AI 中文总结
该研究针对热库哈密顿量为纯离散谱的弗里德里希哈密顿量序列，证明其激发态存活概率近似指数衰减，误差由耦合强度与莱维距离估计，并将结果应用于两能级原子与大腔内无质量玻色场的耦合问题。
AI 中文摘要
我们研究一类弗里德里希哈密顿量，即描述激发态通过秩1扰动与热库耦合的算子，其中热库哈密顿量具有纯离散谱。我们考虑这类哈密顿量序列，其热库哈密顿量通过耦合函数关联的谱测度弱收敛至一个极限测度，该极限测度在激发能附近具有 Hölder 连续密度且为绝对连续。在此假设下，我们证明激发态的存活概率在合适时间尺度上近似指数衰减，且在有利条件下，衰减率由极限测度的费米黄金规则给出。误差根据耦合强度与离散谱测度和极限测度间的莱维距离估计。作为应用，我们处理旋转波近似下束缚于大腔中的无质量玻色场耦合的两能级原子。
英文摘要
We study a class of Friedrichs Hamiltonians, that is, operators describing an excited state coupled to a bath through a rank-one perturbation, in the case where the bath Hamiltonian has purely discrete spectrum. We consider sequences of such Hamiltonians for which the spectral measures associated to the coupling functions by the bath Hamiltonians converge weakly to a limiting measure that is absolutely continuous with a Hölder continuous density near the excited energy. Under this assumption, we show that the survival probability of the excited state decays in an approximately exponential manner on suitable time scales and under favourable conditions, with a decay rate given by Fermi's golden rule for the limiting measure. The error is estimated in terms of the coupling strength and the Lévy distance between the discrete spectral measures and the limiting measure. As an application, we treat a two-level atom coupled to a massless bosonic field confined to a large cavity in the rotating-wave approximation.
Comments19 pages
