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Lanczos-Pascal Approach to Correlation Functions in Chaotic Quantum Systems
Merlin Füllgraf1, Jiaozi Wang1, Robin Steinigeweg1
1University of Osnabrück, Department of Mathematics/Computer Science/Physics, D-49076 Osnabrück, Germany.
Physical Review Letters
|January 20, 2026
Summary
We present a computationally inexpensive method to approximate temporal correlation functions in chaotic many-body systems using Lanczos coefficients. The method shows rapid convergence, especially with smoothly structured coefficients, accurately describing damped oscillations.
Area of Science:
- Quantum mechanics
- Statistical physics
- Computational physics
Background:
- Chaotic many-body systems present challenges in calculating temporal correlation functions.
- Approximations are needed for systems in the thermodynamic limit.
Purpose of the Study:
- To develop an efficient method for approximating temporal correlation functions.
- To utilize Lanczos coefficients for this approximation.
Main Methods:
- The proposed method computes approximations based on Lanczos coefficients.
- Convergence is analyzed with respect to the number of coefficients used.
Main Results:
- The method is computationally inexpensive.
- Rapid convergence is observed when Lanczos coefficients show a smooth structure.
- Agreement with dynamical typicality computations for large systems was found.
Conclusions:
- The method provides accurate approximations for temporal correlation functions.
- Correlation functions can be well-described by a few damped oscillations in these systems.
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