量子统计力学中的自然非平衡态
Natural nonequilibrium states in quantum statistical mechanics
摘要：
讨论了一个量子自旋系统，其中无限热源之间的热流发生在有限区域内。也可能有一个与时间有关的力在起作用。我们的分析是基于一个简单的技术假设有关的时间演化的无限量子自旋系统。这一假设在物理上是自然的，但目前仅在少数特定系统中得到了证明，它说量子信息在时空中的扩散方式是，局部可观测量的交换子的时间积分收敛：$\int_{-\infty}^0dt ||[B,α^tA]||<\infty$。在这种情况下，人们可以定义一个自然的非平衡态。在与时间无关的情况下，这种非平衡态保留了某些表征KMS平衡态的解析性。还得到了一个线性响应公式，该公式在远离平衡点时仍然成立。这里提出的形式主义不包括（对于与时间无关的力）自然非平衡态的时间平移不变性和唯一性被破坏的情况。
英文摘要：
A quantum spin system is discussed, where a heat flow between infinite reservoirs takes place in a finite region. A time dependent force may also be acting. Our analysis is based on a simple technical assumption concerning the time evolution of infinite quantum spin systems. This assumption, physically natural but currently proved for few specific systems only, says that quantum information diffuses in space-time in such a way that the time integral of the commutator of local observables converges: $\int_{-\infty}^0dt ||[B,α^tA]||<\infty$. In this setup one can define a natural nonequilibrium state. In the time independent case, this nonequilibrium state retains some of the analyticity which characterizes KMS equilibrium states. A linear response formula is also obtained which remains true far from equilibrium. The formalism presented here does not cover situations where (for time independent forces) the time translation invariance and uniqueness of the natural nonequilibrium state are broken.
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