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Flux-fluctuation relation for quantum walks on networks.

Nisarg Vyas1, M S Santhanam1

  • 1Indian Institute of Science Education and Research, Physics Department, Pune 411008, India.

Physical Review. E
|February 20, 2026
PubMed
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Researchers derived a quantum flux-fluctuation relation for quantum walks on networks. This quantum relation is similar to classical ones for phase-coherent walks, with quantum effects being minor.

Area of Science:

  • Quantum mechanics
  • Network theory
  • Statistical physics

Background:

  • Classical random walks on networks exhibit a flux-fluctuation relation.
  • This relation connects mean flux and fluctuation strength.
  • Equivalent relations for quantum walks remain largely unexplored.

Purpose of the Study:

  • To establish a quantum version of the flux-fluctuation relation for quantum walks.
  • To analyze its validity and characteristics on arbitrary networks.

Main Methods:

  • Derivation of the quantum flux-fluctuation relation.
  • Numerical simulations of quantum walks on various network types (periodic lattices, scale-free, Erdős-Rényi).

Main Results:

Related Experiment Videos

  • A general quantum flux-fluctuation relation was obtained, valid for networks with nondegenerate unitary walk operator spectra.
  • For phase-coherent quantum walks, the relation closely mirrors its classical counterpart, with minimal quantum effects.
  • Numerical simulations confirmed the analytical findings.

    • Conclusions:

    • The study provides a fundamental relation for quantum walks on networks.
    • It highlights the conditions under which quantum walks behave classically in terms of flux-fluctuations.
    • Implications for quantum walk dynamics under specific spectral conditions were discussed.