Limited sensitivity to analyticity: a manifestation of quantum chaos

Classical Hamiltonian systems generally exhibit an intricate mixture of regular and chaotic motions on all scales of phase space. As a nonintegrability parameter K (the “strength of chaos”) is gradually increased, the analyticity domains of functions describing regular-motion components [e.g., Kolmogorov-Arnol’d-Moser (KAM) tori] usually shrink and vanish at the onset of global chaos (breakup of all KAM tori). It is shown that these phenomena have quantum-dynamical analogs in simple but representative classes of model systems, the kicked rotors and the two-sided kicked rotors. Namely, as K is gradually increased, the analyticity domain ℛ_QE of the quantum-dynamical eigenstates decreases monotonically, and the width of ℛ_QE in the global-chaos regime vanishes in the semiclassical limit. These phenomena are presented as particular aspects of a more general scenario: As K is increased, ℛ_QE gradually becomes less sensitive to an increase in the analyticity domain of the system.     

Construction of Quasi-Periodic Breathers¶via KAM Technique

By developing a KAM theorem which involves an infinitely multiple normal frequency, it is shown that there are plenty of breathers, quasi-periodic in time and super-exponentially localized in space, for the networks of weakly coupled oscillators. This answers an open problem by Aubry [A2] in case the linearized system has no continuous spectrum. Received: 29 March 2001 / Accepted: 10 October 2001     

分子间相互作用对核酸碱基中17O屏蔽张量与四极耦合常数影响的理论计算研究

通过高精度量子化学理论计算的方法研究了分子间弱的非键相互作用对胸腺嘧啶、尿嘧啶、胞嘧啶和鸟嘌呤四种核酸碱基中~(17)O核的屏蔽张量(σO)和四极耦合常数(QCC)的影响.计算结果表明分子间强的氢键作用以及弱的范德华(vd W)相互作用都对~(17)O核的化学位移(δO)具有较大的影响.随着分子间氢键作用的逐渐增强,δO逐渐减小,当采用包含所有弱相互作用的周期性模型进行计算时,理论结果与实验值吻合.进一步的电荷分析显示,~(17)O核化学位移的减小主要是由于分子间氢键作用强度增加导致~(17)O原子的负电荷密度逐渐增加.此外,计算结果表明碱基中分子间氢键网络和弱的范德华作用对碱基~(17)O QCC也具有显著的影响.周期性模型下,碱基上氧原子的局域结构环境得到平衡,~(17)O QCC达到最小值,与实验结果最为接近.以核酸碱基为例,说明了分子间的氢键网络以及分子间弱的相互作用对于准确计算生物样品的核磁共振(NMR)参数非常重要,以小的团簇模型来计算生物体系的核磁参数将会产生较大的偏差.     

Renormalization Group¶and the Melnikov Problem for PDE's

We give a new proof of persistence of quasi-periodic, low dimensional elliptic tori in infinite dimensional systems. The proof is based on a renormalization group iteration that was developed recently in [BGK] to address the standard KAM problem, namely, persistence of invariant tori of maximal dimension in finite dimensional, near integrable systems. Our result covers situations in which the so called normal frequencies are multiple. In particular, it provides a new proof of the existence of small-amplitude, quasi-periodic solutions of nonlinear wave equations with periodic boundary conditions. Received: 29 January 2001 / Accepted: 8 March 2001     

Critical behavior of a KAM surface: I. Empirical results

Kolmogorov-Arnol'd-Moser (KAM) surfaces are studied in the context of a perturbed two-dimensional twist map. In particular, we ask how a KAM surface can disappear as the perturbation parameter is increased. Following Greene, we use cycles to numerically construct the KAM curve and discover that at the critical coupling it shows structure at all length scales. Aspects of this structure are fitted by a scaling analysis; critical indices and scaling functions are determined numerically. Some evidence is presented which suggests that the results are universal.Supported in part by the Materials Research Laboratory Program of the National Science Foundation at the University of Chicago under grant No. NSF-MRL 7924007.Robert R. McCormick and National Science Foundation Fellow     

Eight-quark interactions as a chiral thermometer

A NJL Lagrangian extended to six [1–3] and eight quark interactions [4] is applied to study temperature effects [5] (SU(3) flavor limit, massless case), and [6] (realistic massive case). The transition temperature can be considerably reduced as compared to the standard approach, in accordance with recent lattice calculations [7]. The mesonic spectra built on the spontaneously broken vacuum induced by the’ t Hooft interaction strength, as opposed to the commonly considered case driven by the four-quark coupling, undergoes a rapid crossover to the unbroken phase, with a slope and at a temperature which is regulated by the strength of the OZI violating eight-quark interactions. This strength can be adjusted in consonance with the four-quark coupling and leaves the spectra unchanged, except for the sigma meson mass, which decreases. A first order transition behavior is also a possible solution within the present approach.     

