三种尺度下量子系统的稳定性：无源性、量子弱能量不等式和微局域谱条件
Stability of quantum systems at three scales: Passivity, quantum weak energy inequalities and the microlocal spectrum condition
摘要：
量子弱能量不等式作为量子场态动力学稳定性的一个条件，特别是在弯曲时空中，最近得到了广泛的讨论。我们制定的概念，量子弱能量不等式一般动力系统的静态背景时空，并建立量子弱能量不等式和热力学稳定性之间的联系，在一般设置。我们证明了由准自由Hadamard态诱导的表示中的自由标量场提供了一个示例系统，并指出（1）微局域谱条件，（2）量子弱能量不等式和（3）被动态（例如，基态和热平衡态的混合）基本上是等效的，这是重要的，因为这些条件中的每一个在不同的长度尺度下变得有效。[See论文的标题页为完整的摘要。
英文摘要：
Quantum weak energy inequalities have recently been extensively discussed as a condition on the dynamical stability of quantum field states, particularly on curved spacetimes. We formulate the notion of a quantum weak energy inequality for general dynamical systems on static background spacetimes and establish a connection between quantum weak energy inequalities and thermodynamic stability in the general setting. We show that the free scalar field in representations induced by quasifree Hadamard states provides an example system, and we indicate that (1) the microlocal spectrum condition, (2) quantum weak energy inequalities and (3) the existence of passive states (e.g., mixtures of ground- and thermal equilibrium states) are essentially equivalent, which is significant because each of these conditions becomes effective at a different length scale. [See title page of paper for the full abstract.]
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