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Acta Physica Sinica

级联x^（2）过程产生高量值高阶非线性相移

Xu Zheng Guang, Tao Wang, 朱鹤元, 钱列加, 范滇元, 李富铭

Published May 31, 2005• 0 citations
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Abstract

基于位相失配三倍频(Δk≠0)转换,构建了产生高阶非线性相移的χ(2)级联非线性过程.此过程不涉及三阶等其他非线性效应,仅表现为纯的五阶非线性,所感应的非线性相移正比于I2.进一步的数值计算研究表明χ(2)级联五阶非线性相移不仅符号可控,而且具有丰富的饱和特性,其量值远高于χ(2)级联三阶非线性相移

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基于位相失配三倍频(Δk≠0)转换,构建了产生高阶非线性相移的χ(2)级联非线性过程.此过程不涉及三阶等其他非线性效应,仅表现为纯的五阶非线性,所感应的非线性相移正比于I2.进一步的数值计算研究表明χ(2)级联五阶非线性相移不仅符号可控,而且具有丰富的饱和特性,其量值远高于χ(2)级联三阶非线性相移
The local surface susceptibility chi 1,1(T) is calculated and analysed in detail for a ferromagnetic spherical model on a d-dimensional hypercubic half-space bounded by a free surface in which the exchange coupling, J(1+ Delta ) with Delta >0, is enhanced over the bulk value J. For Delta > Delta c=(2d-2)-1, chi 1,1(T) is found to diverge at a temperature Tcx( Delta ) above the bulk critical temperature, while for Delta < Delta c, chi 1,1(T) behaves as for a surface without enhancement ( Delta =0). The nature of the crossover phenomena is explored; it is shown that for Delta near Delta c and T near Tcx( Delta ), chi 1,1(T) can be represented in a scaled form in accord with the general theory of crossover phenomena.
本文提出一个以等腰三角形构型为基础的原子钟判决实验,直接证伪狭义相对论的相对性原理。 实验构型:一个静止的原子钟(钟S)和一个匀速直线运动的原子钟(钟M),在绝对时间的同一时刻,分别向远处的观测者P发射光信号。P与两者恰好构成等腰三角形——光从两个钟传播到P的距离完全相等,光程差被几何对称性完美消除。 本理论的预言:根据运动守恒公理 c02=v2+u2c_0^2 = v^2 + u^2c02​=v2+u2,运动钟M的内部演化速率被绝对运动挤占,走时更慢。P接收到的两个信号中,钟M的读数系统性地小于钟S的读数。扣除光信号延迟效应后,全宇宙所有观察者都会公认:匀速直线运动的原子钟走得更慢,静止的原子钟没有变慢。 狭义相对论的预言:在钟M的惯性系中,钟S也在运动,钟S也应该更慢。两者互相看对方变慢,不存在客观的“谁真正更慢”。只有掉头重逢时才能根据加速度历史判断。 证伪逻辑:等腰构型下,P不需要做任何“扣除延迟”的操作,只需直接比较两个信号的到达时间。如果P发现运动时钟的读数系统性地小于静止时钟,且差值随速度单调增加,这就是单向钟慢的铁证。相对性原理要求所有惯性系平权,无法解释这种客观的、不对称的钟慢。因此,相对性原理被直接证伪。 只有一个人不承认:随钟M一起运动的观测者。在他的惯性系视角下,他认为钟S更慢。但他的视角是被他的绝对运动误导的——他用来“测量”钟S时间的光信号经过了复杂的传播路径,叠加了延迟效应。全宇宙都同意钟M更慢,只有钟M自己不知道。
在波场理论框架中,物质波包的宏观动能并非传统认知中单纯的运动做功能量,而源于物质波包总波矢(本征光速(c))在内部相位演化速率(u)与宏观平动速度(v)之间的矢量分解与再分配,核心遵循关系式(u^2 + v^2 = c^2)。本文通过严谨推导证明,在低速极限((v \ll c))条件下,该理论导出的动能表达式自动退化为经典牛顿力学动能公式(\frac{1}{2} m_0 v^2),二者数值完全等价;在高速下,动能高阶项与相对论能量公式数值一致,但波场理论给出了更本源的物理机制:能量用于波矢方向再分配,而非质量增加。该结论既验证了波场理论与日常经典物理经验的兼容性,又突破了传统动能定义的局限,为静止质量、宏观运动、高速物理行为提供了统一且自洽的非相对论新解释。
Quantum metrology studies the use of entanglement and other quantum resources to improve precision measurement. An interferometer using N independent particles to measure a parameter χ can achieve at best the "standard quantum limit" (SQL) of sensitivity δχ ∝ N-1/2. The same interferometer using N entangled particles can achieve in principle the "Heisenberg limit" δχ ∝ N-1, using exotic states, e.g., NooN states. Recent theoretical work argues that interactions among particles may be a valuable resource for quantum metrology, allowing scaling beyond the Heisenberg limit. Specifically, a k-particle interaction will produce sensitivity δχ ∝ N-kwith appropriate entangled states and δχ ∝ N-(k-1/2)even without entanglement. Here we demonstrate this "super-Heisenberg" scaling in a nonlinear, non-destructive measurement of the magnetisation of an atomic ensemble.
We study the scaling of the magnetic susceptibility in the square Ising model based upon the delta-expansion in the high temperature phase. The susceptibility chi is expressed in terms of the mass M and expanded in powers of 1/M. The dilation around M=0 by the delta expansion and the parametric extension of the ratio of derivatives of chi, chi^{(ell+1)}/chi^{(ell)} is used as a test function for the estimation of the critical exponent gamma with no bias from information of the critical temperature. Estimation is done with the help of the principle of minimum sensitivity and detailed analysis revealed that ell=0,1 cases provide us accurate estimation results. Critical exponent of the sub-leading scaling term is also estimated.