Particle diffusion Monte Carlo (PDMC)

References

[1] N. Aquino, The role of correlation in the ground state energy of confined helium atom, AIP Conf. Proc. 1579 (2014), no. 1, 136–140. 10.1063/1.4862428Search in Google Scholar

[2] N. Aquino, A. Flores-Riveros and J. F. Rivas-Silva, The compressed helium atom variationally treated via a correlated Hylleraas wave function, Phys. Lett. A 307 (2003), no. 5–6, 326–336. 10.1016/S0375-9601(02)01767-XSearch in Google Scholar

[3] N. Aquino, J. Garza, A. Flores-Riveros, J. F. Rivas-Silva and K. D. Sen, Confined helium atom low-lying S states analyzed through correlated Hylleraas wave functions and the Kohn–Sham model, J. Chem. Phys. 124 (2006), no. 5, Article ID 054311. 10.1063/1.2148948Search in Google Scholar

[4] A. Banerjee, C. Kamal and A. Chowdhury, Calculation of ground-and excited-state energies of confined helium atom, Phys. Lett. A 350 (2006), no. 1–2, 121–125. 10.1016/j.physleta.2005.10.024Search in Google Scholar

[5] E. Barkai, R. Metzler and J. Klafter, From continuous time random walks to the fractional Fokker–Planck equation, Phys. Rev. E 61 (2000), no. 1, Article ID 132. 10.1103/PhysRevE.61.132Search in Google Scholar

[6] C. F. Bunge, J. A. Barrientos and A. V. Bunge, Roothaan–Hartree–Fock ground-state atomic wave functions: Slater-type orbital expansions and expectation values for Z= 2-54, At. Data Nuclear Data Tables 53 (1993), no. 1, 113–162. 10.1006/adnd.1993.1003Search in Google Scholar

[7] A. O. Caldeira and A. J. Leggett, Path integral approach to quantum Brownian motion, Phys. A 121 (1983), no. 3, 587–616. 10.1016/0378-4371(83)90013-4Search in Google Scholar

[8] J. Carlson, Green’s function Monte Carlo study of light nuclei, Phys. Rev. C 36 (1987), no. 5, Article ID 2026. 10.1103/PhysRevC.36.2026Search in Google Scholar

[9] D. Ceperley, G. V. Chester and M. H. Kalos, Monte carlo simulation of a many-fermion study, Phys. Rev. B 16 (1977), no. 7, Article ID 3081. 10.1103/PhysRevB.16.3081Search in Google Scholar

[10] G. W. F. Drake and Z. C. Van, Variational eigenvalues for the S states of helium, Chem. Phys. Lett. 229 (1994), no. 4–5, 486–490. 10.1016/0009-2614(94)01085-4Search in Google Scholar

[11] S. Duane, A. D. Kennedy, B. J. Pendleton and D. Roweth, Hybrid Monte Carlo, Phys. Lett. B 195 (1987), no. 2, 216–222. 10.1016/0370-2693(87)91197-XSearch in Google Scholar

[12] T. D. Frank, Nonlinear Fokker–Planck Equations: Fundamentals and Applications, Springer, Berlin, 2005. Search in Google Scholar

[13] A. L. Garcia and B. J. Alder, Generation of the Chapman–Enskog distribution, J. Comput. Phys. 140 (1998), no. 1, 66–70. 10.1006/jcph.1998.5889Search in Google Scholar

[14] A. Gelman, H. S. Stern, J. B. Carlin, D. B. Dunson, A. Vehtari and D. B. Rubin, Bayesian Data Analysis, Chapman and Hall/CRC, Boca Raton, 2013. 10.1201/b16018Search in Google Scholar

[15] M. Girolami and B. Calderhead, Riemann manifold Langevin and Hamiltonian Monte Carlo methods, J. Roy. Statist. Soc. Ser. B 73 (2011), no. 2, 123–214. 10.1111/j.1467-9868.2010.00765.xSearch in Google Scholar

[16] W. K. Hastings, Monte Carlo sampling methods using markov chains and their applications, Biometrika 57 (1970), no. 1, 97–109. 10.1093/biomet/57.1.97Search in Google Scholar

[17] X. He and L. S. Luo, A priori derivation of the lattice Boltzmann equation, Phys. Rev. E 55 (1997), no. 6, Article ID R6333. 10.1103/PhysRevE.55.R6333Search in Google Scholar

[18] R. H. Heist, F. K. Fong, Maxwell–Boltzmann distribution of M3+-F- interstitial pairs in fluorite-type lattices, Phys. Rev. B 1 (1970), no. 7, Article ID 2970. 10.1103/PhysRevB.1.2970Search in Google Scholar

