Spin–gravity coupling and gravity-induced quantum phases

External gravitational fields induce phase factors in the wave functions of particles. The phases are exact to first order in the background gravitational field, are manifestly covariant and gauge invariant and provide a useful tool for the study of spin–gravity coupling and of the optics of particles in gravitational or inertial fields. We discuss the role that spin–gravity coupling plays in particular problems.     

A closer look at the indications of q-generalized Central Limit Theorem behavior in quasi-stationary states of the HMF model

We give a closer look at the Central Limit Theorem (CLT) behavior in quasi-stationary states of the Hamiltonian Mean Field model, a paradigmatic one for long-range-interacting classical many-body systems. We present new calculations which show that, following their time evolution, we can observe and classify three kinds of long-standing quasi-stationary states (QSS) with different correlations. The frequency of occurrence of each class depends on the size of the system. The different microscopic nature of the QSS leads to different dynamical correlations and therefore to different results for the observed CLT behavior.     

Hamiltonian and Brownian systems with long-range interactions: V. Stochastic kinetic equations and theory of fluctuations

We developed a theory of fluctuations for Brownian systems with weak long-range interactions. For these systems, there exists a critical point separating a homogeneous phase from an inhomogeneous phase. Starting from the stochastic Smoluchowski equation governing the evolution of the fluctuating density field of Brownian particles, we determine the expression of the correlation function of the density fluctuations around a spatially homogeneous equilibrium distribution. In the stable regime, we find that the temporal correlation function of the Fourier components of density fluctuations decays exponentially rapidly, with the same rate as the one characterizing the damping of a perturbation governed by the deterministic mean field Smoluchowski equation (without noise). On the other hand, the amplitude of the spatial correlation function in Fourier space diverges at the critical point T=T_c (or at the instability threshold k=k_m) implying that the mean field approximation breaks down close to the critical point, and that the phase transition from the homogeneous phase to the inhomogeneous phase occurs sooner. By contrast, the correlations of the velocity fluctuations remain finite at the critical point (or at the instability threshold). We give explicit examples for the Brownian Mean Field (BMF) model and for Brownian particles interacting via the gravitational potential and via the attractive Yukawa potential. We also introduce a stochastic model of chemotaxis for bacterial populations generalizing the deterministic mean field Keller-Segel model by taking into account fluctuations and memory effects.     

Two-dimensional Brownian vortices

We introduce a stochastic model of 2D Brownian vortices associated with the canonical ensemble. The point vortices evolve through their usual mutual advection but they experience in addition a random velocity and a systematic drift generated by the system as a whole. The statistical equilibrium state of this stochastic model is the Gibbs canonical distribution. We consider a single species system and a system made of two types of vortices with positive and negative circulations. At positive temperatures, like-sign vortices repel each other (“plasma” case) and at negative temperatures, like-sign vortices attract each other (“gravity” case). We derive the stochastic equation satisfied by the exact vorticity field and the Fokker-Planck equation satisfied by the N-body distribution function. We present the BBGKY-like hierarchy of equations satisfied by the reduced distribution functions and close the hierarchy by considering an expansion of the solutions in powers of 1/N, where N is the number of vortices, in a proper thermodynamic limit. For spatially inhomogeneous systems, we derive the kinetic equations satisfied by the smooth vorticity field in a mean field approximation valid for N→+∞. For spatially homogeneous systems, we study the two-body correlation function, in a Debye-Hückel approximation valid at the order O(1/N). The results of this paper can also apply to other systems of random walkers with long-range interactions such as self-gravitating Brownian particles and bacterial populations experiencing chemotaxis. Furthermore, for positive temperatures, our study provides a kinetic derivation, from microscopic stochastic processes, of the Debye-Hückel model of electrolytes.     

A natural abundance Se solid-state NMR study of inorganic compounds

Various inorganic selenium-based compounds were analysed by ⁷⁷Se solid-state NMR, and a distinct difference in chemical shift ranges for compounds where selenium is present as selenide (Se²⁻) ionically and covalently bonded systems was observed. The selenides exhibit a shift range of approximately −700 to −100 ppm, as opposed to 700 to 1600 ppm for the compounds where there tends to be more direct covalent bonding to the selenium. The anisotropic hyperfine shift observed in NbSe₂ is shown to be axially symmetric, where the H₁₁ component is found to be normal to the Se3-trigonal plane.     

具有长程相互作用S-1/2 XY链的研究

采用平均场Jordan - Wigner 变换分析方法,研究了外场中且具有Z方向均匀长程相互作用自旋－1/2 XY链的热力学性质,得到了系统格点的亥姆赫兹自由能、内能、比热、磁化强度、磁化率等热力学量的解析表达式及其数值解,讨论了系统的一级和两级相变,数值结果在退化条件下与其他文献的结果符合很好. 关键词： XY链')" href="#">XY链 平均场Jordan-Wigner变换 长程相互作用     

地基高频加热激励ELF/VLF波对辐射带高能电子的准线性散射

地球内、外辐射带电子通量的变化对于空间飞行器,尤其是中低轨卫星的防护有着非常重要的影响.基于回旋共振波粒相互作用的准线性理论,使用地基高频发射器发射电波调制低电离层背景电流可以人工激励ELF/VLF波,这些波能使辐射带相对论电子发生抛射角散射沉降进入大气层从而降低其生存期.为了定量地分析人工激励ELF/VLF波散射辐射带高能粒子的可行性,针对内、外辐射带,本文选取了两个典型区域：L=4.6和L=1.5.数值计算结果表明,在内、外辐射带由于ELF/VLF波的人工注入而造成的高能电子损失时间尺度很大程度上取决于冷等离子体参量α^*(∝B²/N₀,这里B是背景磁场,N₀是电子数密度)、电波频谱特性和功率,以及与波发生回旋共振的电子能量.一般来讲,在外辐射带人工ELF/VLF哨声波散射相对论电子使之沉降到大气层要容易得多;低能量的高能电子(200keV)要比高能量的相对论电子(500keV)更有效地通过抛射角散射进入大气层.考虑到高频电波加热电离层激励的ELF/VLF波可能会被捕获在磁层空腔中,来回反射从而得到增强,因此在适当的条件下,地基高频加热装置发射足够的电波功率进入电离层诱导大幅度ELF/VLF波注入到内磁层,能够在1至3天的时间尺度内快速散射外辐射带相对论电子使之沉降,也能够在10天量级的时间尺度里散射生存周期一般为100天甚至更长的内辐射带相对论电子. 关键词： 地基高频加热电离层 ELF/VLF波激励 高能电子散射和沉降 共振波粒相互作用     

Thermosensitive and Switchable Terpyridine‐Functionalized Metallo‐Supramolecular Poly(N‐isopropylacrylamide)

Metallo‐supramolecular polymers offer attractive possibilities to combine the properties of polymers with the characteristics offered by the metal–ligand coordination. Here we present for the first time the combination of metal‐bis(terpyridine) complexes and lower critical solution temperature (LCST) polymers that can be switched by addressing either the thermosensitive polymer or the metal complex. We describe a new strategy for the synthesis of poly(N‐isopropylacrylamide) (PNIPAM) end functionalized with a terpyridine moiety, which is further used for the preparation of Fe^II and Zn^II‐bis(terpyridine PNIPAM). The comparison of the LCST behavior of the uncomplexed ligands and their metal complexes that bear different counter ions is included. Furthermore, the switchability of the synthesized Fe^II system is demonstrated by a decomplexation reaction followed by the characterization of the uncomplexed ligand.