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.
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This work was supported by EPSRC Grant No. EP/M024636/1.
This article belongs to the Topical Collection “Critical Stability of Quantum Few-Body Systems”.
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Valiente, M. From Few to Many Body Degrees of Freedom. Few-Body Syst 59, 101 (2018). https://doi.org/10.1007/s00601-018-1421-8
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DOI: https://doi.org/10.1007/s00601-018-1421-8