Remark on the Connectedness of Space in the Experimental Devices of Aharonov-Bohm Effect

This article shows that in Aharonov-Bohm (AB) effect arrangements, the electron wave propagation space is doubly connected for two real coherent sources, and simply connected under certain condition for two virtual coherent sources, and all known AB experiments belong to the latter case. By the Feynman path integral method, we show that in the former case there is no AB effect, whereas in the latter case there is.     

First-principles study of lithium intercalated bilayer graphene

Lithium intercalated bilayer graphene has been investigated using first-principles density functional theory calculations. Results show that there exist AB and AA stacking sequences for bilayer graphene in which the latter is more favorable for the Li storage and the former will evolve into the latter with the intercalation of Li ions. The relationship between the interlayer distance of two graphene sheets and the intercalated capacity of Li ions is discussed. It is found that structural defect is identified to store Li ions more favorably than pristine bilayer graphene and an isolated C atom vacancy in bilayer graphene can capture three Li ions between two graphene sheets.     

Consensus and ordering in language dynamics

We consider two social consensus models, the AB-model and the Naming Game restricted to two conventions, which describe a population of interacting agents that can be in either of two equivalent states (A or B) or in a third mixed (AB) state. Proposed in the context of language competition and emergence, the AB state was associated with bilingualism and synonymy respectively. We show that the two models are equivalent in the mean field approximation, though the differences at the microscopic level have non-trivial consequences. To point them out, we investigate an extension of these dynamics in which confidence/trust is considered, focusing on the case of an underlying fully connected graph, and we show that the consensus-polarization phase transition taking place in the Naming Game is not observed in the AB model. We then consider the interface motion in regular lattices. Qualitatively, both models show the same behavior: a diffusive interface motion in a one-dimensional lattice, and a curvature driven dynamics with diffusing stripe-like metastable states in a two-dimensional one. However, in comparison to the Naming Game, the AB-model dynamics is shown to slow down the diffusion of such configurations.     

Effect of backscattering on the behavior of a dye ring laser

The effect of backscattering on the behavior of a dye ring laser is investigated by photoelectric counting measurements. It is found that there exist two laser regimes, a low backscattering regime in which the laser exhibits meta-bistability and random mode switching, and a high backscattering regime in which switching is suppressed. In the latter case the photon statistics are similar to those of a single-mode standing wave dye laser.     

Time-Dependent 2D Harmonic Oscillator in Presence of the Aharanov-Bohm Effect

We use the Lewis-Riesenfeld theory to determine the exact form of the wavefunctions of a two-dimensionnal harmonic oscillator with time-dependent mass and frequency in presence of the Aharonov-Bohm effect (AB). We find that the auxiliary equation is independent of the AB magnetic flux. In the particular case of quantized AB magnetic flux the wavefunctions coincide exactly with the wavefunctions of the 2D time-dependent harmonic oscillator. PACS: 03.65Ge; 03.65Fd; 03.65Bz     

Fractional charges in pyrochlore lattices

A pyrochlore lattice is considered where the average electron number of electrons per site is half‐integer, concentrating on the case of exactly half an electron per site. Strong on‐site repulsions are assumed, so that all sites are either empty or singly occupied. When there are in addition strong nearest‐neighbour repulsions, a tetrahedron rule comes into effect, as previously suggested for magnetite. We show that in this case, there exist excitations with fractional charge ±e/2. These are intimately connected with the high degeneracy of the ground state in the absence of kinetic energy terms. When an additional electron is inserted into the system, it decays into two point like excitations with charge ‐e/2, connected by a Heisenberg spin‐chain which carries the electron's spin.     

Theoretical analysis of the transmission phase shift of a quantum dot in the presence of Kondo correlations

We study the effects of Kondo correlations on the transmission phase shift of a quantum dot coupled to two leads in comparison with the experimental determinations made by Aharonov-Bohm (AB) quantum interferometry. We propose here a theoretical interpretation of these results based on scattering theory combined with Bethe ansatz calculations. We show that there is a factor of 2 difference between the phase of the S-matrix responsible for the shift in the AB oscillations and the one controlling the conductance. Quantitative agreement is obtained with experimental results for two different values of the coupling to the leads.     

