Fall 2021 Supplement to Brauneis & Schechter, Copyright: A Contemporary Approach

Impurities in a one-dimensional Bose gas: the flow equation approach

“…For attractive interactions (c < 0), the possibility of deep impurity-boson bound states complicates the analysis. This issue will be addressed in a future publication [39]. It turns out that the The curves show different values of N listed in the insets.…”

“…At the end of our discussion of the one-dimensional Bose-polaron problem, we mention once again that this paper focuses on repulsive boson-impurity interactions, and leaves a rigorous IM-SRG study of the attractive case for the future [39]. However, we must note that our conclusion that the mean-field approximation describes accurately an impurity in a Bose gas cannot be directly extended to a Bose gas with an attractive impurity.…”

“…In this work, we consider the case of repulsive boson-impurity interactions (c > 0). The case of an impurity with attractive interactions will be addressed in a future publication [39]. The energy of the impurity for this problem was already studied with IM-SRG in Ref.…”

“…In this section, we consider attractive boson-impurity interactions, c 2 < 0. This case is more complicated because each boson is attached to the impurity if gN 2|c 2 |, see [39,64]. Therefore, to understand the induced interactions, we must consider N 2|c 2 |/g.…”

“…where δ 1 = 1, since we work with an impenetrable impurity, c 1 → ∞. The function f one−attr reads as [39]…”