Free Fermions and the Classical Compact Groups
Free Fermions and the Classical Compact Groups
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自由费米子和经典紧群
DOI：
10.1007/s10955-018-2029-6
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发表时间：
2017
影响因子：
1.6
通讯作者：
N. O’Connell
中科院分区：
文献类型：
--
作者：
F. D. Cunden;F. Mezzadri;N. O’Connell
具有经典(吸收、反射和周期)边界条件的盒子中非相互作用费米子的基态与经典紧致群的本征值统计之间有着密切的联系。相关的行列式点过程可以在两个自然方向上扩展：(I)我们考虑有界区间上拉普拉斯算子的全族允许的量子边界条件(即自伴扩展)，以及相应的投影相关核；(Ii)我们构造了投影核在有限温度下的宏正则扩张，从Poisson到随机矩阵本征值统计量。在统一的框架下研究了整体和边缘的标度极限，并讨论了普适性问题。有限温度行列式过程是否与某些矩阵模型的特征值统计相对应，先验地并不明显。我们通过构造经典紧群上的Haar测度的有限温度扩张来完成这一图景。所得到的(随机大小)巨正则矩阵模型的本征值统计完全对应于具有经典边界条件的自由费米子的巨正则度量。
There is a close connection between the ground state of non-interacting fermions in a box with classical (absorbing, reflecting, and periodic) boundary conditions and the eigenvalue statistics of the classical compact groups. The associated determinantal point processes can be extended in two natural directions: (i) we consider the full family of admissible quantum boundary conditions (i.e., self-adjoint extensions) for the Laplacian on a bounded interval, and the corresponding projection correlation kernels; (ii) we construct the grand canonical extensions at finite temperature of the projection kernels, interpolating from Poisson to random matrix eigenvalue statistics. The scaling limits in the bulk and at the edges are studied in a unified framework, and the question of universality is addressed. Whether the finite temperature determinantal processes correspond to the eigenvalue statistics of some matrix models is, a priori, not obvious. We complete the picture by constructing a finite temperature extension of the Haar measure on the classical compact groups. The eigenvalue statistics of the resulting grand canonical matrix models (of random size) corresponds exactly to the grand canonical measure of free fermions with classical boundary conditions.
有限温度下的 KPZ 模型和自由费米子
DOI：
--
发表时间：
2021
期刊：
影响因子：
--
作者：
Takashi Imamura;Matteo Mucciconi;Tomohiro Sasamoto;Tomohiro Sasamoto;Tomohiro Sasamoto;Tomohiro Sasamoto
通讯作者：
Tomohiro Sasamoto