暴胀热Krylov复杂度
Thermal Krylov complexity and entropy of inflationary modes with different comoving-wavenumber dependences
AI总结：
该研究在三种共动动量修正框架下探究原初扰动的热Krylov复杂度与热K熵，通过推导热波函数等分析量子信息动力学，为区分暴胀宇宙学的量子引力修正提供了有效探针。
摘要：
本研究在三种共动动量修正框架下探究原初扰动的热Krylov复杂度与热K熵，这些框架包括正则标量场暴胀（标准暴胀）、非平凡声速及修正色散关系。采用热场双态纯化方法，我们推导得到热波函数，并获得有效温度与压缩角的演化，进一步对比了闭合与开放热量子系统的量子信息动力学。数值结果表明，共动动量会抑制标准暴胀中Krylov可观测量的增长；在非平凡声速模型中，更大的修正强度会增强其振荡行为，而修正色散关系模型中的紫外修正会诱导阶段依赖的振荡。通过分析Lanczos系数与耗散强度，我们发现系统耗散会抑制量子相干振荡，仅在非平凡声速足够大时才会出现持续振荡，而修正色散关系则产生单调演化。这些独特特征为区分暴胀宇宙学中的量子引力修正提供了有效的量子信息探针。
英文摘要：
We study thermal Krylov complexity and Krylov entropy for primordial scalar modes in three inflationary models with different comoving-wavenumber dependences. These models are canonical single-field inflation, a non-trivial sound speed model, and a modified dispersion relation model. We construct a purified two-mode thermal state and first study its unitary Krylov evolution in an ideal closed system. In the parameter range considered here, the sound-speed correction increases the mean values and oscillation amplitudes of the Krylov quantities. The modified dispersion relation produces a stage-dependent oscillatory structure. We then introduce an independent effective open-system parametrization. The normalized Krylov distribution is controlled by a geometric ratio that combines thermal occupation, coherent spreading, and effective attenuation. We derive explicit expressions for Krylov complexity and Krylov entropy. We also obtain their low- and high-temperature limits. The sound-speed correction enhances the geometric ratio in the adopted parameter range. For the modified dispersion relation, coherent spreading and effective attenuation compete. These results show how thermal occupation and modified mode frequencies control Krylov-space spreading in the three inflationary models.
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