Comparing to Other References

• Conventions
  • from_geometric
• Bertaina and Giorgini, Phys. Rev. Lett. 106, 110403 (2011)
  • table_I()
  • conventional_table_I()
  • figure_4()
  • c0_by_kF4()
  • figure_4_fit()
  • figure_4_reproduction()
  • conventional_figure_4()
  • energy_comparison()
  • contact_comparison()
• Beane et al. Phys. Rev. A, 107:043314 (2023)
  • contact_by_kF4()
  • Fermi_Liquid_Energy_by_Fermi_Gas_Energy()
  • Mean_Field_Energy_by_Fermi_Gas_Energy()
  • contact_comparison()
  • energy_comparison()
• Bertaina, EPJ Special Topics, 217(1):153–162, (2013)
  • figure_2()
  • conventional_figure_2()
  • energy_comparison()
  • contact_by_kF4()
  • contact_comparison()
• Boettcher et al., Phys. Rev. Lett. 116, 045303 (2016)
  • figure_3()
  • figure_3_reproduction()
• Pilati, Orso, Bertaina. Phys. Rev. A, 103:063314, (2021)
  • figure_2_P_0_and_N_98()
  • conventional_figure_2_P_0_and_N_98()
  • energy_comparison()
  • contact_comparison()
• Galea et al., Phys. Rev. A, 93(2):023602 (2016)
  • figure_6()
  • conventional_figure_6()
  • energy_comparison()
  • contact_comparison()
• Shi, Chiesa, and Zhang, Phys. Rev. A 92, 033603 (2015)
  • table_II()
  • conventional_table_II()
  • energy_comparison()
  • contact_comparison()
• Adding a Reference
  • Bibliographic Information
  • Results and Plotting

We provide some utilities for drawing figures with data from the above sources.

tdg.references.REFERENCES

The references parameters in the functions below expects a set of modules; each module represents a different reference.

This variable contains all available references.

Some references have data that has been superseded by works from the same author, or are far outside the typical parameter range. Pass a truthy include_all kwarg to include these in comparison figures. (For an example see PRL106110403.)

tdg.references.contact_comparison(ax, *, references=REFERENCES, **kwargs)

Plots the values of \(c/k_F^4\) provided by different references for comparison with contact_by_kF4().

Parameters

• ax (matplotlib axis) – Where to plot the references’ results.

• alpha (torch.tensor) – If a reference provides a function (rather than just points), pass alpha to it. Also sets the limits for the x-axis of the plot.

#!/usr/bin/env python

import torch
import matplotlib.pyplot as plt
import tdg.references

fig, ax = plt.subplots(1,1, figsize=(8,6))

alpha = torch.linspace(-0.625, +0.625, 1000)
tdg.references.contact_comparison(ax, alpha=alpha)

ax.set_xlim([min(alpha), max(alpha)])
ax.legend()
fig.tight_layout()
plt.show()

(Source code, png, hires.png, pdf)

tdg.references.energy_comparison(ax, *, references=REFERENCES, **kwargs)

Plots the difference between the Fermi Liquid and Mean Field energies normalized by the energy of the free Fermi Gas, \((E_{FL}-E_{MF})/E_{FG}\).

Parameters

• ax (matplotlib axis) – Where to plot the references’ results.

• alpha (torch.tensor) – If a reference provides a function (rather than just points), pass alpha to it. Also sets the limits for the x-axis of the plot.

#!/usr/bin/env python

import torch
import matplotlib.pyplot as plt
import tdg.references

fig, ax = plt.subplots(1,1, figsize=(8,6))

alpha = torch.linspace(-1.0, +1.0, 1000)
tdg.references.energy_comparison(ax, alpha=alpha)

ax.set_xlim([min(alpha), max(alpha)])
ax.set_ylim([-0.08, 0.3])
ax.legend()
fig.tight_layout()
plt.show()

(Source code, png, hires.png, pdf)

Some references provide equation of state information.