驱动高斯场论中功累积量标度行为的交叉

中文摘要 AI 辅助

我们推导了驱动 $O(N)$ 高斯场论的有限温度功特征函数（CFW），并获得了所有零温过剩功累积量的闭式表达式。对于有能隙的协议，我们使用绝热微扰理论（APT）推导出在任一边界处具有非零一阶导数的协议满足 $\tau_Q^{-2}$ 标度，其中 $\tau_Q$ 为协议持续时间；更平滑的边界导致更快的衰减。对于以指数 $p$ 接近临界点的幂律协议，我们确定了临界激发与正则贡献之间的竞争。第 $n$ 阶累积量的临界贡献在 $d+n<2p+4$ 时遵循 Kibble--Zurek（KZ）标度 $\tau_Q^{-p(d+n)/(p+2)}$，在 $d+n=2p+4$ 时获得对数修正 $\tau_Q^{-2p}\log\tau_Q$，并在高于此条件时按 $\tau_Q^{-2p}$ 标度，其中 $d$ 为空间维度。这一在可解模型中对 APT--KZ 交叉的解析研究，为研究它们在相互作用场论中的竞争提供了基础。

英文摘要

We derive the finite-temperature characteristic function of work (CFW) for a driven $O(N)$ Gaussian field theory and obtain closed-form expressions for all zero-temperature excess-work cumulants. For gapped protocols, we use adiabatic perturbation theory (APT) to derive the $τ_Q^{-2}$ scaling for protocols with a nonzero first derivative at either boundary, where $τ_Q$ is the protocol duration; smoother boundaries lead to faster decay. For power-law protocols approaching the critical point with exponent $p$, we determine the competition between critical excitations and the regular contribution. The $n$th cumulant's critical contribution follows Kibble--Zurek (KZ) scaling $τ_Q^{-p(d+n)/(p+2)}$ for $d+n<2p+4$, acquires a logarithmic correction $τ_Q^{-2p}\logτ_Q$ at $d+n=2p+4$, and scales as $τ_Q^{-2p}$ above this condition, where $d$ is the spatial dimension. This analytical study of the APT--KZ crossover in a solvable model provides a basis for studying their competition in interacting field theories.

发表机构

• School of Physics, Peking University（北京大学物理学院）
• Collaborative Innovation Center of Quantum Matter（量子物质协同创新中心）
• Frontiers Science Center for Nano-optoelectronics, Peking University（北京大学纳米光电前沿科学中心）

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