Multicritical behavior at the kosterlitz-thouless critical point

A multicritical critical point for the two dimensional planar model is analyzed by studying an exactly soluable limit of a related model—the generalized Villain model. The statistical mechanics of this model is written in terms of vortex and symmetry breaking excitations. In these terms, the problem reduces to a kind of two dimensional problem with interacting electric charges and magnetic monopoles. In this form, the problem is manifestly self-dual. The multicritical behavior is exhibited in a three-dimensional phase space in which the axes are the coupling strength of a “square” symmetry breaking which favors four possible directions for the planar model vectors. The analysis of this multicritical point shows that it is the intersection of at least six critical lines—each with continuously varying critical indices. Two of these lines are described by the exactly soluable gaussian model. The other four are isomorphic to one another, and each one has—as a point on the line—a critical point of the Ashkin-Teller model. We argue that each of these lines might be in an equivalent universality class to the line of critical points which occurs in the Baxter and Ashkin-Teller models. We make a suggestion about which point on these critical lines might be in the same universality class as our multicritical point. Correlation functions at the intersection point are calculated and used to develop an expansion of critical indices about this point. This expansion gives a potential method for calculating the critical behavior along the critical lines of the model.     

Dynamics of magnetic charges in artificial spin ice

Artificial spin ice has been recently implemented in two-dimensional arrays of mesoscopic magnetic wires. We propose a theoretical model of magnetization dynamics in artificial spin ice under the action of an applied magnetic field. Magnetization reversal is mediated by domain walls carrying two units of magnetic charge. They are emitted by lattice junctions when the local field exceeds a critical value Hc required to pull apart magnetic charges of opposite sign. Positive feedback from Coulomb interactions between magnetic charges induces avalanches in magnetization reversal.     

Universality of One-Dimensional Fermi Systems,I. Response Functions and Critical Exponents

The critical behavior of one-dimensional interacting Fermi systems is expected to display universality features, called Luttinger liquid behavior. Critical exponents and certain thermodynamic quantities are expected to be related among each other by model-independent formulas. We establish such relations, the proof of which has represented a challenging mathematical problem, for a general model of spinning fermions on a one dimensional lattice; interactions are short ranged and satisfy a positivity condition which makes the model critical at zero temperature. Proofs are reported in two papers: in the present one, we demonstrate that the zero temperature response functions in the thermodynamic limit are Borel summable and have anomalous power-law decay with multiplicative logarithmic corrections. Critical exponents are expressed in terms of convergent expansions and depend on all the model details. All results are valid for the special case of the Hubbard model.     

无铅四方相钙钛矿短周期超晶格压电效应机理研究

超晶格压电行为与内部正离子之间的内在联系尚缺乏相关的研究.本文基于密度泛函理论的第一性原理方法,研究了三种无铅四方相钙钛矿铁电超晶格(BaTiO_3/SrTiO_3,KNbO_3/KTaO_3和BaTiO_3/KNbO_3)中A,B位正离子对整体的极化和压电贡献.通过计算超晶格不同轴向应变条件下原子结构和Born有效电荷,获得了超晶格和各个正离子的极化值和压电系数.结果表明,在轴向压缩应变条件下(-0.15—0 A),无铅超晶格中的正离子位移D(A)和D(B)受到抑制,在拉应变时位移才显著增大,因此极化和压电行为不明显.在轴向拉伸应变作用下(0—0.15 A),无铅超晶格中各原子的极化贡献显著增大,特别是B位原子Ti,Nb和Ta的极化贡献使得总的极化强度也显著提高,并当拉应变达到一定值,超晶格才会出现明显的压电行为.无铅超晶格的极化和压电行为主要由B位正离子贡献.     

Critical behavior of two-dimensional spin models and charge asymmetry in the Coulomb gas

Many two-dimensional spin models can be transformed into Coulomb-gas systems in which charges interact via logarithmic potentials. For some models, such as the eight-vertex model and the Ashkin-Teller model, the Coulomb-gas representation has added significantly to the insight in the phase transitions. For other models, notably theXY model and the clock models, the equivalence has been instrumental for almost our entire understanding of the critical behavior. Recently it was shown that theq-state Potts model and then-vector model are equivalent to a Coulomb gas with an asymmetry between positive and negative charges. Fieldlike operators in these spin models transform noninteger charges and magnetic monopoles. With the aid of exactly solved models the Coulombgas representation allows analytic calculation of some critical indices.     

相反拓扑指数的Laguerre-Gaussian模的产生和模间相互作用的实验研究

实验研究了带有相反拓扑指数的Laguerre-Gaussian(LG)模间的相互作用，发现含有相反拓扑指数的两个LG模在传播过程中其光场发生变化，观察到随着传播距离的增加，两个LG模的中心位相奇点会逐渐连成为一个弧形暗线形状.实验上验证了带有相反拓扑指数的光学涡流中的螺旋位错在传播过程中会演变为边位错这一理论结果.     

