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%% This BibTeX bibliography file was created using BibDesk.
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%% http://bibdesk.sourceforge.net/
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%% Created for Pierre-Francois Loos at 2022-09-30 16:13:18 +0200
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%% Created for Pierre-Francois Loos at 2022-10-05 14:42:12 +0200
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%% Saved with string encoding Unicode (UTF-8) *
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%% Saved with string encoding Unicode (UTF-8)
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@article{Ceperley_1983,
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title = {The simulation of quantum systems with random walks: A new algorithm for charged systems},
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journal = {Journal of Computational Physics},
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volume = {51},
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number = {3},
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pages = {404-422},
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year = {1983},
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issn = {0021-9991},
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doi = {https://doi.org/10.1016/0021-9991(83)90161-4},
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url = {https://www.sciencedirect.com/science/article/pii/0021999183901614},
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author = {D Ceperley},
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abstract = {Random walks with branching have been used to calculate exact properties of the ground state of quantum many-body systems. In this paper, a more general Green's function identity is derived which relates the potential energy, a trial wavefunction, and a trial density matrix to the rules of a branched random walk. It is shown that an efficient algorithm requires a good trial wavefunction, a good trial density matrix, and a good sampling of this density matrix. An accurate density matrix is constructed for Coulomb systems using the path integral formula. The random walks from this new algorithm diffuse through phase space an order of magnitude faster than the previous Green's Function Monte Carlo method. In contrast to the simple diffusion Monte Carlo algorithm, it is an exact method. Representative results are presented for several molecules.}
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}
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abstract = {Random walks with branching have been used to calculate exact properties of the ground state of quantum many-body systems. In this paper, a more general Green's function identity is derived which relates the potential energy, a trial wavefunction, and a trial density matrix to the rules of a branched random walk. It is shown that an efficient algorithm requires a good trial wavefunction, a good trial density matrix, and a good sampling of this density matrix. An accurate density matrix is constructed for Coulomb systems using the path integral formula. The random walks from this new algorithm diffuse through phase space an order of magnitude faster than the previous Green's Function Monte Carlo method. In contrast to the simple diffusion Monte Carlo algorithm, it is an exact method. Representative results are presented for several molecules.},
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author = {D Ceperley},
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date-modified = {2022-10-05 14:41:32 +0200},
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doi = {https://doi.org/10.1016/0021-9991(83)90161-4},
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issn = {0021-9991},
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journal = {J. Comput. Phys.},
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number = {3},
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pages = {404-422},
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title = {The simulation of quantum systems with random walks: A new algorithm for charged systems},
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url = {https://www.sciencedirect.com/science/article/pii/0021999183901614},
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volume = {51},
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year = {1983},
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bdsk-url-1 = {https://www.sciencedirect.com/science/article/pii/0021999183901614},
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bdsk-url-2 = {https://doi.org/10.1016/0021-9991(83)90161-4}}
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@article{Kalos_1962,
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title = {Monte Carlo Calculations of the Ground State of Three- and Four-Body Nuclei},
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author = {Kalos, M. H.},
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journal = {Phys. Rev.},
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volume = {128},
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issue = {4},
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pages = {1791--1795},
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numpages = {0},
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year = {1962},
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month = {Nov},
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publisher = {American Physical Society},
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doi = {10.1103/PhysRev.128.1791},
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url = {https://link.aps.org/doi/10.1103/PhysRev.128.1791}
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}
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author = {Kalos, M. H.},
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doi = {10.1103/PhysRev.128.1791},
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issue = {4},
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journal = {Phys. Rev.},
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month = {Nov},
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numpages = {0},
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pages = {1791--1795},
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publisher = {American Physical Society},
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title = {Monte Carlo Calculations of the Ground State of Three- and Four-Body Nuclei},
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url = {https://link.aps.org/doi/10.1103/PhysRev.128.1791},
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volume = {128},
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year = {1962},
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bdsk-url-1 = {https://link.aps.org/doi/10.1103/PhysRev.128.1791},
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bdsk-url-2 = {https://doi.org/10.1103/PhysRev.128.1791}}
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@article{Kalos_1970,
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title = {Energy of a Boson Fluid with Lennard-Jones Potentials},
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author = {Kalos, M. H.},
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journal = {Phys. Rev. A},
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volume = {2},
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issue = {1},
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pages = {250--255},
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numpages = {0},
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year = {1970},
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month = {Jul},
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publisher = {American Physical Society},
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doi = {10.1103/PhysRevA.2.250},
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url = {https://link.aps.org/doi/10.1103/PhysRevA.2.250}
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}
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author = {Kalos, M. H.},
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doi = {10.1103/PhysRevA.2.250},
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issue = {1},
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journal = {Phys. Rev. A},
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month = {Jul},
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numpages = {0},
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pages = {250--255},
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publisher = {American Physical Society},
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title = {Energy of a Boson Fluid with Lennard-Jones Potentials},
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url = {https://link.aps.org/doi/10.1103/PhysRevA.2.250},
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volume = {2},
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year = {1970},
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bdsk-url-1 = {https://link.aps.org/doi/10.1103/PhysRevA.2.250},
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bdsk-url-2 = {https://doi.org/10.1103/PhysRevA.2.250}}
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@article{Moskowitz_1986,
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author = {Moskowitz,Jules W. and Schmidt,K. E. },
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title = {The domain Green’s function method},
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journal = {The Journal of Chemical Physics},
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volume = {85},
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number = {5},
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pages = {2868-2874},
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year = {1986},
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doi = {10.1063/1.451046},
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URL = {
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https://doi.org/10.1063/1.451046
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},
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eprint = {
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https://doi.org/10.1063/1.451046
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}
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}
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author = {Moskowitz,Jules W. and Schmidt,K. E.},
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date-modified = {2022-10-05 14:41:57 +0200},
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doi = {10.1063/1.451046},
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journal = {J. Chem. Phys.},
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number = {5},
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pages = {2868-2874},
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title = {The domain Green's function method},
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volume = {85},
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year = {1986},
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bdsk-url-1 = {https://doi.org/10.1063/1.451046}}
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@misc{note,
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note = {As $\tau \rightarrow 0$ and $N \rightarrow \infty$ with $N\tau=t$, the operator $T^N$ converges to $e^{-t(H-E \Id)}$. We then have $G^E_{ij} \rightarrow \int_0^{\infty} dt \mel{i}{e^{-t(H-E \Id)}}{j}$, which is the Laplace transform of the time-dependent Green's function $\mel{i}{e^{-t(H-E \Id)}}{j}$.}}
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@ -344,13 +340,12 @@ eprint = {
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year = {2012}}
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@book{Ceperley_1979,
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author = {D.M. Ceperley and M.H Kalos},
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editor={K.Binder},
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chapter={4},
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publisher = {Springer, Berlin},
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title = {Monte Carlo Methods in Statistical Physics},
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year = {1979}}
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author = {D.M. Ceperley and M.H Kalos},
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chapter = {4},
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editor = {K.Binder},
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publisher = {Springer, Berlin},
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title = {Monte Carlo Methods in Statistical Physics},
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year = {1979}}
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@article{Carlson_2007,
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author = {J. Carlson},
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