Binary-component micelle and vesicle: Free energy and asymmetric distributions of amphiphiles between monolayers of vesicle

The real-space two-dimensional self-consistent field theory (SCFT) is employed to study the free energies of micelles and vesicles constituted by binary amphiphilic diblock copolymer AB in homopolymer A. With increasing volume fraction of copolymer AB, there are morphological transitions from the circle micelles to oblate circle-like micelles, to compound structure with inverted micelles in the inner center and micelles outer layer, and to vesicles. Special attentions are paid to the role of the copolymer AB in controlling free energies of the micelles and vesicles, by examining the effect of length ratio of A/B with the fixed whole chain length of AB copolymer, the length effect of A or B block with the corresponding fixed length of B or A block, for one component of copolymer, and the effect of different amphiphile compositions for binary-component copolymer system. The quantity η is provided to describe the asymmetric density distribution of amphiphiles between the inner and outer monolayers of vesicles, and to quantify the relative asymmetric extent of the density distribution between two species of copolymers in binary component vesicles.     

The case of weak birefringence in integrated photoelasticity

The main difficulties connected with the application of integrated photoelasticity are as follows: (1) in general (when rotation of the principal axes is present) one has to measure three characteristic parameters for each ray (instead of two in two-dimensional photoelasticity and in the frozen stress method); (2) the characteristics parameters are connected with the stress distribution in a very complicated manner: to determine the stress distribution from their basis is difficult.If the birefringence is weak, then measurements can be simplified. In the latter case a usual plane polariscope may be used for measurements, and simple approximate integral relationships between the experimental data and the distribution of birefringence on the ray are valid, if rotation of the principal axes is moderate. The paper attempts to establish the domain where application of these relationships is justified. By the aid of numerical experiments it is shown that simple integral relationships can be applied if optical retardation is less than a quarter of a wavelength and rotation of the principal axes is less than π/6. In the latter case by investigating a three-dimensional model the parameter of isoclinic and the optical phase retardation are measured exactly in the same way as by investigating a two-dimensional model.     

Is the Static Magnetic Vector Potential Screened by a Thick Superconducting Shield

In 1986 Tonomura and his co-workers reported the results of a test for the existence of the magnetic Aharonov-Bohm (AB) effect using permalloy toroids with a superconducting niobium coating. Classical Maxwell theory suggests that the group may have been able to observe the AB effect only because their superconducting shield was quite thin (2.5 penetration depths), and that, had a very thick shield been used, no AB effect would have been observable. However, orthodox quantum mechanics predicts that a static vector potential penetrates a superconducting shield of any thickness in cases where the magnetic flux inside the sample is an odd integer times h/2e. Regardless of which view is correct, it is argued in this paper that a superconductor only screens leakage or fringing field to the extent that it screens vector potential, so that there are doubts that the experiment answered the critics of earlier experiments, as was claimed.     

A geometric and an algebraic model for tri-nuclear molecules

A geometrical model for tri-nuclear molecules is reviewed. For an analytical solution the nuclei have to be prolately deformed and in a line connected to each other. Furthermore, there have to be two heavy and one light cluster, the latter sandwiched between the two heavy clusters. As an alternative we also study an algebraic model of tri-cluster molecules based on a U(7) group. This model allows arbitrary orientations of the center of masses.     

面心立方(001)方向AB合金薄膜表面层的有序无序相变

采用平均场近似方法对两组元面心立方合金薄膜的有序无序相转变过程进行模拟计算，结果表明，合金薄膜的有序无序相变受薄膜层数奇偶性的影响.薄膜层数奇偶性不同，会导致薄膜具有不同的相结构和热力学性质.在弱表面偏析作用下，对于偶数层薄膜，由于薄膜边界对称性破缺，对应体组分x=0.5的化学势区间，偶数层薄膜有序无序相变过程中出现了中间温度相和浸润现象.而奇数层薄膜的有序无序相变类似体材料的相变.在强表面偏析作用下，由于受表面偏析作用和有限尺寸效应影响，对应体组分x=0.5的化学势区间，奇数层薄膜中出现AB(AB)关键词： 合金薄膜 有序无序相变 浸润现象 准热力学相变     

Macroscopic test of the Aharonov-Bohm effect

The Aharonov-Bohm (AB) effect is a purely quantum mechanical effect. The original (classified as type-I) AB-phase shift exists in experimental conditions where the electromagnetic fields and forces are zero. It is the absence of forces that makes the AB effect entirely quantum mechanical. Although the AB-phase shift has been demonstrated unambiguously, the absence of forces in type-I AB effects has never been shown. Here, we report the observation of the absence of time delays associated with forces of the magnitude needed to explain the AB-phase shift for a macroscopic system.     

