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Quantum dynamics in multistate harmonic models using tensor-train thermofield dynamics and semiclassical mapping

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We present quantum dynamics of the multi-state harmonic model using exact tensor-train calculations. This validates approximate methods for complex systems, showing reliable predictions in specific regimes.

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Area of Science:

  • Quantum dynamics
  • Condensed-phase systems
  • Computational chemistry

Background:

  • Accurate quantum dynamics simulations are crucial for understanding chemical processes.
  • Developing and validating computational methods for complex systems remains a challenge.
  • The multi-state harmonic (MSH) model offers a general framework for effective model Hamiltonians.

Purpose of the Study:

  • To present numerically exact quantum dynamics of the MSH model using tensor-train (TT) calculations.
  • To benchmark various approximate semiclassical and mixed quantum-classical dynamics methods against exact TT results.
  • To establish the MSH model as a tool for validating nonadiabatic dynamics methods.

Main Methods:

  • Numerically exact tensor-train (TT)-based calculations for quantum dynamics.
  • Rank-adaptive TT-KSL scheme for efficient wavepacket propagation.
  • TT-thermofield dynamics for finite-temperature simulations.
  • Benchmarking against linearized semiclassical (LSC), symmetrical quasiclassical, classical mapping models (CMMs), mean-field Ehrenfest, and fewest-switches surface hopping dynamics.

Main Results:

  • Exact quantum dynamics of the MSH model were computed using TT methods.
  • Approximate methods were systematically benchmarked across various MSH model parameters.
  • In the adiabatic-inverted regime, strong coupling and low reorganization energy led to convergence of approximate methods with exact results.
  • Discrepancies were observed in nonadiabatic or normal regimes, with resolution-of-identity LSC and CMMs showing reliable predictions.

Conclusions:

  • The MSH model, combined with TT calculations, provides a robust framework for studying quantum dynamics.
  • The study identifies regimes where different approximate methods perform reliably or show discrepancies.
  • This work establishes the MSH model as a valuable tool for validating nonadiabatic dynamics methods in complex condensed-phase systems.