发表机构
Universidad Carlos III de Madrid; Friedrich-Alexander-Universität Erlangen-Nürnberg（马德里卡洛斯三世大学; 埃尔朗根-纽伦堡大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究推导了共享共同形式域的无界哈密顿量产生的量子演化差异的状态依赖界，并将其应用于带结构化玻色子场的自旋-玻色子模型，证明了旋转波近似的定量界，该界在大频率极限下近似精确。
AI 中文摘要
我们推导了由共享共同形式域的无界哈密顿量产生的两次量子演化之间差异的状态依赖界。主要技术工具是在半双线性形式层面而非算子层面进行的分部积分，这消除了对共同不变算子域的需求。所得估计涉及两个生成元的时间积分之差的范数，而非其范数的积分，因此对快振荡项产生的平均效应敏感。作为应用，我们证明了带结构化玻色子场的自旋-玻色子模型的旋转波近似的定量界，该模型由一般测度空间上的任意质量色散关系和适当类的形状因子描述。证明涉及对高频标度的仔细分析。该界在状态的稠密子空间上成立，是完全显式的，且其中涉及的所有常数仅依赖于模型的参数，而不依赖于频率标度，因此在大频率极限下该近似变得精确。
英文摘要
We derive state-dependent bounds on the difference between two quantum evolutions generated by unbounded Hamiltonians sharing a common form domain. The main technical tool is a second integration by parts, performed at the level of sesquilinear forms rather than at the operator level, which removes the need for a common invariant operator domain. The resulting estimate involves the norm of the time-integrated difference of the two generators, rather than the integral of its norm, and is therefore sensitive to the averaging effects produced by fast-oscillating terms. As an application we prove a quantitative bound on the rotating-wave approximation for spin-boson models with a structured boson field, described by an arbitrary massive dispersion relation on a general measure space and by a suitable class of form factors. The proof involves a careful analysis of the high-frequency scaling. The bound holds on a dense subspace of states, is fully explicit, and all the constants entering it depend only on the parameters of the model and not on the frequency scale, so that the approximation becomes exact in the limit of large frequency.
Comments26 pages
