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Flux-fluctuation relation for quantum walks on networks
1Indian Institute of Science Education and Research, Physics Department, Pune 411008, India.
Physical Review. E
|February 20, 2026
Summary
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:
- 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.
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