Open Access
Issue
ESAIM: M2AN
Volume 56, Number 6, November-December 2022
Page(s) 2197 - 2238
DOI https://doi.org/10.1051/m2an/2022079
Published online 08 December 2022
  1. E. Teller, The crossing of potential surfaces. J. Phys. Chem. 41 (1937) 109–116. [CrossRef] [Google Scholar]
  2. A. Kammonen, P. Plecháč, M. Sandberg and A. Szepessy, Canonical quantum observables for molecular systems approximated by ab initio molecular dynamics. Ann. Henri Poincare 19 (2018) 2727–2781. [CrossRef] [MathSciNet] [Google Scholar]
  3. R.F. Feynman, Statistical Mechanics: A Set of Lectures. Westview Press, Boulder, CO (1998). [Google Scholar]
  4. G. Morandi, F. Napoli and E. Ercolessi, Statistical Mechanics: An Intermediate Course. World Scientific Publishing, Singapore (2001). [CrossRef] [Google Scholar]
  5. G.W. Ford and M. Kac, On the quantum Langevin equation. J. Statist. Phys. 46 (1987) 803–810. [CrossRef] [MathSciNet] [Google Scholar]
  6. H. Hoel and A. Szepessy, Classical Langevin dynamics derived from quantum mechanics. Discrete Continuous Dyn. Syst. B 25 (2020) 4001–4038. [CrossRef] [MathSciNet] [Google Scholar]
  7. J.-P. Hansen and I.R. McDonald, Theory of Simple Liquids. Academic Press, London and New York (1985). [Google Scholar]
  8. H.-M. Stiepan and S. Teufel, Semiclassical approximations for Hamiltonians with operator-valued symbols. Comm. Math. Phys. 320 (2013) 821–849. [CrossRef] [MathSciNet] [Google Scholar]
  9. E. Wigner, On the quantum correction for thermodynamic equilibrium. Phys. Rev. 40 (1932) 749–759. [CrossRef] [Google Scholar]
  10. P.-L. Lions and T. Paul, Sur les mesures de Wigner. Revista Matemática Iberoamericana 9 (1993) 553–618. [CrossRef] [MathSciNet] [Google Scholar]
  11. A. Figalli, M. Ligabò and T. Paul, Semiclassical limit for mixed states with singular and rough potentials. Indiana Univ. Math. J. 61 (2012) 193–222. [CrossRef] [MathSciNet] [Google Scholar]
  12. M. Zworski, Semiclassical Analysis. American Mathematical Society, Providence, RI (2012). [CrossRef] [Google Scholar]
  13. A. Martinez, An Introduction to Semiclassical and Microlocal Analysis. Springer Verlag, New York (2002). [CrossRef] [Google Scholar]
  14. A. Bouzounia and D. Robert, Uniform semiclassical estimates for the propagation of quantum observables. Duke Math. J. 111 (2002) 223–252. [CrossRef] [MathSciNet] [Google Scholar]
  15. G. François and T. Paul, Semiclassical evolution with low regularity. J. Math. Pures App. 151 (2021) 257–311. [CrossRef] [Google Scholar]
  16. S. Habershon, D.E. Manolopoulos, T.E. Markland and T.F. Miller 3rd, Ring-polymer molecular dynamics: quantum effects in chemical dynamics from classical trajectories in an extended phase space. Ann. Rev. Phys. Chem. 64 (2013) 387–413. [CrossRef] [PubMed] [Google Scholar]
  17. A. Pérez, M.E. Tuckerman and M.H. Müser, A comparative study of the centroid and ring-polymer molecular dynamics methods for approximating quantum time correlation functions from path integrals. J. Chem. Phys. 130 (2009) 184105. [CrossRef] [Google Scholar]
  18. T. Dornheim, S. Groth, A.V. Filinov and M. Bonitz, Path integral Monte Carlo simulation of degenerate electrons: permutation-cycle properties. J. Chem. Phys. 151 (2019) 014108. [CrossRef] [PubMed] [Google Scholar]
  19. L.C. Evans, Partial Differential Equation. American Mathematical Society, Providence, RI (1998). [Google Scholar]
  20. L. Amour, L. Jager and J. Nourrigat, The Weyl symbol of Schrödinger semigroups. Ann. Henri Poincare 16 (2015) 1479–1488. [CrossRef] [MathSciNet] [Google Scholar]
  21. G. Papanicolaou and R. Hersh, Non-commuting random evolutions, and an operator-valued Feynman-Kac formula. Comm. Pure Appl. Math. XXV (1972) 337–367. [Google Scholar]
  22. I. Karatzas and S.E. Shreve, Brownian Motion and Stochastic Calculus. Springer Verlag, New York (1998). [CrossRef] [Google Scholar]
  23. T.H. Gronwall, Note on the derivatives with respect to a parameter of the solutions of a system of differential equations. Ann. Math. 20 (1919) 292–296. [CrossRef] [MathSciNet] [Google Scholar]
  24. E. Cancès, C. Le Bris and P.-L. Lions, Molecular simulation and related topics: some open mathematical problems. Nonlinearity 21 (2008) T165–T176. [CrossRef] [Google Scholar]
  25. B. Leimkuhler and C. Matthews, Molecular Dynamics: With Deterministic and Stochastic Numerical Methods. Springer, Berlin (2015). [CrossRef] [Google Scholar]
  26. D. Marx and J. Hutter, Ab Initio Molecular Dynamics: Basic Theory and Advanced Methods. Cambridge University Press, Cambridge (2009). [CrossRef] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you