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arXiv · 2606.27648

Memory and thermal amplification in spin--cavity squared commutators

Yong-Hong Ma·Hui-Hui Xu·Jian-Zhuang Wu·Quan-Zhen Ding·Wu-Ming Liu·Xin-Yu Zhao·E Wu
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Abstract

Squared commutators in the Holstein--Primakoff limit of a spin--cavity system provide a compact way to separate propagation from covariance growth in a finite-temperature reservoir with memory. In the finite-temperature NMQSD construction, the linear quadrature commutator is fixed by the retarded spin--cavity propagator, whereas a quadratic commutator carries the same retarded factor together with a covariance factor. For a zero-mean Gaussian state, \(C_{R_i^2,R_j}(t)=4|\kappa_{ij}(t)|^2V_{ii}(t)\); the symmetrized expression gives the spin-side and mixed channels. Since \(\bar n\) enters the covariance sector but not the homogeneous retarded kernel, raising \(\bar n\) from 0 to 1 leaves the linear transfer unchanged while increasing the quadratic signal. Varying the bath-memory rate and the counter-rotating coupling within the stable HP region then shows how stored cavity history changes both the transfer weight and its distribution in time. The calculation separates memory-dependent propagation from thermal covariance growth in collective spin--cavity dynamics.

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Yong-Hong Ma, Hui-Hui Xu, Jian-Zhuang Wu, Quan-Zhen Ding, Wu-Ming Liu, Xin-Yu Zhao, E Wu. 2026-06-26. Memory and thermal amplification in spin--cavity squared commutators. https://arxiv.org/abs/2606.27648

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