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Exponential parameterization of wave functions for quantum dynamics: Time-dependent Hartree in second quantization.

Niels Kristian Madsen1, Mads Bøttger Hansen1, Alberto Zoccante1

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We developed a new quantum dynamics method using second-quantization (SQ) formulation for efficient calculations. This approach, particularly the exponential time-dependent Hartree (X-TDH) method, enables the study of large molecular systems.

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Area of Science:

  • Quantum dynamics
  • Computational chemistry
  • Theoretical physics

Background:

  • Accurate simulation of molecular dynamics is crucial for understanding chemical reactions.
  • Existing methods often face computational limitations for large systems.
  • Time-dependent Hartree (TDH) methods offer a promising avenue for quantum dynamics.

Purpose of the Study:

  • To derive and implement efficient equations for time evolution of variational wave functions.
  • To develop a second-quantization (SQ) formulation for quantum dynamics.
  • To enable scalable simulations of large molecular systems.

Main Methods:

  • Derivation of equations for linear (L-TDH) and exponential (X-TDH) parameterizations within SQ formalism.
  • Utilizing state-transfer operators for exact and approximate wave functions.
  • Implementation with linear scaling with respect to degrees of freedom (M).

Main Results:

  • Detailed expressions for efficient L-TDH and X-TDH evaluation.
  • Demonstrated significant computational cost reduction for X-TDH compared to L-TDH.
  • Validated linear scaling for large systems, including Henon-Heiles potentials and polycyclic aromatic hydrocarbons.

Conclusions:

  • The SQ formulation and X-TDH method provide a computationally efficient approach for quantum dynamics.
  • These methods significantly reduce computational cost for systems with many operator terms.
  • Paves the way for studying time-resolved quantum dynamics of large molecules.