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arXiv 1702.06142quant-phhep-thmath-phmath.MP
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光谱中的位置

Locality from the Spectrum

Jordan S. Cotler, Geoffrey R. Penington, Daniel H. Ranard

备注：
40 pages, 2 figures
发表信息：
Commun. Math. Phys. (2019) 368: 1267
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摘要：

描述量子系统的关键是它的局部自由度，这使得能够在希尔伯特空间中解释子系统和动力学。虽然希尔伯特空间的局部张量因子分解的选择通常隐含在哈密顿量或拉格朗日量的写作中，但局部张量因子的识别并不是希尔伯特空间本身所固有的。相反，唯一的基不变的数据的哈密尔顿是它的频谱，这并不明显地确定本地结构。这种模糊性突出表现为对偶性的存在，其中相同的能谱可以描述具有非常不同的局部自由度的两个系统。我们认为，事实上，能量谱本身几乎总是编码一个独特的描述当地的自由度时，这样的描述存在，允许一个明确地确定当地的子系统，以及它们如何相互作用。因此，我们几乎总是可以在只给出它的谱的情况下，用它的局部表示写出一个哈密顿量。在特殊情况下，可以从给定的频谱中提取多个对偶局部描述，但一般情况下，局部描述是唯一的。

英文摘要：

Essential to the description of a quantum system are its local degrees of freedom, which enable the interpretation of subsystems and dynamics in the Hilbert space. While a choice of local tensor factorization of the Hilbert space is often implicit in the writing of a Hamiltonian or Lagrangian, the identification of local tensor factors is not intrinsic to the Hilbert space itself. Instead, the only basis-invariant data of a Hamiltonian is its spectrum, which does not manifestly determine the local structure. This ambiguity is highlighted by the existence of dualities, in which the same energy spectrum may describe two systems with very different local degrees of freedom. We argue that in fact, the energy spectrum alone almost always encodes a unique description of local degrees of freedom when such a description exists, allowing one to explicitly identify local subsystems and how they interact. As a consequence, we can almost always write a Hamiltonian in its local presentation given only its spectrum. In special cases, multiple dual local descriptions can be extracted from a given spectrum, but generically the local description is unique.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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