论文标题
流体动力极限中大偏差的动力学：非相互作用系统
Dynamics of large deviations in the hydrodynamic limit: Non-interacting systems
论文作者
论文摘要
我们研究了沿量子链传递的能量统计的动力学，该量子沿量子链传递，该链链在不均匀的初始状态中制备，通过在两个不同温度下加入两个相同的半无限部分获得的相同的半无限部分获得。特别是，我们将横向场和谐波链视为非相互作用的费米和肺泡激发的原型模型。在大时空尺度的所谓流体动力学限制中，我们首先讨论能量密度和电流的平均值，然后针对波动的统计数据，我们精确地计算了传递的能量的缩放累积生成函数。从后者中，获得了相关的大偏差函数的演变。根据沿经典轨迹向弹道移动的准粒子的半古典图片，提供了对我们结果的自然解释。讨论了在非相互作用的费米和玻色子的情况下，转移的能量缩放累积量与大偏差函数之间的相似性和差异。
We study the dynamics of the statistics of the energy transferred across a point along a quantum chain which is prepared in the inhomogeneous initial state obtained by joining two identical semi-infinite parts thermalized at two different temperatures. In particular, we consider the transverse field Ising and harmonic chains as prototypical models of non-interacting fermionic and bosonic excitations, respectively. Within the so-called hydrodynamic limit of large space-time scales we first discuss the mean values of the energy density and current, and then, aiming at the statistics of fluctuations, we calculate exactly the scaled cumulant generating function of the transferred energy. From the latter, the evolution of the associated large deviation function is obtained. A natural interpretation of our results is provided in terms of a semi-classical picture of quasi-particles moving ballistically along classical trajectories. Similarities and differences between the transferred energy scaled cumulant and the large deviation functions in the cases of non-interacting fermions and bosons are discussed.
