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Spin systems where the difference in chemical shifts of the coupled nuclei is greater than ten times J are called first-order spin systems. These nuclei are weakly coupled, and their chemical shifts and coupling constant can generally be estimated from the well-separated signals in the spectrum.
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Updated: Dec 17, 2025

In Situ Monitoring of Diffusion of Guest Molecules in Porous Media Using Electron Paramagnetic Resonance Imaging
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Quantum diffusion in spin chains with phase space methods.

Jonathan Wurtz1, Anatoli Polkovnikov1

  • 1Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA.

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Summary
This summary is machine-generated.

The cluster truncated Wigner approximation (CTWA) bridges microscopic quantum dynamics and long-time hydrodynamics. This method accurately captures emergent diffusive behavior in quantum spin systems, overcoming limitations of exact simulations.

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Area of Science:

  • Quantum physics
  • Condensed matter theory
  • Statistical mechanics

Background:

  • Connecting microscopic quantum dynamics with macroscopic hydrodynamic behavior in strongly correlated systems remains a significant challenge.
  • Determining hydrodynamic coefficients like diffusion constants and viscosity from microscopic models is difficult due to limitations in exact quantum simulations (small system sizes, short times).

Purpose of the Study:

  • To demonstrate that the cluster truncated Wigner approximation (CTWA) can overcome the limitations of exact simulations in studying quantum systems.
  • To investigate the dynamics of strongly correlated quantum systems, specifically spin-1/2 chains and spin ladders, and their transition from short-time to long-time behavior.

Main Methods:

  • The study employs the cluster truncated Wigner approximation (CTWA), a method that maps quantum Hamiltonian dynamics to classical Hamiltonian dynamics in an expanded phase space.
  • CTWA is applied to XXZ next-nearest-neighbor spin-1/2 chains and XY spin ladders.
  • The method requires sampling from fluctuating initial conditions, contrasting with Dirac mean-field approaches.

Main Results:

  • CTWA successfully reproduces the crossover from short-time spin relaxation to emergent long-time diffusive behavior in the studied quantum spin systems.
  • For random initial states, CTWA accurately predicts the entire spin spectral function.
  • The importance of incorporating initial state fluctuations is highlighted, as neglecting them leads to inaccurate predictions.

Conclusions:

  • The cluster truncated Wigner approximation (CTWA) provides a viable and accurate method for connecting microscopic quantum dynamics with long-time hydrodynamics.
  • CTWA overcomes the computational limitations of exact quantum simulations for studying emergent phenomena in strongly correlated quantum systems.
  • Accurate modeling necessitates the inclusion of initial state fluctuations, as demonstrated by the failure of mean-field approximations.