Response Functions as Quantifiers of Non-Markovianity.

Area of Science:

• Quantum Information Theory
• Open Quantum Systems
• Quantum Thermodynamics

Background:

• Dynamical maps typically model quantum systems interacting with their environment (baths) assuming initial system-bath state factorization.
• Quantifying non-Markovianity, a measure of memory effects in quantum dynamics, is crucial for understanding open quantum systems.

Purpose of the Study:

• To derive dynamical maps for initially correlated or entangled system-bath states using linear response theory.
• To develop a simpler and more universally applicable quantifier for quantum non-Markovianity.
• To investigate non-Markovianity in the context of the Caldeira-Leggett model.

Main Methods:

• Application of linear response theory to derive dynamical maps for non-factorized initial states.
• Development of a novel quantifier for quantum non-Markovianity based on time-translational invariant maps.
• Analytical investigation of the Caldeira-Leggett model with an Ohmic bath.

Main Results:

• Dynamical maps can be derived for initially correlated system-bath states, not just factorized ones.
• The new quantifier simplifies the assessment of non-Markovianity.
• A classical Brownian particle coupled to an Ohmic bath can exhibit non-Markovian behavior, dependent on initial state preparation.
• No monotonic relationship was found between the non-Markovianity quantifier and system-bath coupling strength or bath properties for a peaked spectral density.

Conclusions:

• Linear response theory offers a powerful tool for studying quantum dynamics with initial correlations.
• The developed quantifier provides a more accessible route to identifying and analyzing non-Markovian effects.
• Initial state preparation plays a significant role in the emergence of non-Markovianity, even in seemingly classical systems.