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A novel small matrix decomposition (SMatPI) simplifies path integral calculations for systems interacting with dissipative baths. This method efficiently computes the reduced density matrix by reducing complex terms to negligible magnitudes.

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Area of Science:

  • Quantum Mechanics
  • Statistical Physics
  • Computational Chemistry

Background:

  • Calculating the reduced density matrix for systems coupled to dissipative environments is computationally challenging.
  • Path integral methods are powerful but often suffer from high dimensionality and entanglement complexity.
  • Dissipative harmonic baths introduce memory effects that complicate quantum dynamics.

Purpose of the Study:

  • To develop a computationally efficient method for obtaining the reduced density matrix of a system interacting with a dissipative harmonic bath.
  • To introduce a small matrix decomposition (SMatPI) technique for simplifying path integral expressions.
  • To analyze the time scales governing temporal entanglement and bath-induced memory.

Main Methods:

  • A recursive small matrix decomposition (SMatPI) of the path integral is employed.
  • Entangled influence functional terms are spread over time intervals until they become negligible.
  • A diagrammatic approach is used to describe the theoretical framework, complemented by analytical and numerical calculations.

Main Results:

  • SMatPI allows for efficient summation over path integral variables via multiplication of small matrices.
  • The required time for temporal entanglement to become negligible is found to be comparable to the bath-induced memory time.
  • The properties and structure of the resulting propagator matrices are analyzed.

Conclusions:

  • The SMatPI method offers a significant simplification for calculating reduced density matrices in dissipative quantum systems.
  • The findings provide insights into the relationship between temporal entanglement and bath memory effects.
  • The method is applicable to complex multistate systems, demonstrating its versatility.