# Static Impurities in a Weakly Interacting Bose Gas

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## Abstract

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## 1. Introduction

## 2. Formulation

#### 2.1. Model

#### 2.2. Effective Field Theory Approach

#### 2.3. Limit of Dilute Bose Gas

## 3. Results

#### 3.1. 3D Case

#### 3.2. 2D Case

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

## References

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**Figure 1.**Dimensionless functions ${\epsilon}_{1,2}\left(\frac{{a}_{I}}{\xi};\infty \right)$ determining the one-impurity energy in 3D dilute Bose gas.

**Figure 2.**Mean-field and the first-order quantum corrections ${\epsilon}_{1,2}\left(\frac{{a}_{I}}{\xi};\frac{R}{\xi}\right)$ to the energy of 3D dilute Bose gas generated by two impurities for $\frac{{a}_{I}}{\xi}=\pm 0.01$ and $\frac{{a}_{I}}{\xi}=\pm 1$.

**Figure 3.**Dimensioless one-impurity binding energy terms ${\epsilon}_{1,2}\left(\frac{{a}_{I}}{\xi};\infty \right)$ (see Equation (23)) in 2D case.

**Figure 4.**The two-impurity dimensionless binding energy corrections ${\epsilon}_{1,2}\left(\frac{{a}_{I}}{\xi};\frac{R}{\xi}\right)$ in 2D dilute Bose gas.

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**MDPI and ACS Style**

Panochko, G.; Pastukhov, V.
Static Impurities in a Weakly Interacting Bose Gas. *Atoms* **2022**, *10*, 19.
https://doi.org/10.3390/atoms10010019

**AMA Style**

Panochko G, Pastukhov V.
Static Impurities in a Weakly Interacting Bose Gas. *Atoms*. 2022; 10(1):19.
https://doi.org/10.3390/atoms10010019

**Chicago/Turabian Style**

Panochko, Galyna, and Volodymyr Pastukhov.
2022. "Static Impurities in a Weakly Interacting Bose Gas" *Atoms* 10, no. 1: 19.
https://doi.org/10.3390/atoms10010019