Temporal breakdown and Borel resummation in the complex Langevin method

We reexamine the Parisi–Klauder conjecture for complex e^iθ/2?⁴$e^{i\theta /2}{?}^4$ measures with a Wick rotation angle 0≤θ/2≤π/2$0\le \theta /2\le \pi /2$ interpolating between Euclidean signature and Lorentzian signature. Our main result is that the asymptotics for short stochastic times t$t$ encapsulates information also about the equilibrium aspects. The moments evaluated with the complex measure and with the real measure defined by the stochastic Langevin equation have the same t→0$t\to 0$ asymptotic expansion which is shown to be Borel summable. The Borel transform correctly reproduces the time dependent moments of the complex measure for all t$t$, including their t→∞$t\to \infty$ equilibrium values. On the other hand the results of a direct numerical simulation of the Langevin moments are found to disagree from the ‘correct’ result for t$t$ larger than a finite t_c$t_c$. The breakdown time t_c$t_c$ increases powerlike for decreasing strength of the noise’s imaginary part but cannot be excluded to be finite for purely real noise. To ascertain the discrepancy we also compute the real equilibrium distribution for complex noise explicitly and verify that its moments differ from those obtained with the complex measure.     

Volterra算子及其伴随算子线性组合的数值域

经典Volterra算子$V$及其伴随算子$V^*$在复空间$L^2[0,1]$中起着关键作用. 关于$V$和$V^*$的线性组合的性质, 我们给出了确保$z_1V+z_2V^*(z_1,z_2\in\mathbb{C})$满足增生性质的等价条件. 本文描述了$(u+iv)I+mV+nV^*(u,v,m,n\in\mathbb{R},m+n\geq0)$数值域的精确表示.     

带非线性源项的Riesz回火分数阶扩散方程的预估校正方法

本文针对带非线性源项的Riesz回火分数阶扩散方程,利用预估校正方法离散时间偏导数,并用修正的二阶Lubich回火差分算子逼近Riesz空间回火的分数阶偏导数,构造出一类新的数值格式.给出了数值格式在一定条件下的稳定性与收敛性分析,且该格式的时间与空间收敛阶均为二阶.数值试验表明数值方法是有效的.     

$p$-双调和算子的第一特征值的等周上界和 Reilly 型不等式

在本文中,我们给出了嵌入到欧氏空间中的$n$维闭超曲面上$p$-双调和算子的第一特征值的一些等周上界.我们也给出了浸入到高维流形如欧氏空间,球面和射影空间中的闭子流形上$p$-双调和算子的第一特征值的一些Reilly-型不等式.     

带有两个重夸克的重子谱计算中几个困难问题的研究

由两个重夸克和一个轻夸克组成的重子可以看作是一个两体系统.它的两个重夸克组成一个玻色型的双夸克团.利用B–S方程导出了它的轻夸克和重的双夸克之间的等效相互作用势.在利用这种势计算重子质量的过程中,发现有几个困难问题需要深入探讨.它们是:(1)算符排序,(2)由非相对论展开带来的误差,(3)自旋–自旋耦合,(4)在标量双夸克组成的重子态和矢量双夸克组成的重子态之间的混合.本文详细地讨论并适当地处理了这些问题.     

超快速COSY类2D NMR实验弛豫假峰的抑制

在脉冲梯度场基础上研究了进一步缩短COSY类2D NMR实验数据采集时间的新方法.利用主动屏蔽梯度场线圈的梯度场恢复时间仅为100μs数量级这一特点,提出一类基于脉冲梯度场消除弛豫假峰的脉冲序列.并以DQF-COSY脉冲序列为例加以验证.实验结果表明:采用文中的方法,取序列重复时间远小于T₁和T₂是切实可行的;梯度场技术能很好地抑制弛豫假蜂以达到2D NMK数据的快速采集.     

Visualising many-body electron dynamics using one-body densities and orbitals

As experimental techniques begin to probe electronic motions in increasing detail, the need is arising for compact and informative visualisations of simulations of such processes. The inherent challenge is that a full many-electron wavefunction is a high-dimensional object, representing the complicated correlations of strongly repulsive bodies in a small molecular volume. A general procedure is needed to distill this to a smaller amount of information that does not rely on any specific level of approximation. The result should allow for easy and intuitive interpretation while drawing out nontrivial aspects of the underlying many-body dynamics, such as the complex phase information inherent of a nonstationary state. Current visualisation schemes based on physical observables or the qualitative information contained in simple wavefunctions, such as time-dependent configuration-interaction-singles (TD-CIS) and time-dependent self-consistent-field (TD-SCF), are discussed. This information is compared to an analysis based on the one-body reduced density operator (1-RDO), which is well-defined for general wavefunctions. It is seen that the distinction between two paradigms of many-body dynamics, electron transport and energy transport, is reflected in the coherences of a difference-1-RDO, or lack thereof.     

Quantization of electromagnetic field in quadratic continuous nonlinear absorptive dielectrics

This paper reports that in the quantization of electromagnetic field in the dielectrics, the wave equation with regard to the Green function is analytically solved by a direct integral method for a quadratic continuous nonlinear absorptive dielectric medium. The quantization of the electromagnetic field in such a nonlinear absorptive dielectric is carried out for which the material dielectric function is assumed as a separable variable about the frequency and the space coordinate. The vacuum field fluctuations for different spatial continuous variations of dielectric function are numerically calculated, which shows that the present result is self-consistent.     

Hermitian Operators Conjugate to Two-Mode Number-Difference Operator Studied in Entangled State Representation

In similar to the derivation of phase angle operator conjugate to the number operator by Arroyo Carrasco- Moya Cessay we deduce the Hermitian phase operators that are conjugate to the two-mode number-difference operator and the three-mode number combination operator. It is shown that these operators are on the same footing in the entangled state representation as the one of Turski in the coherent state representation.     

Heat Content Asymptotics for Oblique Boundary Conditions

We consider the short-time heat content asymptotics for oblique boundary conditions. The first few coefficients in the asymptotic expansion are calculated.