Denoising and Extension of Response Functions in the Time Domain.

Area of Science:

• Quantum Mechanics
• Condensed Matter Physics
• Quantum Information

Background:

• Response functions (e.g., electron Green's functions, susceptibilities) characterize quantum system behavior under external perturbations.
• These functions are fundamental in quantum field theories, quantum computing, and experimental measurements.
• A key property is their intrinsic causality, linking past causes to future effects.

Purpose of the Study:

• To explore the implications of causality and spectral properties of response functions.
• To demonstrate how these properties can be leveraged for data analysis and theoretical modeling.
• To establish a framework for constructing reliable extensions of experimental data.

Main Methods:

• Theoretical analysis of response functions in quantum systems.
• Exploitation of the connection between causality and positive spectral functions in equilibrium/steady-state.
• Application of Hilbert space inner product properties to data processing.

Main Results:

• Response functions in equilibrium/steady-state systems correspond to positive spectral functions.
• The positive definite nature of response functions allows for noise reduction in measured data.
• A method is presented to construct positive definite extensions for finite time-interval data, ensuring positive spectra.

Conclusions:

• The inherent causality and spectral properties of response functions offer powerful tools for quantum system analysis.
• These findings have implications for improving the accuracy of experimental measurements and theoretical predictions.
• The developed methods ensure the physical validity (positive spectra) of processed quantum data.