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Momentum-dependent quantum Ruelle-Pollicott resonances in translationally invariant many-body systems.

Marko Žnidarič1

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We explore Ruelle-Pollicott resonances in quantum many-body systems. Different correlation functions decay at distinct rates, revealing insights into system dynamics and symmetries.

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Area of Science:

  • Quantum physics
  • Statistical mechanics
  • Condensed matter theory

Background:

  • Ruelle-Pollicott resonances are crucial for understanding dynamical properties of classical and quantum systems.
  • Investigating these resonances in translationally invariant quantum many-body lattice systems provides insights into complex behaviors like chaos and thermalization.

Purpose of the Study:

  • To analyze Ruelle-Pollicott resonances in quantum many-body lattice systems using spectral properties of operator propagators.
  • To understand the momentum dependence of correlation function decay rates and their relation to system symmetries.

Main Methods:

  • Studying the spectra of momentum-resolved operator propagators on infinite quantum many-body lattice systems.
  • Analyzing the kicked Ising model as a specific case to observe resonance structures and decay behaviors.
  • Theoretically predicting the size of the annular random matrix-like ring in the spectrum.

Main Results:

  • Different correlation functions exhibit distinct decay rates, influenced by system symmetries.
  • The spectrum often features a random matrix-like annular ring and isolated resonances.
  • A mixing regime with power-law decay of correlation functions was identified, showing timescale differences due to conserved operators.

Conclusions:

  • The study provides a theoretical framework for understanding Ruelle-Pollicott resonances in quantum many-body systems.
  • Momentum-resolved analysis reveals intricate details about correlation function dynamics and system symmetries.
  • A conjecture for the singular values of the operator propagator suggests a singularity at a specific point.