论文标题
计算$ d $维潜力中非相互作用费米子的统计数据
Counting statistics for non-interacting fermions in a $d$-dimensional potential
论文作者
论文摘要
我们开发了一种原理方法，以在$ n $非互动的无旋转费用$ d $ $ d $（$ d> 1 $）的一般潜力中计算$ n $非互动的无纺丝费米的基础统计数据。在狭窄的电势中，在有界域中支持费米气体。在$ d = 1 $中，对于特定电位，该系统与标准随机矩阵集合有关。我们研究了大部分支持中宏观尺寸的域中$ \ cal {d} $在域中$ {\ cal d} $ $ {\ cal n} _ {\ cal d} $的量子波动。我们表明，$ {\ cal n} _ {\ cal d} $的差异为$ n^{（d-1）/d}（a_d \ log log n + b_d）$对于大$ n $，并获得$ a_d $ a_d $的明显依赖性，b_d $ of $ {$ cal d} $（cal d} $（in cal d} $）（in cal d} $ cal d} $ cal d and（for）（for）（\ cal d} $ n of）in for a in n of d} $ {\ cal d and）这概括了微观域的自由屈服结果，从$ d = 1 $中，由随机矩阵理论从dyson-mehta渐近学给出。这使我们猜想了子系统$ \ cal {d} $的纠缠熵的类似渐近学，在任何维度上，得到$ d = 1 $的精确结果的支持。
We develop a first-principle approach to compute the counting statistics in the ground-state of $N$ noninteracting spinless fermions in a general potential in arbitrary dimensions $d$ (central for $d>1$). In a confining potential, the Fermi gas is supported over a bounded domain. In $d=1$, for specific potentials, this system is related to standard random matrix ensembles. We study the quantum fluctuations of the number of fermions ${\cal N}_{\cal D}$ in a domain $\cal{D}$ of macroscopic size in the bulk of the support. We show that the variance of ${\cal N}_{\cal D}$ grows as $N^{(d-1)/d} (A_d \log N + B_d)$ for large $N$, and obtain the explicit dependence of $A_d, B_d$ on the potential and on the size of ${\cal D}$ (for a spherical domain in $d>1$). This generalizes the free-fermion results for microscopic domains, given in $d=1$ by the Dyson-Mehta asymptotics from random matrix theory. This leads us to conjecture similar asymptotics for the entanglement entropy of the subsystem $\cal{D}$, in any dimension, supported by exact results for $d=1$.
