A diathermal wall between two heat baths at different temperatures can be mimicked by a layer of independent spin pairs with some internal energy and where each spin $σ_a$ is flipped by thermostat $a$ ($a=1,2$). The transition rates are determined from the modified detailed balance discussed in Ref.[1]. Generalized heat capacities, excess heats, the housekeeping entropy flow and the thermal conductivity in the steady state are calculated. The joint probability distribution of the heat cumulated exchanges at any time is computed explicitly. We obtain the large deviation function of heat transfer via a variety of approaches. In particular, by a saddle-point method performed accurately, we obtain the explicit expressions not only of the large deviation function, but also of the amplitude prefactor, in the long-time probability density for the heat current. The following physical properties are discussed : the effects of typical time scales of the mesoscopic dynamics which do not appear in equilibrium statistical averages and the limit of strict energy dissipation towards a thermostat when its temperature goes to zero. We also derive some properties of the fluctuations in the two-spin system viewed as a thermal machine performing cycles.
The narrow peak on the frequency dependance of the susceptibility of the harmonical oscillator in contact with thermostat with bosonic excitations. Exactly-solvable model
Quantum dimer model with Z_2 liquid ground-state: interpolation between cylinder and disk topologies and toy model for a topological quantum-bit
我们考虑最近引入的kagome晶格上的量子二聚体模型（QDM）[Phys. Rev. Lett. 89，137202（2002）]。实现了Z_2液相，准确地获得了其光谱。当晶格具有非平凡的几何形状（圆柱体、环面等）时，它显示拓扑退化。我们讨论和解决两个扩展的模型，其中沿线引入扰动：第一个引入的势能项排斥（或吸引）沿线的二聚体被添加，第二个扰动允许创建，移动或破坏单体。对于每一个这些扰动，我们表明，存在一个临界值以上，在热力学极限，简并的基态是解除从2（在一个圆柱）到1。在这两种情况下，前两个能级之间的间隙的精确值是通过映射到横场中的伊辛链来获得的。该模型提供了一个拓扑量子比特的可解哈密顿量的例子，其中两个微扰在二维子空间中充当对角算子和横截算子。我们讨论了如何交叉的过渡可能被用于量子比特的操作，以优化同时的操作频率和由于退相干的损失。
