开放量子系统中的强到弱对称破缺：从离散粒子到连续流体动力学
Strong-to-Weak Symmetry Breaking in Open Quantum Systems: From Discrete Particles to Continuum Hydrodynamics
AI总结：
研究开放量子系统中强到弱对称破缺现象，揭示其在不同维度下的行为及连续流体动力学描述的出现时间。
摘要：
我们探讨了在U(1)对称（即电荷守恒）的开放系统动力学下，自发强到弱对称破缺（SW-SSB）的出现。我们为量子态和经典概率分布定义了这一现象，并在三个互补的模型中进行了探索，其中一个在短时间显示出非平凡的量子相干性。我们的主要结论如下。在一维情况下，强对称性在任何有限时间都不会自发破缺；然而，探测强到弱对称破缺的相关函数在长度尺度上发展出有序性，这些尺度以时间线性增长，参数上比电荷扩散快得多。我们通过多种不同的SW-SSB探测方法提供了数值证据，并从场论分析中推导出这一尺度。此外，我们将这一尺度与通过测量周围环境推断子区域内部电荷的问题联系起来，并构建了显式的解码协议，以说明其起源。在二维情况下，场论和数值模拟支持有限时间的伯尔尼齐-科斯特利茨-托夫利斯型SW-SSB相变。相比之下，在连续流体动力学中，SW-SSB在二维或更多维度中发生在极小的时间。因此，SW-SSB相变时间可以被解释为连续流体动力学描述的出现，或者更准确地说，是在此时间之后，非流体动力学信息如离散粒子世界线无法再被推断的时间尺度。我们通过分析一个模型来支持这一观点，其中我们利用SW-SSB从底层量子动力学推导出经典的随机流体动力学描述。
英文摘要：
We explore the onset of spontaneous strong-to-weak symmetry breaking (SW-SSB) under U(1)-symmetric (i.e., charge-conserving) open-system dynamics. We define this phenomenon for quantum states and classical probability distributions, and explore it in three complementary models, one of which exhibits nontrivial quantum coherence at short times. Our main conclusions are as follows. In one dimension, the strong symmetry is not spontaneously broken at any finite time; however, correlators probing strong-to-weak symmetry breaking develop order on length scales that grow linearly in time, parametrically faster than charge diffusion. We provide numerical evidence for this scaling in multiple distinct probes of SW-SSB, and derive it from a field-theory analysis. Moreover, we relate this scaling to the problem of inferring the charge inside a subregion by measuring its surroundings, and construct explicit decoding protocols that illustrate its origin. In two dimensions, field theory and numerical simulations support a finite-time Berezinskii-Kosterlitz-Thouless-like SW-SSB transition. Within continuum hydrodynamics, by contrast, SW-SSB happens at infinitesimal time in two or more dimensions. The SW-SSB transition time can thus be interpreted as marking the emergence of a continuum hydrodynamic description, or (more precisely) the timescale beyond which non-hydrodynamic information such as discrete particle worldlines can no longer be inferred. We support this picture by analyzing a model in which we exploit SW-SSB to derive a classical stochastic hydrodynamic description from the underlying quantum dynamics.
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