[19] C. Huiszoon and W. J. Briels, The static dipole polarizabilities of helium and molecular hydrogen by differential diffusion Monte Carlo, Chem. Phys. Lett. 203 (1993), no. 1, 49–54. 10.1016/0009-2614(93)89309-6Search in Google Scholar

[20] R. Jordan, D. Kinderlehrer and F. Otto, The variational formulation of the Fokker–Planck equation, SIAM J. Math. Anal. 29 (1998), no. 1, 1–17. 10.1137/S0036141096303359Search in Google Scholar

[21] H. A. Kramers, Brownian motion in a field of force and the diffusion model of chemical reactions, Physica 7 (1940), no. 4, 284–304. 10.1016/S0031-8914(40)90098-2Search in Google Scholar

[22] B. H. Lavenda, Nonequilibrium Statistical Thermodynamics, Wiley, New York, 1985. Search in Google Scholar

[23] W. L. McMillan, Ground state of liquid He 4, Phys. Rev. 138 (1965), no. 2A, 442–451. 10.1103/PhysRev.138.A442Search in Google Scholar

[24] R. Metzler, E. Barkai and J. Klafter, Anomalous diffusion and relaxation close to thermal equilibrium: A fractional Fokker–Planck equation approach, Phys. Rev. Lett. 82 (1999), no. 18, Article ID 3563. 10.1103/PhysRevLett.82.3563Search in Google Scholar

[25] R. M. Neal, Mcmc using Hamiltonian dynamics, Handbook of Markov Chain Monte Carlo, Chapman & Hall/CRC, Boca Raton (2011), 113–162. 10.1201/b10905-6Search in Google Scholar

[26] S. H. Patil, Wavefunctions for the confined hydrogen atom based on coalescence and inflexion properties, J. Phys. B 35 (2002), no. 2, Article ID 255. 10.1088/0953-4075/35/2/305Search in Google Scholar

[27] G. Roberts and O. Stramer, Langevin diffusions and metropolis-Hastings algorithms, Methodol. Comput. Appl. Probab. 4 (2003), no. 4, 337–358. 10.1023/A:1023562417138Search in Google Scholar

[28] M. Rodriguez-Bautista, C. Diaz-Garcia, A. M. Navarrete-Lopez, R. Vargas and J. Garza, Roothaan’s approach to solve the Hartree–Fock equations for atoms confined by soft walls: Basis set with correct asymptotic behavior, J. Chem. Phys. 143 (2015), no. 3, Article ID 034103.e. 10.1063/1.4926657Search in Google Scholar PubMed

[29] K. K. Sabelfeld, Monte Carlo Methods in Boundary Value Problems, Springer, Berlin, 1991. 10.1007/978-3-642-75977-2Search in Google Scholar

[30] E. Schrödinger, An undulatory theory of the mechanics of atoms and molecules, Phys. Rev. 28 (1926), no. 6, Article ID 1049. 10.1103/PhysRev.28.1049Search in Google Scholar

[31] N. Trivedi and D. M. Ceperley, Green-function Monte Carlo study of quantum antiferromagnets, Phys. Rev. B 40 (1989), no. 4, Article ID 2737. 10.1103/PhysRevB.40.2737Search in Google Scholar

[32] N. Trivedi and D. M. Ceperley, Ground-state correlations of quantum antiferromagnets: A green-function monte carlo study, Phys. Rev. B 41 (1990), no. 7, Article ID 4552. 10.1103/PhysRevB.41.4552Search in Google Scholar

[33] G. E. Uhlenbeck and L. S. Ornstein, On the theory of the Brownian motion, Phys. Rev. 36 (1930), no. 5, Article ID 823. 10.1103/PhysRev.36.823Search in Google Scholar

[34] W. Wagner, A random walk model for the Schrödinger equation, Math. Comput. Simulation 143 (2018), 138–148. 10.1016/j.matcom.2016.07.012Search in Google Scholar

[35] T. D. Young, R. Vargas and J. Garza, A Hartree–Fock study of the confined helium atom: Local and global basis set approaches, Phys. Lett. A 380 (2016), no. 5–6, 712–717. 10.1016/j.physleta.2015.11.021Search in Google Scholar

[36] Z. Zarezadeh, Cellular automaton-based pseudorandom number generator, Complex Systems 26 (2017), no. 4, 373–389. 10.25088/ComplexSystems.26.4.373Search in Google Scholar

[37] NIST, Atomic Spectra Database Ionization Energies Data (2018). Search in Google Scholar