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Area of Science:

  • Quantum mechanics
  • Condensed matter physics
  • Statistical mechanics

Background:

  • Integrable many-body quantum systems exhibit predictable dynamics.
  • Perturbations can disrupt integrability, leading to chaotic behavior.
  • Understanding transport properties in such systems is crucial.

Purpose of the Study:

  • To investigate the transition from integrability to chaos in quantum systems under perturbation.
  • To analyze spin transport in the Heisenberg chain with impurities.
  • To explore the impact of infinitesimal and small extensive perturbations.

Main Methods:

  • Theoretical analysis of spin transport.
  • Examination of the Heisenberg chain model with impurities.
  • Thermodynamic limit considerations.

Main Results:

  • Infinitesimal perturbations induce diffusive spin transport in the thermodynamic limit.
  • A modified Matthiessen's rule is required for nonballistic systems.
  • Diffusion constant dependence on impurity density reveals a remnant of integrability.
  • Interacting scattering and impurity density show non-intuitive effects on transport.

Conclusions:

  • Small perturbations rapidly drive integrable systems towards chaos.
  • The Heisenberg chain with impurities exhibits a unique transport regime.
  • Further research is needed to fully understand complex scattering effects.