QFiND.jl

QFiND.jl provides routines for constructing an effective discrete representation of a system-bath model. In other words, this codes provides an approximation of the bath correlation function $C(t)$ for a given spectral density $J(\omega)$

$$ \begin{aligned} C(t)&=\frac{1}{2\pi} \int_{-\infty}^{\infty} \mathrm{d}\omega J(\omega)\left[\mathrm{coth}\left(\frac{\beta \omega}{2}\right)+1\right] \mathrm{e}^{-i \omega t}\\ &\approx \sum_{k=1}^M \frac{1}{2} g_k^2 \mathrm{e}^{-i\omega_k t} \end{aligned} $$

where $\omega_k,g_k \in ℝ \backslash \{0\}$. The code allows for the estimation of frequencies and coefficients in the system plus bath model.

Installation

    julia> using Pkg

    julia> Pkg.add(; url="https://github.com/DOC-package/QFiND.jl")

Simple usage

Please see ./examples.

Documentation

For more details, please refer to the documentation.

Cite QFiND

If you find the framework useful in your research, we would be grateful if you could cite our publications:

• H. Takahashi and R. Borrelli, J. Chem. Phys. 161, 151101 (2024). (https://doi.org/10.1063/5.0232232)
• H. Takahashi and R. Borrelli, J. Chem. Theory Comput. 21, 2206–2218 (2025). (https://doi.org/10.1021/acs.jctc.4c01728)

Here are the bibtex entries:

@article{TakahashiBorrelli2024JCP,
  title = {Effective Modeling of Open Quantum Systems by Low-Rank Discretization of Structured Environments},
  author = {Takahashi, Hideaki and Borrelli, Raffaele},
  year = {2024},
  month = oct,
  journal = {The Journal of Chemical Physics},
  volume = {161},
  number = {15},
  pages = {151101},
  issn = {0021-9606},
  doi = {10.1063/5.0232232}
}

@article{TakahashiBorrelli2025JCTC,
  title = {Discretization of {{Structured Bosonic Environments}} at {{Finite Temperature}} by {{Interpolative Decomposition}}: {{Theory}} and {{Application}}},
  shorttitle = {Discretization of {{Structured Bosonic Environments}} at {{Finite Temperature}} by {{Interpolative Decomposition}}},
  author = {Takahashi, Hideaki and Borrelli, Raffaele},
  year = {2025},
  month = mar,
  journal = {Journal of Chemical Theory and Computation},
  volume = {21},
  number = {5},
  pages = {2206--2218},
  publisher = {American Chemical Society},
  issn = {1549-9618},
  doi = {10.1021/acs.jctc.4c01728}
}

Authors

Hideaki Takahashi (hideaki.takahashi@unito.it)

License

This project is distributed under the MIT License.