indirect methods are concerned with the simplification of the many-body problem by substituting the full, microscopic interactions by pseudopotentials which are designed to reproduce collisional information at specified energies, or binding energies in the few-body sector. These simplified interactions yield more tractable theories of the many-body problem, and are equivalent to effective field theory of interactions. Direct methods, which so far are most useful in one spatial dimension, have the goal of attacking the many-body problem at once by using few-body information only. Here, I will present non-perturbative direct methods to study one-dimensional fermionic and bosonic gases in one dimension.