AI 中文总结
研究受监控横向场伊辛链中，量子跳跃或受控测量序列下的功统计，发现随机跳跃下功分布从梳状结构演变为高斯形式，受控跳跃中平均功呈线性或亚线性增长，连续观测则使孤立淬火分布趋于高斯。
AI 中文摘要
我们研究了受监控横向场伊辛链中的功统计，该链同时经历横向场的量子淬火和随机量子跳跃或受控测量序列。对于广义测量，我们在两点能量测量方案中推导了功统计的轨迹分辨生成函数。使用费米子高斯态形式对其进行评估，我们表明，在随机跳跃动力学下，随着检测事件数量的增加，功分布从梳状结构演变为基本高斯形式，并具有收缩的次高斯尾部。对于受控跳跃协议，当连续跳跃因果断开时，每次跳跃添加的能量是恒定的，但当它们位于彼此的光锥内时，能量减少然后饱和，分别产生平均功的线性和亚线性增长。对于监控淬火，连续观测消除了孤立淬火分布的精细结构，并再次将统计推向高斯行为。
英文摘要
We investigate work statistics in monitored transverse-field Ising chains subjected to both a quantum quench of the transverse field and either stochastic quantum jumps or controlled measurement sequences. For generalized measurements, we derive a trajectory-resolved generating function for work statistics in the two-point energy measurement scheme. Evaluating it using a fermionic Gaussian-state formalism, we show that, under stochastic jump dynamics, the work distribution crosses over from a comb-like structure to an essentially Gaussian form with shrinking sub-Gaussian tails, as the number of detection events grows. For controlled jump protocols, the energy added by each jump is constant when successive jumps are causally disconnected but decreases and then saturates when they lie within each other's light cone, leading to linear growth of average work in the former case and a transient sublinear regime followed by linear growth with a reduced slope in the latter. For monitored quenches, continuous observation washes out the fine structure of the isolated-quench distribution and again drives the statistics toward Gaussian behavior. Together, these results establish work statistics as a trajectory-resolved diagnostic of measurement-induced energy injection and of the emergence or breakdown of additivity in monitored many-body dynamics.
