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Quantum metric statistics for random-matrix families
Journal of Physics A: Mathematical and Theoretical ( IF 2.1 ) Pub Date : 2020-06-18 , DOI: 10.1088/1751-8121/ab91d6
M V Berry 1 , Pragya Shukla 2
Affiliation  

The quantum metric tensor G ij for parameterised families of quantum states, in particular the trace G = tr G ij , depends on the symmetry of the system (e.g. time-reversal), and the dimension N of the underlying matrices. Modelling the families by the stationary Gaussian ensembles of random-matrix, theory, we calculate the probability distribution of G , exactly for N = 2, and approximately for N = 3 and N → ∞. Codimension arguments establish the scalings of the distributions near the singularities at G → ∞ and G = 0, near which asymptotics gives the explicit analytic behaviour. Numerical simulations support the theory.

中文翻译:

随机矩阵族的量子度量统计

参数化的量子态族的量子度量张量G ij,尤其是迹线G = tr G ij,取决于系统的对称性(例如时间反转)以及基础矩阵的维数N。通过随机矩阵的平稳高斯集合理论对族进行建模,我们精确地计算出N的G的概率分布,其中N = 2,近似于N = 3和N→∞。余维参数在G→∞和G = 0处的奇异点附近建立分布的标度,在渐近点附近渐近性给出了明确的分析行为。数值模拟支持该理论。
更新日期:2020-06-19
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