AI 中文总结
该研究在NRQCD和pNRQCD框架下推导通用林德布拉德方程，首次从通用林德布拉德框架得到耦合单态-八态玻尔兹曼方程，还推导了单态玻尔兹曼方程的领头量子修正，为夸克偶素输运描述建立了更系统的理论基础。
AI 中文摘要
近期，在非相对论量子色动力学（NRQCD）框架内，一组耦合的单态-八态通用林德布拉德方程（ULEs）被推导出来，用于描述夸克胶子等离子体（QGP）中的夸克偶素动力学，这些方程提供了涵盖量子布朗和量子光学区域的统一量子描述。本工作进一步发展了该框架，并建立了其与半经典输运的联系。我们首先在势非相对论量子色动力学（pNRQCD）有效场论内推导通用林德布拉德方程，证明其与NRQCD ULEs的小偶极极限一致；随后推导NRQCD ULEs的半经典极限，得到一组耦合的单态-八态玻尔兹曼方程。据我们所知，这是首次直接从通用林德布拉德框架推导玻尔兹曼输运方程，所得方程在小偶极近似之外仍有效，可描述重夸克对从紧凑到广泛分离构型的演化。取其小偶极极限可与Yao等人[Phys. Rev. D 99, 096028 (2019)]推导的玻尔兹曼方程直接对比，后者在pNRQCD内基于Davies久期方程推导，依赖旋转波近似（RWA）。结果发现单态方程近乎完全一致，而八态方程包含额外的碰撞项，描述八态散射态连续谱内的跃迁，这是基于RWA的推导所缺失的。最后，我们推导了单态玻尔兹曼方程的领头量子修正，我们的结果为QGP中夸克偶素的半经典输运描述建立了更通用、系统的理论基础。
英文摘要
Recently, a set of coupled singlet-octet universal Lindblad equations (ULEs) was derived within the framework of non-relativistic QCD (NRQCD) to describe quarkonium dynamics in the quark-gluon plasma (QGP). These equations provide a unified quantum description spanning the quantum Brownian and quantum optical regimes. In this work, we further develop this framework and establish its connection with semiclassical transport. We first derive the universal Lindblad equations within the potential non-relativistic QCD (pNRQCD) effective field theory and show that they coincide with the small-dipole limit of the NRQCD ULEs. We then derive the semiclassical limit of the NRQCD ULEs, obtaining a set of coupled singlet-octet Boltzmann equations. To our knowledge, this is the first derivation of Boltzmann transport equations directly from the universal Lindblad framework. The resulting equations are valid beyond the small-dipole approximation, allowing the evolution of heavy-quark pairs from compact to widely separated configurations. Taking their small-dipole limit allows a direct comparison with the Boltzmann equations of Yao et al. [Phys. Rev. D 99, 096028 (2019)], which were derived within pNRQCD from the Davies secular equation, relying on the rotating-wave approximation (RWA). While the singlet equations are found to be in near-complete agreement, the octet equation contains an additional collision term describing transitions within the continuum of octet scattering states, which is absent from the RWA-based derivation. Finally, we derive the leading quantum correction to the singlet Boltzmann equation. Our results establish a more general and systematic theoretical foundation for the semiclassical transport description of quarkonium in the QGP.
Comments21 pages, excluding appendices
