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Lanczos-Pascal Approach to Correlation Functions in Chaotic Quantum Systems.

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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.

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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.