Strong Squeezing of Duffing Oscillator in a Highly Dissipative Optomechanical Cavity System

In the conventional scheme of generating strong mechanical squeezing by the joint effect between mechanical parametric amplification and sideband cooling, the resolved sideband condition is required so as to overcome the quantum backaction heating. In the unresolved sideband regime, to suppress the quantum backaction, a χ⁽²⁾ nonlinear medium is introduced to the cavity. The result shows that the quantum backaction heating effect caused by unwanted counter-rotating term can be completely removed. Hence, the strong mechanical squeezing can be obtained even for the system far from the resolved-sideband regime.     

Properties of bounded stochastic processes employed in biophysics

Abstract

Realistic stochastic modeling is increasingly requiring the use of bounded noises. In this work, properties and relationships of commonly employed bounded stochastic processes are investigated within a solid mathematical ground. Four families are object of investigation: the Sine-Wiener (SW), the Doering–Cai–Lin (DCL), the Tsallis–Stariolo–Borland (TSB), and the Kessler–Sørensen (KS) families. We address mathematical questions on existence and uniqueness of the processes defined through Stochastic Differential Equations, which often conceal non-obvious behavior, and we explore the behavior of the solutions near the boundaries of the state space. The expression of the time-dependent probability density of the Sine-Wiener noise is provided in closed form, and a close connection with the Doering–Cai–Lin noise is shown. Further relationships among the different families are explored, pathwise and in distribution. Finally, we illustrate an analogy between the Kessler–Sørensen family and Bessel processes, which allows to relate the respective local times at the boundaries.     

The coupled-cluster formalism – a mathematical perspective

ABSTRACT

The Coupled-Cluster (CC) theory is one of the most successful high precision methods used to solve the stationary Schrödinger equation. In this article, we address the mathematical foundation of this theory with focus on the advances made in the past decade. Rather than solely relying on spectral gap assumptions (non-degeneracy of the ground state), we highlight the importance of coercivity assumptions – Gårding type inequalities – for the local uniqueness of the CC solution. Based on local strong monotonicity, different sufficient conditions for a local unique solution are suggested. One of the criteria assumes the relative smallness of the total cluster amplitudes (after possibly removing the single amplitudes) compared to the Gårding constants. In the extended CC theory the Lagrange multipliers are wave function parameters and, by means of the bivariational principle, we here derive a connection between the exact cluster amplitudes and the Lagrange multipliers. This relation might prove useful when determining the quality of a CC solution. Furthermore, the use of an Aubin–Nitsche duality type method in different CC approaches is discussed and contrasted with the bivariational principle.     

颗粒材料三维应力路径下的接触组构特性

颗粒材料的宏观应力变形特征与其微观接触力、组构等紧密相关.一般而言,强接触系统属于颗粒内部体系的传力结构,其对应的组构张量是影响宏观应力性质的重要因素.细观数值方法(如离散单元法)能够反映物理试验的基本规律,并且可以方便地提取宏微观数据来研究颗粒体系的应力变形机制.采用离散单元法(discrete element method,DEM)进行一系列等$p$等$b$应力路径下颗粒材料的真三轴试验,在此基础上研究了三维应力路径下颗粒材料的宏微观力学参数的演化过程、三维组构张量与应力张量多重联系以及强接触体系反映的宏观应力特征.研究表明:颗粒体系偏应力峰值状态和临界状态均存在与加载路径无关的宏微观特征;三维应力路径下组构张量与应力张量存在非共轴性,但其联合不变量演化过程表现出加载路径无关的特征;与弱接触系统的组构张量相比,强接触系统的组构张量更能反映宏观应力张量的特征;强弱接触体系的组构张量对颗粒体系宏观响应的贡献不同,其分界点存在一定取值范围,但采用平均接触力较为简单合理.      

含参广义集值强向量平衡问题的稳定性

本文借助集合极限的性质和弱f-性假设证明了含参广义集值强向量平衡问题解集映射的下半连续性,其方法不同于最近文献(Zhao,2016和Meng,2018).此外,建立了含参广义集值强向量平衡问题解集连通性的充分条件,并举例验证了所得结果的正确性.本文得结果推广和改进了已有文献(Gong,2008,Xu,2009,Chen,2010,Xu,2013和Zhao,2013)中相应结果.     

Rate constants of the reactions of O(3P) atoms with Br2 and NO2 over the temperature range 220-950 K

The kinetics of the reactions of Br₂ and NO₂ with ground state oxygen atoms have been studied over a wide temperature range, T = 220-950 K, using a low-pressure flow tube reactor coupled with a quadrupole mass spectrometer: O + NO₂ → NO + O₂ (1) and O + Br₂ → Br + BrO (2). The rate constant of reaction (1) was determined under pseudo–first-order conditions, either monitoring the kinetics of O-atom or NO₂ consumption in excess of NO₂ or of the oxygen atoms, respectively: k₁ = (6.1 ± 0.4) × 10⁻¹² exp((155 ± 18)/T) cm³ molecule⁻¹ s⁻¹ (where the uncertainties represent precision at the 2σ level, the estimated total uncertainty on k₁ being 15% at all temperatures). The temperature dependence of k₁, found to be in excellent agreement with multiple previous low-temperature data, was extended to 950 K. The rate constant of reaction (2) determined under pseudo–first-order conditions, monitoring the kinetics of Br₂ consumption in excess of O-atoms, showed upward curvature at low and high temperatures of the study and was fitted with the following three-parameter expression: k₂ = 9.85 × 10⁻¹⁶ T^1.41 exp(543/T) cm³ molecule⁻¹ s⁻¹ at T = (220-950) K, which is recommended from the present study with an independent of temperature conservative uncertainty of 15% on k₂.     

Statistical inference for Vasicek-type model driven by Hermite processes

Let $Z$ denote a Hermite process of order $q\ge 1$ and self-similarity parameter $H\in (\frac{1}{2},1)$. This process is $H$-self-similar, has stationary increments and exhibits long-range dependence. When $q=1$, it corresponds to the fractional Brownian motion, whereas it is not Gaussian as soon as $q?2$. In this paper, we deal with a Vasicek-type model driven by $Z$, of the form $d{X}_t=a(b?X_t)dt+d{Z}_t$. Here, $a>0$ and $b\in \mathbb{R}$ are considered as unknown drift parameters. We provide estimators for $a$ and $b$ based on continuous-time observations. For all possible values of $H$ and $q$, we prove strong consistency and we analyze the asymptotic fluctuations.