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We derived an upper bound for quantum transport diffusivity in dissipative spin systems. This bound, D≤D_{0}+(αv_{LR}τ+βξ)v_{C}, uses measurable parameters to constrain sub-ballistic diffusion.

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Area of Science:

  • Quantum physics
  • Condensed matter physics
  • Statistical mechanics

Background:

  • Quantum Markovian systems exhibit complex transport phenomena.
  • Dissipation and decoherence significantly impact quantum dynamics.
  • Understanding transport bounds is crucial for quantum information science.

Purpose of the Study:

  • To establish a general upper bound for diffusivity in dissipative quantum spin systems.
  • To relate quantum transport to measurable microscopic and local parameters.
  • To generalize existing bounds like the Lieb-Robinson bound to dissipative regimes.

Main Methods:

  • Derivation of a novel upper bound for diffusivity.
  • Analysis of a specific model: spin-half XXZ chain with on-site dephasing.
  • Utilizing concepts of Lieb-Robinson velocity and decoherence time.

Main Results:

  • An explicit upper bound on diffusivity: D≤D_{0}+(αv_{LR}τ+βξ)v_{C}.
  • The bound depends on microscopic interactions (D_{0}, v_{LR}, v_{C}, ξ) and local measurements (τ, α, β).
  • Demonstration with the XXZ spin chain, showing constrained sub-ballistic diffusion.

Conclusions:

  • The derived bound provides a powerful tool for characterizing quantum transport in open systems.
  • It bridges the gap between microscopic Hamiltonians and observable transport properties.
  • This work advances the understanding of quantum dynamics in the presence of dissipation.