Semiclassical limits of quantum partition functions on infinite graphs
Semiclassical limits of quantum partition functions on infinite graphs
复制标题
无限图上量子配分函数的半经典极限
DOI：
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发表时间：
2015
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通讯作者：
B. Güneysu
中科院分区：
文献类型：
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作者：
B. Güneysu
我们证明了如果H表示可能局部无限赋权图（X，B，m）上对应于标准Dirichlet型的算子，并且如果v：X → π使得H + v/progol被定义为对所有progol> 0的形式和，则量子配分函数tr（e−β prognosis（H+v/prognosis））收敛于∑x∈ ε −βv（x），当prognosis → 0 +，对于所有β > 0，不管e−βv是否先验可和。这个事实可以解释为一个半经典极限，它允许几何Weyl型收敛结果。我们还证明了自然的推广这半经典的限制一大类的协变薛定谔算子的厄米向量丛上的（X，m，B），一个结果，特别适用于磁薛定谔算子的定义（X，m，B）。
We prove that if H denotes the operator corresponding to the canonical Dirichlet form on a possibly locally infinite weighted graph (X, b, m), and if v : X → ℝ is such that H + v/ħ is well-defined as a form sum for all ħ > 0, then the quantum partition function tr(e−βħ(H+v/ħ)) converges to ∑x∈Xe−βv(x) as ħ → 0 +, for all β > 0, regardless of the fact whether e−βv is a priori summable or not. This fact can be interpreted as a semiclassical limit, and it allows geometric Weyl-type convergence results. We also prove natural generalizations of this semiclassical limit to a large class of covariant Schrodinger operators that act on sections in Hermitian vector bundle over (X, m, b), a result that particularly applies to magnetic Schrodinger operators that are defined on (X, m, b).