Fixed point behavior of cumulants in the three-dimensional Ising universality class

High-order cumulants and factorial cumulants of conserved charges are suggested for the study of the critical dynamics in heavy-ion collision experiments. In this paper, using the parametric representation of the three-dimensional Ising model which is believed to belong to the same universality class as quantum chromo-dynamics, the temperature dependence of the second- to fourth-order (factorial) cumulants of the order parameter is studied. It is found that the values of the normalized cumulants are independent of the external magnetic field at the critical temperature, which results in a fixed point in the temperature dependence of the normalized cumulants. In finite-size systems simulated using the Monte Carlo method, this fixed point behavior still exists at temperatures near the critical. This fixed point behavior has also appeared in the temperature dependence of normalized factorial cumulants from at least the fourth order. With a mapping from the Ising model to QCD, the fixed point behavior is also found in the energy dependence of the normalized cumulants (or fourth-order factorial cumulants) along different freeze-out curves.     

Resistive Plates Carrying a Steady Current: Electric Potential and Surface Charges Close to the Battery

We treat the problem of two resistive plates carrying a steady current in the same direction. We consider a linear battery orthogonal to the direction of the current in the middle of the plates. We study the behavior of the surface charges close to the battery. We calculate the potential and electric field in the space outside the plates. We also consider the case of a single resistive plate carrying a steady current.     

Pair interactions of heavy vortices in quantum fluids

The dynamics of quantum vortex pairs carrying heavy doping matter trapped inside their cores is studied. The nonlinear classical matter field formalism is used to build a universal mathematical model of a heavy vortex applicable to different types of quantum mixtures. It is shown how the usual vortex dynamics typical for undoped pairs qualitatively changes when heavy dopants are used: heavy vortices with opposite topological charges (chiralities) attract each other, while vortices with the same charge are repelled. The force responsible for such behavior appears as a result of superposition of vortices velocity fields in the presence of doping substance and can be considered as a special realization of the Magnus effect. The force is evaluated quantitatively and its inverse proportionality to the distance is demonstrated. The mechanism described in this paper gives an example of how a light nonlinear classical field may realize repulsive and attractive interactions between embedded heavy impurities.     

Frictional figures of merit for single layered nanostructures

We determine the frictional figures of merit for a pair of layered honeycomb nanostructures, such as graphane, fluorographene, MoS2 and WO2 moving over each other, by carrying out ab initio calculations of interlayer interaction under constant loading force. Using the Prandtl-Tomlinson model we derive the critical stiffness required to avoid stick-slip behavior. We show that these layered structures have low critical stiffness even under high loading forces due to their charged surfaces repelling each other. The intrinsic stiffness of these materials exceeds critical stiffness and thereby the materials avoid the stick-slip regime and attain nearly dissipationless continuous sliding. Remarkably, tungsten dioxide displays a much better performance relative to others and heralds a potential superlubricant. The absence of mechanical instabilities leading to conservative lateral forces is also confirmed directly by the simulations of sliding layers.     

Branes at angles,torons, stability and supersymmetry

We elucidate some properties of the relation between two T-dual systems in tori, branes at angles and branes wrapping the whole torus carrying fluxes. We analyze different features of these systems: charges, low energy spectrum, tadpole cancellation, symmetry groups,…, and the correspondence between the two viewpoints. Particular attention is paid to supersymmetry and stability conditions. While on the branes at angles side stability and supersymmetry can be expressed as conditions on the angles between the two branes at the intersection, on the dual side supersymmetry has to do with a correction to Hermite Yang–Mills and a modified notion of stability should be considered.     

Effect of non-uniform efficiency on higher-order cumulants in heavy-ion collisions

We perform a systematic study on the effect of non-uniform track efficiency correction in higher-order cumulant analysis in heavy-ion collisions. Through analytical derivation, we find that the true values of cumulants can be successfully reproduced by the efficiency correction with an average of the realistic detector efficiency for particles with the same charges within each single phase space. The theoretical conclusions are supported by a toy model simulation by tuning the non-uniformity of the efficiency employed in the track-by-track efficiency correction method. The valid averaged efficiency is found to suppress the statistical uncertainties of the reproduced cumulants dramatically. Thus, usage of the averaged efficiency requires a careful study of phase space dependence. This study is important for carrying out precision measurements of higher-order cumulants in heavy-ion collision experiments at present and in future.     

Effects of charge fluctuation on two-membrane instability and fusion

Membrane fusion is fundamental to diverse biological processes ranging from intercellular and intracellular transport to egg fertilization. We study the effects of coupling between membrane undulation and charge fluctuation on its fusion. We find that, at concentrations of millimolar range, multivalent cations such as calcium in solution induce a strong correlated-charge fluctuation on each membrane, leading to inversion and overcondensation of surface charges. When the charge fluctuation is cooperatively coupled to undulation, two apposing membranes undergo a dynamic instability to spontaneous growth of in-phase undulation with submicron wavelengths, thereby greatly reducing fusion barrier.     