Fluorescence Characteristics of Bisphenol A in Room Temperature Ionic Liquids

Room temperature ionic liquids (RTILs) are emerging as a new class of ‘green’ solvents for use in a wide range of chemical processes. RTILs can sensitize or quench fluorescence of organic chemicals and their interactions still remain unclear, especially for weakly fluorescent chemicals. Herein, we report the effects of six RTILs on the fluorescence behavior of bisphenol A (BPA). The fluorescence intensities (FIs) of BPA in a RTIL-acetonitrile system were significantly quenched compared to acetonitrile. The quenching effect was stronger for [C_nMIM]BF₄ than [C_nMIM]PF₆. A decreasing trend of fluorescence lifetime (FL) of BPA was observed for [C₆MIM]PF₆ (4.26 to 3.86 ns) and [C₁₄MIM]PF₆ (4.15 to 3.78 ns) with increasing RTIL concentrations in the range of 1–10 mM. The quenching mode was consistent with a static quenching mechanism based on the consistency of FL and FI results. The emission bands of BPA and RTILs did not interfere with each other when RTILs were used as the solvent. The investigated RTILs enhanced the FIs of strongly fluorescing chemicals (12.0?~?19.0-fold for norfloxacin and 6.1?~?8.5-fold for dansyl chloride), but quenched those of weakly fluorescing chemicals (BPA). These results demonstrate that RTILs have different fluorescent effects on organic chemicals with different fluorophores. The interactions between RTILs and BPA result from many factors in addition to viscosity, such as solvent electrostatic dielectric constant, refractive index, density, polarization and molecular interaction. These results provide a theoretical foundation for application of RTILs in the analysis of weakly fluorescing chemical.     

Schrödinger operators with symmetries

We consider the stationary Schrödinger operator H of a many-body system M with two-body rotation invariant interactions. The operator H is reduced with respect to the symmetries of permutation of identical particles, rotations and reflections, into a direct sum of operators H^τ̃, where τ̃ is an index of the irreducible representations of the symmetry group of the system.The spectra of the operators H^τ̃ were investigated in a series of papers of G.M. Zislin and A.G. Sigalov ([20], [21], [31]-[35]). In a recent paper [3] we have developed the spectral theory of these operators on the basis of the Weinberg equations.In the present work we complete and simplify this theory. In particular we treat in detail the case where the given system can be decomposed into two identical subsystems. For such systems there is a certain coupling between permutation and rotation-reflection symmetries, because a permutation, which interchanges the two subsystems, imposes a reflection on the relative position vector of the two centers of mass. This requires a modification of the theorem on essential spectrum as formulated in [3] in the case where such a division is not possible. The importance of this special case, as exemplified by diatomic molecules, fully justifies such a detailed treatment.This special case was treated by Zislin [34] under the assumption that the interactions are essentially multiplicative, relatively compact two-body interactions. Our method allows for general relatively compact two-body interactions, and can without difficulty be generalized to many-body interactions.Moreover, the method based on the Weinberg equation is suitable for a further analysis of the spectra of these operators.     

瓜环与喹啉及其衍生物的相互作用

利用荧光光谱分析方法考察六、七及八元瓜环与喹啉、异喹啉、7-甲基喹啉相互作用的结构特征以及光学特性。与核磁共振技术比较,荧光光谱分析方法具有高灵敏性的特点,不仅可观察到喹啉及其衍生物与七元瓜环相互作用而引起的荧光性质变化;还能观察到它们与六元瓜环或八元瓜环相互作用所产生的变化,这是通常的NMR方法所不能实现的。实验表明喹啉、异喹啉、7-甲基喹啉与六、七及八元瓜环有包结作用,形成多种不同包结比的稳定包结配合物。实验也证实,瓜环与客体之间相互作用受到3种效应的协同影响:(1)疏水性的笼体效应(瓜环以其特殊的疏水性笼状结构,可与多种有机物发生疏水性的笼体作用);(2)亲水性的端口效应(瓜环端口环绕的羰基氧通过离子-偶极相互作用来键合金属离子或有机分子的带电部分);(3)相互作用的客体分子或瓜环笼体空间大小,即尺寸效应。     

内嵌富勒烯[M@C_(70)](M=Li,Na,K,Be,Mg,Ca)与[Mg(H_2O)_6]~(2+)相互作用的密度泛函理论研究

使用密度泛函理论方法,对内嵌多种碱金属及碱土金属原子(M=Li,Na,K,Be,Mg,Ca)的富勒烯C70与水合Mg(II)离子之间的相互作用进行了理论研究.首先对各原子(M=Li,Na,K,Be,Mg,Ca)嵌入C70后的形成能进行了讨论,之后计算了[M@C70]各体系与[Mg(H_2O)6]2~+的相互作用能,并采用自然键轨道理论(NBO)研究了电荷转移的情况,最后进行了电子密度拓扑分析.结果表明,内嵌原子半径越大,[M@C70]各体系的热力学稳定性就越高,转移至[Mg(H_2O)6]2~+的电荷也随之增加,二者之间的相互作用属于闭壳层相互作用及共价作用.     

