量子接触过程
Quantum contact process
摘要：
接触过程是一个典型的经典随机系统，即使在一维也表现出临界行为。它的特点是非平衡相变到吸收状态，已被广泛研究，并表明属于定向渗透普适类。当同样的过程在量子环境中被考虑时，我们所知道的就少得多了。到目前为止，主要是半经典的研究已经进行，在低维的过渡的性质仍然是一个有争议的问题。同样从数字的角度来看，这个系统可能看起来相当简单-特别是在一个维度上-缺乏结果。特别是吸收状态的存在提出了一个重大的挑战，似乎影响直接针对稳定状态的算法的可靠性。在这里，我们进行实时数值模拟的量子接触过程的开放动力学和阐明的存在和吸收状态的性质相变在一个维度。我们发现的过渡是连续的证据，并提供第一次估计的临界指数。除了概念上的兴趣之外，量子接触过程的简单性使其成为审查开放量子非平衡系统数值方法的理想基准问题。
英文摘要：
The contact process is a paradigmatic classical stochastic system displaying critical behavior even in one dimension. It features a non-equilibrium phase transition into an absorbing state that has been widely investigated and shown to belong to the directed percolation universality class. When the same process is considered in a quantum setting much less is known. So far mainly semi-classical studies have been conducted and the nature of the transition in low dimensions is still a matter of debate. Also from a numerical point of view, from which the system may look fairly simple --- especially in one dimension --- results are lacking. In particular the presence of the absorbing state poses a substantial challenge which appears to affect the reliability of algorithms targeting directly the steady-state. Here we perform real-time numerical simulations of the open dynamics of the quantum contact process and shed light on the existence and on the nature of an absorbing state phase transition in one dimension. We find evidence for the transition being continuous and provide first estimates for the critical exponents. Beyond the conceptual interest, the simplicity of the quantum contact process makes it an ideal benchmark problem for scrutinizing numerical methods for open quantum non-equilibrium systems.
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