Exact and asymptotic local virial theorems for finite fermionic systems
M. Brack, A. Koch, M. V. N. Murthy, J. Roccia
备注：
LaTeX, 34 pp., 12 figures; final version (v5) to be published in J. Phys. A. This version contains only the part of the previous version (v3) on local virial theorems; the semiclassical theory has appeared as arXiv:0912.4374v1 [math-ph] and is published in Phys. Rev. E 81, 011118 (2010)
我们研究了一个被限制在势$V(\bfr)$中的$N$费米子系统的粒子和动能密度。在较早的论文[J. Phys. A：Math. Gen. { \bf 36}，1111（2003）]中，对于任意维的各向同性谐振子，导出了局部（即在任何给定点$\bfr$）的粒子密度和动能密度的一些精确和渐近关系。在本文中，我们表明，这些{ \it本地维里定理}（LVT）也恰好为任意维的线性势和一维盒。我们还调查这些LVTs的有效性时，他们被施加到任意光滑的潜力。我们制定广义LVT的支持下，与密度振荡的经典系统的封闭的非周期轨道的半经典理论。我们测试的有效性，这些广义定理的数值各种地方的潜力。虽然他们正式只适用于大粒子数$N$渐近，我们表明，他们实际上是令人惊讶的准确也为中等值的$N$。
英文摘要：
We investigate the particle and kinetic-energy densities for a system of $N$ fermions confined in a potential $V(\bfr)$. In an earlier paper [J. Phys. A: Math. Gen. {\bf 36}, 1111 (2003)], some exact and asymptotic relations involving the particle density and the kinetic-energy density locally, i.e. at any given point $\bfr$, were derived for isotropic harmonic oscillators in arbitrary dimensions. In this paper we show that these {\it local virial theorems} (LVT) also hold exactly for linear potentials in arbitrary dimensions and for the one-dimensional box. We also investigate the validity of these LVTs when they are applied to arbitrary smooth potentials. We formulate generalized LVTs that are supported by a semiclassical theory which relates the density oscillations to the closed non-periodic orbits of the classical system. We test the validity of these generalized theorems numerically for various local potentials. Although they formally are only valid asymptotically for large particle numbers $N$, we show that they practically are surprisingly accurate also for moderate values of $N$.
Stellar dynamics within the virial theorem: asymptotic small-parameters time expansion of the Ermakov-Lewis-Leach invariant as an infinite series of conservation laws
On the Riemann-Hilbert approach to the asymptotic analysis of the correlation functions of the Quantum Nonlinear Schrodinger equation. Non-free fermionic case
Asymptotic distinguishability measures for shift-invariant quasi-free states of fermionic lattice systems
我们应用F.嗨，M. Mosonyi和T. Ogawa [arXiv：0707.2020，to appear in J. Math. Phys.] CAR代数上局部忠实移不变拟自由态的渐近假设检验问题。我们使用多变量扩展Szego的定理，以显示存在的平均Beschoff和Hoeffding界和平均相对熵，并表明这些数量出现在适当的设置作为最佳的误差指数。
Fourth-neighbour two-point functions of the XXZ chain and the Fermionic basis approach
本文对XXZ量子自旋链的关联函数理论的费米基方法作了一个描述性的评述。重点是明确的短距离关联函数，这将是在一种方式，允许其直接在计算机上实现的公式。在费米子基方法中，与模型的可积结构相容的一大类固定约化密度矩阵假定为因子分解形式。这意味着，局部算子的所有期望值和所有两点函数，特别地，可以被表示为仅两个函数$ρ$和$ω$及其导数中的多变量多项式，其系数在模型的变形参数$q$中是有理的。这些系数是“代数的起源”。它们不依赖于密度矩阵的选择，密度矩阵仅影响$ρ$和$ω$的形式。作为一个例子，我们详细计算了温度为$T$，磁场为$h$时，$q$处于临界区的巨正则系综。我们比较我们的精确结果的第四个邻居两点函数的渐近公式为$h, T = 0$和有限的$h$和$T$。