内嵌富勒烯[M@C70] (M=Li, Na, K, Be, Mg, Ca)与[Mg(H2O)6]2+相互作用的密度泛函理论研究

使用密度泛函理论方法, 对内嵌多种碱金属及碱土金属原子(M=Li, Na, K, Be, Mg, Ca)的富勒烯C70与水合Mg(II)离子之间的相互作用进行了理论研究. 首先对各原子(M=Li, Na, K, Be, Mg, Ca)嵌入C70后的形成能进行了讨论, 之后计算了[M@C70]各体系与[Mg(H2O)6]2+的相互作用能, 并采用自然键轨道理论(NBO)研究了电荷转移的情况, 最后进行了电子密度拓扑分析. 结果表明, 内嵌原子半径越大, [M@C70]各体系的热力学稳定性就越高, 转移至[Mg(H2O)6]2+的电荷也随之增加, 二者之间的相互作用属于闭壳层相互作用及共价作用.     

Dispersion of low frequency phonons in the deuterated naphthalene crystal

The dispersion curves of the external and the four lowest internal phonon modes in d₈-naphthalene (C₁₀D₈) crystal have been measured by coherent inelastic neutron scattering for the [010] and [100] directions at 98K and partially at 5K. The results are compared with calculations based on model atom-atom “6-exp” potential with the Kitaigorodski set of parameters for C-C, C-H and H-H interactions.     

多价抗衡离子诱导聚甲基丙烯酸N,N-二甲基氨基乙酯(PDMAEMA)刷构象转变的UCST行为

本文应用分子场理论,研究pH、[Fe(CN)_6]~(3-)诱导聚甲基丙烯酸N,N-二甲基氨基乙酯(PDMAEMA)刷的上临界溶解温度(UCST)构象转变与结构特性.理论模型考虑p H和[Fe(CN)_6]~(3-)对PDMAEMA刷体系的静电调控作用.研究发现,在不同[Fe(CN)_6]~(3-)浓度、不同p H条件下,PDMAEMA刷呈现了UCST构象转变行为.由于p H调节PDMAEMA单体质子化,[Fe(CN)_6]~(3-)通过与PDMAEMA带正电荷的单体结合,形成了在PDMAEMA链内以[Fe(CN)_6]~(3-)为中介的带电单体间的静电吸引结合.随着温度升高,[Fe(CN)_6]~(3-)与PDMAEMA带正电荷的单体结合被破坏,[Fe(CN)_6]~(3-)在链内凝聚导致的静电屏蔽效应减弱,PDMAEMA链内带电单体间的静电排斥增强,PDMAEMA刷的构象呈现了从塌缩到溶胀的UCST转变行为,并且在较高[Fe(CN)_6]~(3-)浓度条件下,PDMAEMA刷构象转变的UCST增高.在较低p H值条件下,较多的PDMAEMA单体被质子化,[Fe(CN)_6]~(3-)与PDMAEMA带正电单体的结合增强,PDMAEMA刷构象转变的UCST增大.基于pH和[Fe(CN)_6]~(3-)对PDMAEMA刷体系中的静电调控效应,可以预言,在较小p H和较大[Fe(CN)_6]~(3-)浓度条件下,PDMAEMA链在垂直培基表面沿着链方向形成结节状结构.这是由于以[Fe(CN)_6]~(3-)为中介的链内带电单体间的静电吸引作用增强,导致临近单体间汇聚结节.我们的理论结果符合实验观测,由此表明,pH调节PDMAEMA单体的带电状态,以及[Fe(CN)_6]~(3-)在PDMAEMA链内凝聚导致的静电屏蔽效应,决定着PDMAEMA刷的UCST构象转变和结构特性.     

Stability of Driven Systems with Growing Gaps, Quantum Rings, and Wannier Ladders

We consider a quantum particle in a periodic structure submitted to a constant external electromotive force. The periodic background is given by a smooth potential plus singular point interactions and has the property that the gaps between its bands are growing with the band index. We prove that the spectrum is pure point—i.e., trajectories of wave packets lie in compact sets in Hilbert space—if the Bloch frequency is nonresonant with the frequency of the system and satisfies a Diophantine-type estimate, or if it is resonant. Furthermore, we show that the KAM method employed in the nonresonant case produces uniform bounds on the growth of energy for driven systems.     

