“回归均衡”的又一次回归
Another Return of 'Return to Equilibrium'
摘要：
在假设相互作用强度{ \it足够弱}的条件下，建立了一类描述原子与黑体辐射相互作用或自旋与标量玻色子热浴相互作用的量子力学模型的“{ \it返回平衡}”性质.对于描述第一类系统的模型，我们关于相互作用强度的上限是{ \it独立}于温度$T$（具有$0<T\leq T_0<\infty$），而对于自旋玻色子模型，它在热力学上趋于零，如$T\to 0$。我们的结果适用于相互作用的形状因子与物理现实的红外行为。我们分析的三个关键要素是：辐射场的Araki-Woods表示的一种合适的具体形式，结合最近维里定理的正交换子方法，以及相互作用系统和非相互作用系统的平衡态之差的范数界（对于与黑体辐射耦合的原子系统，仅假设相互作用强度足够弱，该公式对{ \it all}温度$T\geq 0$有效）。
英文摘要：
The property of ``{\it return to equilibrium}'' is established for a class of quantum-mechanical models describing interactions of a (toy) atom with black-body radiation, or of a spin with a heat bath of scalar bosons, under the assumption that the interaction strength is {\it sufficiently weak}. For models describing the first class of systems, our upper bound on the interaction strength is {\it independent} of the temperature $T$, (with $0<T\leq T_0<\infty$), while, for the spin-boson model, it tends to zero logarithmically, as $T\to 0$. Our result holds for interaction form factors with physically realistic infrared behaviour. Three key ingredients of our analysis are: a suitable concrete form of the Araki-Woods representation of the radiation field, Mourre's positive commutator method combined with a recent virial theorem, and a norm bound on the difference between the equilibrium states of the interacting and the non-interacting system (which, for the system of an atom coupled to black-body radiation, is valid for {\it all} temperatures $T\geq 0$, assuming only that the interaction strength is sufficiently weak).
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