# Dispersion and Damping of Phononic Excitations in Fermi Superfluid Gases in 2D

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## Abstract

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## 1. Introduction

## 2. Gaussian Pair Fluctuation Approximation

## 3. Results and Discussion

#### 3.1. Sound Mode as Pole of the Propagator

#### 3.2. Response Function

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**The (complex) determinant of the inverse fluctuation propagator is shown as a function of u, for ${E}_{b}=1.8$ and $\beta =0.87$. The color reveals the phase (along a color wheel from red over the spectrum to violet and then back to red). Curves show contours of the real and imaginary values.

**Figure 2.**Paths traced by the complex sound velocity when varying temperature from zero to the critical temperature, for different binding energies ${E}_{b}=1.5,1.8,2,2.5,3\left({E}_{F}\right)$.

**Figure 3.**Sound velocity c as a function of temperature for ${E}_{b}=1.5,1.8,2,2.5,3\left({E}_{F}\right)$.

**Figure 4.**Damping factor $\kappa $ as a function of temperature for ${E}_{b}=1.5,1.8,2,2.5,3\left({E}_{F}\right)$.

**Figure 5.**Sound velocity ${c}_{resp}$ as a function of temperature for ${E}_{b}=1.5,1.8,2,2.5,3\left({E}_{F}\right)$. Inset: this sound velocity for temperatures close to ${T}_{C}$.

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**MDPI and ACS Style**

Lumbeeck, L.-P.; Tempere, J.; Klimin, S.
Dispersion and Damping of Phononic Excitations in Fermi Superfluid Gases in 2D. *Condens. Matter* **2020**, *5*, 13.
https://doi.org/10.3390/condmat5010013

**AMA Style**

Lumbeeck L-P, Tempere J, Klimin S.
Dispersion and Damping of Phononic Excitations in Fermi Superfluid Gases in 2D. *Condensed Matter*. 2020; 5(1):13.
https://doi.org/10.3390/condmat5010013

**Chicago/Turabian Style**

Lumbeeck, Lars-Paul, Jacques Tempere, and Serghei Klimin.
2020. "Dispersion and Damping of Phononic Excitations in Fermi Superfluid Gases in 2D" *Condensed Matter* 5, no. 1: 13.
https://doi.org/10.3390/condmat5010013