Frustrations in low-dimensional magnetic systems

On the basis of exact analytical solutions for spin-spin correlation functions in the one-dimensional 3-state [1] and 4-state [2] standard Potts models and Ising model [3] with allowance for the interactions between nearest neighbors J and next-nearest neighbors J′, phenomena of the appearance and disappearance of frustrations have been investigated, depending on the signs of J and J′ and the ratio of the interactions. In the Ising model, these phenomena have been studied on triangular, hexagonal, and kagomé lattices on the basis of exact analytical solutions for the maximum values of the Kramers-Wannier matrices obtained in [4, 5].     

Results in One, Two, and Three Dimensions, for Delta Functions, Square Wells, and Delta Shells, Respectively

 I will outline three-particle calculations, and results, in one dimension [1–4] with delta-function interactions, in two dimensions [5–11] for square wells and in three dimensions [12] with delta shells. The presentation will be that of my own work, obtained together with colleagues. The initial approach is that of expansions of the wave function in terms of hyperspherical adiabatic functions, usually deduced from hyperspherical harmonics. Received October 29, 2001; accepted for publication November 23, 2001     

Stabilization of chaotic and non-permanent food-web dynamics

Several decades of dynamical analyses of food-web networks [1-6] have led to important insights into the effects of complexity, omnivory and interaction strength on food-web stability [6-8]. Several recent insights [7, 8] are based on nonlinear bioenergetic consumer-resource models [9] that display chaotic behavior in three species food chains [10, 11] which can be stabilized by omnivory [7] and weak interaction of a fourth species [8]. We slightly relax feeding on low-density prey in these models by modifying standard food-web interactions known as type II functional responses [12]. This change drastically alters the dynamics of realistic systems containing up to ten species. Our modification stabilizes chaotic dynamics in three species systems and reduces or eliminates extinctions and non-persistent chaos [11] in ten species systems. This increased stability allows analysis of systems with greater biodiversity than in earlier work and suggests that dynamic stability is not as severe a constraint on the structure of large food webs as previously thought. The sensitivity of dynamical models to small changes in the predator-prey functional response well within the range of what is empirically observed suggests that functional response is a crucial aspect of species interactions that must be more precisely addressed in empirical studies.Received: 7 December 2003, Published online: 14 May 2004PACS: 05.45.-a Nonlinear dynamics and nonlinear dynamical systems - 05.45.Jn High-dimensional chaos - 05.45.Pq Numerical simulations of chaotic systems - 87.23.-n Ecology and evolution     

Synthesis and Raman spectroscopic investigation of a new self‐assembly monolayer material 4‐[N‐phenyl‐N‐(3‐methylphenyl)‐amino]‐benzoic acid for organic light‐emitting devices

We have synthesized 4‐[N‐phenyl‐N‐(3‐methylphenyl)‐amino]‐benzoic acid (4‐[PBA]) and investigated its molecular vibrations by infrared and Raman spectroscopies as well as by calculations based on the density functional theory (DFT) approach. The Fourier transform (FT) Raman, dispersive Raman and FT‐IR spectra of 4‐[PBA] were recorded in the solid phase. We analyzed the optimized geometric structure and energies of 4‐[PBA] in the ground state. Stability of the molecule arising from hyperconjugative interactions and charge delocalization was studied using natural bond orbital analysis. The results show that change in electron density in the σ* and π* antibonding orbitals and E₂ energies confirm the occurrence of intramolecular charge transfer within the molecule. Theoretical calculations were performed at the DFT level using the Gaussian 09 program. Selected experimental bands were assigned and characterized on the basis of the scaled theoretical wavenumbers by their total energy distribution. The good agreement between the experimental and theoretical spectra allowed positive assignment of the observed vibrational absorption bands. Finally, the calculation results were applied to simulate the Raman and IR spectra of the title compound, which show agreement with the observed spectra. Copyright © 2011 John Wiley & Sons, Ltd.     

Quenching of Pyrene Fluorescence by Calix[4]arene and Calix[4]resorcinarenes

Interactions involving calixarene and its derivatives are of major importance due to their widespread applications as unique hosts. Fluorescence from a common probe pyrene is used to study interactions involving calix[4]resorcinarene [1a] and its tetra-morpholine derivative [1b] in 1 M aqueous NaOH. These compounds efficiently quench the pyrene fluorescence. A comparison with the fluorescence quenching behavior of N-methylmorpholine clearly indicates the presence of long-range interactions involving 1a and 1b; the interactions are specific to the calixarene molecular framework. This is not the case for a tetra-nitro-substituted calix[4]arene [2b], an electron/charge acceptor quencher, as p-nitrophenol also shows similar interactions with pyrene. Effectiveness of cesium as the quencher of pyrene fluorescence is reduced in the presence of electron/charge donating 1b; fluorescence enhancement is observed upon addition of cesium as the concentration of 1b is increased in the solution. The role of calixarene framework in interactions involving such compounds is established.