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Ring-polymer, centroid, and mean-field approximations to multi-time Matsubara dynamics.

Kenneth A Jung1, Pablo E Videla1, Victor S Batista1

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New multi-time dynamics methods, including ring-polymer molecular dynamics (RPMD) and centroid molecular dynamics (CMD), are derived. RPMD shows higher short-time accuracy for multi-time correlation functions than CMD.

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Area of Science:

  • Quantum Chemistry
  • Computational Physics
  • Statistical Mechanics

Background:

  • Matsubara dynamics are crucial for quantum systems.
  • Generalizing these dynamics to multiple time points is essential for advanced simulations.
  • Existing methods may lack accuracy for complex multi-time correlations.

Purpose of the Study:

  • To formally derive multi-time generalizations of path-integral molecular dynamics methods.
  • To analyze the short-time accuracy of these novel multi-time dynamics.
  • To provide theoretical justification for using path-integral approximations in multi-time correlation calculations.

Main Methods:

  • Generalization of Matsubara dynamics to the multi-time realm.
  • Formal derivation of multi-time ring-polymer molecular dynamics (RPMD), thermostatted RPMD (TRPMD), centroid molecular dynamics (CMD), and mean-field Matsubara dynamics.
  • Short-time accuracy analysis of the derived methodologies.

Main Results:

  • Successful derivation of multi-time RPMD, TRPMD, CMD, and mean-field Matsubara dynamics.
  • TRPMD demonstrates accuracy up to the third order (t3) for multi-time correlation functions of linear operators.
  • CMD shows accuracy only up to the first order (t), indicating reduced accuracy compared to single-time methods.

Conclusions:

  • The developed multi-time dynamics methods offer a robust framework for quantum simulations.
  • TRPMD provides a more accurate approximation for multi-time correlation functions than CMD.
  • This work validates the use of path-integral-based approximations for calculating multi-time correlation functions.