低维无带隙系统绝热极限的突破
Breakdown of the adiabatic limit in low dimensional gapless systems
摘要：
一般认为，一般系统可以通过足够慢的参数变化可逆地从一种状态转换到另一种状态。支持这一论断的一个标准论点是基于将系统的能量或熵展开为斜坡速度中的泰勒级数的可能性。在这里，我们表明，这一论点是有效的，只有在足够高的维度，可以打破低维无隙系统。我们确定了系统对慢斜坡响应的三种一般机制：（A）平均场，（B）非解析，（C）非绝热。在最后一个区域中，斜坡速度趋于零和系统尺寸趋于无穷大的极限不对易，并且在热力学极限中不存在绝热过程。我们通过数值模拟来支持我们的结果。我们的发现可能与凝聚态、原子物理学、量子计算、量子光学、宇宙学等相关。
英文摘要：
It is generally believed that a generic system can be reversibly transformed from one state into another by sufficiently slow change of parameters. A standard argument favoring this assertion is based on a possibility to expand the energy or the entropy of the system into the Taylor series in the ramp speed. Here we show that this argumentation is only valid in high enough dimensions and can break down in low-dimensional gapless systems. We identify three generic regimes of a system response to a slow ramp: (A) mean-field, (B) non-analytic, and (C) non-adiabatic. In the last regime the limits of the ramp speed going to zero and the system size going to infinity do not commute and the adiabatic process does not exist in the thermodynamic limit. We support our results by numerical simulations. Our findings can be relevant to condensed-matter, atomic physics, quantum computing, quantum optics, cosmology and others.
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