On a Hypothetical Explanation of the Aharonov-Bohm Effect

I study in detail a proposal made by T. H. Boyer in an attempt to explain classically the Aharonov-Bohm (AB) effect. Boyer claims that in an AB experiment, the perturbation the external incident particle produces on the charge and current distributions within the solenoid will affect back the motion of the external particle. With a qualitative analysis based on energetic considerations, Boyer seemed to arrive at the conclusion that this perturbation could give account of the AB effect. In this paper I make explicit calculations which show that Boyer's conjecture fails. Indeed I find that the perturbation produced on the solenoid, and then its effect on the external charge, is independent of the solenoid current and consequently cannot account for the AB effect, which is current dependent.     

Chaos in neural systems

The occurence of chaos in continuous-time neural network models is demonstrated through two examples, (i) a single neuron with an unusual kind of periodic input and (ii) a randomly connected network of 26 neurons with 7 incoming synapses per neuron, half the neurons being subject to a steady external stimulus. The former case is susceptible to exhaustive analysis, while the latter, discovered by computer simulation, is more attuned to neurobiological reality.     

Dynamics of irregular copolymers

Reptation dynamics of AB copolymers with irregular chemical structure are considered theoretically. It is shown that interactions between A and B monomers could result in a significant slowdown of copolymer dynamics in the disordered (macroscopically homogeneous) state. The dynamical copolymer length N* showing the crossover to the strongly retarded dynamics is calculated. It is shown that contour-length fluctuations (internal reptation modes) give rise to a strong reduction of the slowdown effect and to a strong increase of N* which becomes unrealistically high in the case of a genuinely random chemical structure. The following scaling dependence of N* is predicted for irregular block copolymers: N* proportional, variant delta(-8)chi(-8)n(-8)(0)N(3)(e), where delta is the degree of block polydispersity, chi the Flory AB interaction parameter, and n(0) the mean block length. The strongest dynamical effect of AB interactions is predicted for correlated random copolymers near the critical point related to the formation of microdomain superstructures.     

How do smectic liquid crystals of different molecular length mix in thin films?

We present a model for the structure of binary mixtures of smectic compounds in freely suspended films of 2-7 layers. The compounds are the hexyl (6AB) and dodecyl (10AB) homologues of p, p'-dialkylazoxybenzene that differ by about 40% in molecular length. X-ray reflectivity indicates that no demixing occurs between 6AB and 10AB molecules, while also there is no indication found of increased roughness at the film surfaces. However, the surface layers are somewhat expanded compared to the interior layers. This can be explained by backfolding of the dodecyl end chains of 10AB molecules at the surface via two gauche kinks, which ensures dense packing. This model is supported by surface tension measurements that indicate an increased amount of alkyl groups at the surfaces.     

Computer simulations of the growth of synthetic peptide fibres

We present a coarse-grained computer model designed to study the growth of fibres in a synthetic self-assembling peptide system. The system consists of two 28 residue a \alpha -helical sequences, denoted AB and CD, in which the interactions between the half peptides, A, B, C and D, may be tuned individually to promote different types of growth behaviour. In the model, AB and CD are represented by double ended rods, with interaction sites distributed along their lengths. Monte Carlo simulations are performed to follow fibre growth. It is found that lateral and longitudinal growth of the fibre are governed by different mechanisms --the former is diffusion limited with a very small activation energy for the addition of units, whereas the latter occurs via a process of secondary nucleation at the fibre ends. As a result, longitudinal growth generally proceeds more slowly than lateral growth. Furthermore, it is shown that the aspect ratio of the growing fibre may be controlled by adjusting the temperature and the relative strengths of the interactions. The predictions of the model are discussed in the context of published data from real peptide systems.     

Quantum transport through two series Aharonov--Bohm interferometers with zero total magnetic flux

With the help of nonequilibrium Green's function technique, the electronic transport through series Aharonov--Bohm (AB) interferometers is investigated. We obtain the AB interference pattern of the transition probability characterized by the algebraic sum \phi and the difference \theta of two magnetic fluxes, and particularly a general rule of AB oscillation period depending on the ratio of integer quantum numbers of the fluxes. A parity effect is observed, showing the asymmetric AB oscillations with respect to the even and odd quantum numbers of the total flux in antiparallel AB interferometers. It is also shown that the AB flux can shift the Fano resonance peaks of the transmission spectrum.