Higher-order disorder correlations control reflected phonon counting statistics
Abstract
We investigate how structural correlations beyond the power spectrum affect phonon counting in a one-dimensional acoustic stack. An integer-thickness construction cancels the extensive leading backscattering term and leaves a finite-chain reflection amplitude determined by endpoint innovations. For symmetric independent innovations with unit variance and fourth moment μ4, the normalized reflected-power second moment tends to (μ4+5)/4. With vacuum environmental inputs, a two-phonon Fock input therefore gives an ensemble-averaged reflected factorial correlation g(2)=(μ4+5)/8. Two explicitly constructed ensembles with identical mean and complete two-point correlation function yield g(2)=3/4 and 9/8, placing their counting variances on opposite sides of the Poisson value. Conditional tensor averaging also gives a general fourth-order resistance-growth coefficient for arbitrary impedance contrast, including a positive higher-scattering contribution not recovered by shifting the lowest-order spectrum. Exact enumeration confirms the fixed-N, small-detuning limit and shows that increasing N at fixed detuning produces a crossover governed by accumulated higher-order bulk scattering rather than convergence to the endpoint formula. Further calculations test bandwidth, thickness error, propagation loss and thermal background. The result concerns disorder-averaged pulse statistics; it neither creates nonclassicality from coherent input nor changes the conditional factorial correlation of an individually resolved passive sample.
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BibTeX
@misc{sedrakyan2026higherorder,
title = {{Higher-order disorder correlations control reflected phonon counting statistics}},
author = {Ara Sedrakyan},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.25153},
eprint = {2610.25153},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.25153},
}
RIS
TY - UNPB
TI - Higher-order disorder correlations control reflected phonon counting statistics
AU - Ara Sedrakyan
PY - 2026
DA - 2026/10/18
PB - arXiv
DO - 10.48550/arxiv.2610.25153
UR - https://arxiv.org/abs/2610.25153
AB - We investigate how structural correlations beyond the power spectrum affect phonon counting in a one-dimensional acoustic stack. An integer-thickness construction cancels the extensive leading backscattering term and leaves a finite-chain reflection amplitude determined by endpoint innovations. For symmetric independent innovations with unit variance and fourth moment μ_4, the normalized reflected-power second moment tends to (μ_4+5)/4. With vacuum environmental inputs, a two-phonon Fock input therefore gives an ensemble-averaged reflected factorial correlation g^(2)=(μ_4+5)/8. Two explicitly constructed ensembles with identical mean and complete two-point correlation function yield g^(2)=3/4 and 9/8, placing their counting variances on opposite sides of the Poisson value. Conditional tensor averaging also gives a general fourth-order resistance-growth coefficient for arbitrary impedance contrast, including a positive higher-scattering contribution not recovered by shifting the lowest-order spectrum. Exact enumeration confirms the fixed-N, small-detuning limit and shows that increasing N at fixed detuning produces a crossover governed by accumulated higher-order bulk scattering rather than convergence to the endpoint formula. Further calculations test bandwidth, thickness error, propagation loss and thermal background. The result concerns disorder-averaged pulse statistics; it neither creates nonclassicality from coherent input nor changes the conditional factorial correlation of an individually resolved passive sample.
ER -