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Researchers established connections between Nakajima-Zwanzig memory kernels and influence functions for quantum systems. This work offers a new method for understanding non-Markovian dynamics and quantum sensing.

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Area of Science:

  • Quantum mechanics
  • Quantum dynamics
  • Condensed matter physics

Background:

  • Quantum systems coupled to baths exhibit memory effects, often studied via Nakajima-Zwanzig memory kernels or influence functions.
  • Formal connections between these two formalisms for describing quantum dynamics have been previously unknown.

Purpose of the Study:

  • To establish the formal connections between Nakajima-Zwanzig memory kernels and influence functions.
  • To develop a non-perturbative method for constructing memory kernels from influence functions.
  • To provide a framework for interpreting approximate path integral methods and enabling Hamiltonian learning.

Main Methods:

  • Examining the system propagator for N-level systems linearly coupled to Gaussian baths.
  • Developing a non-perturbative, diagrammatic approach to construct memory kernels from influence functions.
  • Utilizing reduced system trajectories for Hamiltonian learning.

Main Results:

  • Explicit connections between Nakajima-Zwanzig memory kernels and influence functions were established.
  • A novel non-perturbative, diagrammatic method was devised to construct memory kernels from influence functions.
  • A Hamiltonian learning procedure was proposed to extract bath spectral density from system trajectories.

Conclusions:

  • The established connections advance the understanding of non-Markovian quantum dynamics.
  • The developed methods offer new avenues in quantum sensing and engineering.
  • This work serves as a foundation for future theoretical and experimental advancements in quantum dynamics.