Extracting Chern numbers from the equilibrium transport noise of multiband bosons
Abstract
We show that the equilibrium transport noise of a multiband bosonic system carries a measurable imprint of its Chern numbers, and we give the protocol that extracts them. For electrons the topological part of the Berry curvature is absent from the transport noise: over a filled band it yields the quantized anomalous Hall conductivity, yet at a Fermi surface the Chern number is invisible to the fluctuations of the Hall current. That cancellation is an accident of the Fermi surface: magnons and phonons populate every band thermally, each with its own Chern number, so the harmonic sector of the Hodge decomposition is not a single constant, and a variance does not annihilate it. What survives is the occupation-weighted dispersion of Chern numbers. That current noise sees band geometry is known, and at zero temperature the antisymmetric part of the noise sum rule already returns a Chern number; the new element is an object with no zero-temperature analogue, existing only when several bands are populated and weighted differently. We derive it from a fluctuating Boltzmann equation and resolve the energy-magnetization subtraction at the level of fluctuations: the subtracted term is a curl, contributing exactly zero to the current a transport measurement records, and no magnetization auto-correlation enters the antisymmetric cross-spectrum at any wavevector. Measurement uses an equilibrium sum rule on that cross-spectrum, with no drive and hence no suppression: its frequency-integrated form cannot in practice separate topological from geometric content, for a rank reason, whereas the frequency-resolved form does, at accessible resolution. The protocol is specified for Cu(1,3-bdc), with calibration and robustness characterized. A driven alternative lies twelve orders below the equilibrium floor. Two independent implementations agree on every convention-free quantity.
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BibTeX
@misc{wang2026extracting,
title = {{Extracting Chern numbers from the equilibrium transport noise of multiband bosons}},
author = {Zhi-Wei Wang and Samuel L. Braunstein},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.18527},
eprint = {2608.18527},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.18527},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Extracting Chern numbers from the equilibrium transport noise of multiband bosons
AU - Zhi-Wei Wang
AU - Samuel L. Braunstein
PY - 2026
DA - 2026/09/06
PB - arXiv
DO - 10.48550/arxiv.2608.18527
UR - https://arxiv.org/abs/2608.18527
AB - We show that the equilibrium transport noise of a multiband bosonic system carries a measurable imprint of its Chern numbers, and we give the protocol that extracts them. For electrons the topological part of the Berry curvature is absent from the transport noise: over a filled band it yields the quantized anomalous Hall conductivity, yet at a Fermi surface the Chern number is invisible to the fluctuations of the Hall current. That cancellation is an accident of the Fermi surface: magnons and phonons populate every band thermally, each with its own Chern number, so the harmonic sector of the Hodge decomposition is not a single constant, and a variance does not annihilate it. What survives is the occupation-weighted dispersion of Chern numbers. That current noise sees band geometry is known, and at zero temperature the antisymmetric part of the noise sum rule already returns a Chern number; the new element is an object with no zero-temperature analogue, existing only when several bands are populated and weighted differently. We derive it from a fluctuating Boltzmann equation and resolve the energy-magnetization subtraction at the level of fluctuations: the subtracted term is a curl, contributing exactly zero to the current a transport measurement records, and no magnetization auto-correlation enters the antisymmetric cross-spectrum at any wavevector. Measurement uses an equilibrium sum rule on that cross-spectrum, with no drive and hence no suppression: its frequency-integrated form cannot in practice separate topological from geometric content, for a rank reason, whereas the frequency-resolved form does, at accessible resolution. The protocol is specified for Cu(1,3-bdc), with calibration and robustness characterized. A driven alternative lies twelve orders below the equilibrium floor. Two independent implementations agree on every convention-free quantity.
ER -