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Studying Soft-matter and Biological Systems over a Wide Length-scale from Nanometer and Micrometer Sizes at the Small-angle Neutron Diffractometer KWS-2
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Asymptotic neutron scattering laws for anomalously diffusing quantum particles.

Gerald R Kneller1

  • 1Centre de Biophysique Moléculaire, CNRS, Rue Charles Sadron, 45071 Orléans, France; Université d'Orléans, Chateau de la Source-Ave. du Parc Floral, 45067 Orléans, France; and Synchrotron-SOLEIL, L'Orme de Merisiers, 91192 Gif-sur-Yvette, France.

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This study presents a model-free method for analyzing neutron scattering data from quantum particles exhibiting anomalous diffusion. It reveals how quantum effects influence particle behavior and provides a new relation for the fractional diffusion constant.

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Area of Science:

  • Condensed matter physics
  • Quantum mechanics
  • Statistical mechanics

Background:

  • Anomalous diffusion describes particle movement deviating from classical Brownian motion.
  • Quasielastic neutron scattering (QENS) is a powerful technique for probing atomic and molecular dynamics.
  • Understanding quantum particle diffusion is crucial in various physical systems.

Purpose of the Study:

  • To develop a model-free approach for analyzing QENS data of anomalously diffusing quantum particles.
  • To investigate the role of quantum effects in intermediate scattering functions and velocity autocorrelation functions.
  • To establish a Green-Kubo type relation for the fractional diffusion constant.

Main Methods:

  • Analysis of time-dependent mean square displacements (MSD) with growth proportional to t(α).
  • Inclusion of confined diffusion (α = 0).
  • Examination of the asymptotic form of MSD and its relation to quantum time correlation functions.

Main Results:

  • A model-free framework for QENS analysis of quantum anomalous diffusion is established.
  • Quantum symmetry properties are shown to influence the intermediate scattering function and velocity autocorrelation spectrum.
  • A Green-Kubo relation is derived for the fractional diffusion constant using the real part of the velocity autocorrelation function.

Conclusions:

  • The developed theory provides an exact description in the diffusive regime and at moderate momentum transfers.
  • This approach offers new insights into quantum diffusion phenomena and their characterization via QENS.
  • The findings are applicable to systems where quantum particles exhibit anomalous diffusion.