Vortex condensation in the Chern-Simons Higgs model: An existence theorem

It is shown that there is a critical value of the Chern-Simons coupling parameter so that, below the value, there exists self-dual doubly periodic vortex solutions, and, above the value, the vortices are absent. Solutions of such a nature indicate the existence of dyon condensates carrying quantized electric and magnetic charges.     

Heavy fragment production cross sections from 1.05 GeV/nucleon 56Fe in C, Al, Cu, Pb, and CH2 targets

We have obtained charge-changing cross sections and partial cross sections for fragmentation of 1.05 GeV/nucleon Fe projectiles incident on H, C, Al, Cu, and Pb nuclei. The energy region covered by this experiment is critical for an understanding of galactic cosmic ray propagation and space radiation biophysics. Surviving primary beam particles and fragments with charges from 12 to 25 produced within a forward cone of half-angle 61 mrad were detected using a silicon detector telescope to identify their charge and the cross sections were calculated after correction of the measured yields for finite target thickness effects. The cross sections are compared to model calculations and to previous measurements. Cross sections for the production of fragments with even-numbered nuclear charges are seen to be enhanced in almost all cases.     

Half-plane diffraction of Gaussian beams carrying two vortices of equal charges

This paper derives explicit expressions for the propagation of Gaussian beams carrying two vortices of equal charges m=±1 diffracted at a half-plane screen, which enables the study of the dynamic evolution of vortices in the diffraction field. It shows that there may be no vortices, a pair or several pairs of vortices of opposite charges m=+1, -1 in the diffraction field. Pair creation, annihilation and motion of vortices may appear upon propagation. The off-axis distance additionally affects the evolutionary behaviour. In the process the total topological charge is equal to zero, which is unequal to that of the vortex beam at the source plane. A comparison with the free-space propagation of two vortices of equal charges and a further extension are made.     

Shared aperture metasurface antenna for electromagnetic vortices generation with different topological charges

Vortex beams carrying orbital angular momentum (OAM) have aroused great interest of both scientific and engineering communities. Encouragingly, generating OAM with different topological charges in a shared aperture is regarded as a potential route to expanding the communication capacity, which yet is an academic challenging task. In this work, a paradigm of designing metasurface-based shared aperture antenna for generating polarization-dependent vortex beams with distinct topological charges is proposed. Anisotropic unit cells that can tailor different resonance phase profiles in two orthogonal orientations are used to assemble a metasurface reflector. As a proof-of-concept, a planar reflector antenna is designed with two Vivaldi sources, which can generate x- and y-polarized vortex beams with topological charges of l=-1 and l=-2, respectively. Both the simulation results and the measurement results are in good agreement, which demonstrates the feasibility of our design. Significantly, this work provides a new route to achieving vortex beams carrying different topological charges in the same frequency band, which may have potential applications in communication systems.     

Statistical Distribution of Quantum Entanglement for a Random Bipartite State

We compute analytically the statistics of the Renyi and von Neumann entropies (standard measures of entanglement), for a random pure state in a large bipartite quantum system. The full probability distribution is computed by first mapping the problem to a random matrix model and then using a Coulomb gas method. We identify three different regimes in the entropy distribution, which correspond to two phase transitions in the associated Coulomb gas. The two critical points correspond to sudden changes in the shape of the Coulomb charge density: the appearance of an integrable singularity at the origin for the first critical point, and the detachment of the rightmost charge (largest eigenvalue) from the sea of the other charges at the second critical point. Analytical results are verified by Monte Carlo numerical simulations. A short account of part of these results appeared recently in Nadal et al. (Phys. Rev. Lett. 104:110501, 2010).     

Nonmonotonic Behavior in Hard-Core and Widom–Rowlinson Models

We give two examples of nonmonotonic behavior in symmetric systems exhibiting more than one critical point at which spontanoous symmetry breaking appears or disappears. The two systems are the hard-core model and the Widom–Rowlinson model, and both examples take place on a variation of the Cayley tree (Bethe lattice) devised by Schonmann and Tanaka. We obtain similar, though less constructive, examples of nonmonotonicity via certain local modifications of any graph, e.g., the square lattice, which is known to have a critical point for either model. En route we discuss the critical behavior of the Widom–Rowlinson model on the ordinary Cayley tree. Some results about monotonicity of the phase transition phenomenon relative to graph structure are also given.     

介质阻挡放电中电介质参量对放电时间特性的影响

采用介质参量不对称的装置,在大气压氩气介质阻挡放电中,研究了不同电介质温度及不同电介质材料对放电时间特性的影响.实验发现,外加电压较低时,正负半周的放电时间波形没有明显的差别;外加电压较高时,正负半周的放电脉冲个数不同.分析表明,电介质温度以及材料均影响壁电荷的积累,进而使放电特性发生改变. 关键词： 介质阻挡放电 时间特性 壁电荷 介电常数