On the role of frustration in excitable systems

We study the role of frustration in excitable systems that allow for oscillations either by construction or in an induced way. We first generalize the notion of frustration to systems whose dynamical equations do not derive from a Hamiltonian. Their couplings can be directed or undirected; they should come in pairs of opposing effects like attractive and repulsive, or activating and repressive, ferromagnetic and antiferromagnetic. As examples we then consider bistable frustrated units as elementary building blocks of our motifs of coupled units. Frustration can be implemented in these systems in various ways: on the level of a single unit via the coupling of a self-loop of positive feedback to a negative feedback loop, on the level of coupled units via the topology or via the type of coupling which may be repressive or activating. In comparison to systems without frustration, we analyze the impact of frustration on the type and number of attractors and observe a considerable enrichment of phase space, ranging from stable fixed-point behavior over different patterns of coexisting options for phase-locked motion to chaotic behavior. In particular we find multistable behavior even for the smallest motifs as long as they are frustrated. Therefore we confirm an enrichment of phase space here for excitable systems with their many applications in biological systems, a phenomenon that is familiar from frustrated spin systems and less known from frustrated phase oscillators. So the enrichment of phase space seems to be a generic effect of frustration in dynamical systems. For a certain range of parameters our systems may be realized in cell tissues. Our results point therefore on a possible generic origin for dynamical behavior that is flexible and functionally stable at the same time, since frustrated systems provide alternative paths for the same set of parameters and at the same "energy costs."     

Magnetic dipolar ordering on geometrically frustrated brick-shaped lattices

The magnetic ordering of frustrated arrays of nanoscale islands can be strongly influenced by the array patterns. We theoretically present three kinds of artificial geometrically frustrated systems with different brick-shaped geometries, defined as brick-shaped lattices, and investigate their magnetic dipolar ordering at the ground state using the Monte Carlo method. The simulated results show that the magnetic ordering of three brick-shaped frustrated lattices depends strongly on the strength of dipolar interactions, depending on the lattice spacing. It is found that the long-range dipolar interactions tend to suppress the long-range ordered state and induce the short-range quasi-ice state at each vertex of the lattices. In addition, the correlations for neighboring spin pairs are closely related to not only the dipolar coupling strength but also the geometry of the lattices.     

Phase transitions in the frustration network

The distribution of the frustrated plaquettes is calculated as a function of disorder for two and three dimensional random Ising- andXY-models. It is shown that in all cases the frustrated plaquettes are highly correlated and that at a critical value of disorder a phase transition occurs in the frustration network which can be viewed as a dissociation of plaquettes. The critical disorder is calculated using duality transformations. We show that in the two and three dimensional random Ising systems two types of nonmagnetic phases exist which differ qualitatively by their distribution of frustrated plaquettes and consequently by their domain wall structure.     

大学物理实验中DIY学习方法的应用与实践

大学物理实验是大学生学习物理的基础,是提高学生实践操作能力的关键环节.结合我校大学物理实验教学过程中发现的问题,提出一种让学生主动获取操作能力的方法,即DIY(DO IT YOURSELF)学习方法,可以使大学生从理论学习逐步向实践动手能力转变,使大学物理实验真正成为提高大学生实践能力、创新能力的平台.     

Frustration, area law, and interference in quantum spin models

We study frustrated quantum systems from a quantum information perspective. Within this approach, we find that highly frustrated systems do not follow any general "area law" of block entanglement, while weakly frustrated ones have area laws similar to those of nonfrustrated systems away from criticality. To calculate the block entanglement in systems with degenerate ground states, typical in frustrated systems, we define a "cooling" procedure of the ground state manifold and propose a frustration degree and a method to quantify constructive and destructive interference effects of entanglement.     

Two disordered phases of the beta-tin structure in binary semiconductors

The Ising model on a beta-tin structure has a phase diagram containing three distinct phases involving order, disorder, and a frustrated ordering. The x-ray crystallographic observation that no ordered beta-tin phases exist at room temperature in compound semiconductors may indicate either "paramagnetic" (dynamic) or frustrated (static) disorder. Density functional pseudopotential calculations determine which regimes real materials fall into and predict that in materials such as GaSb, there may be two temperature-driven transitions between beta-tin structures: from ordered, to frustrated order, to disordered.     

用Proteus仿真二极管特性实验

物理实验中,二极管是最常用的电子元器件。教学中为了让学生理解二极管的特性和使用,借助于Protues软件设计了二极管特性实验仿真教学。通过仿真波形图或实时效果图示,使学生理解利用普通二极管的单向导电特性做整流电路,将交流电变换成直流电,稳压二极管能够稳定输出电压,发光二极管发出亮光,能够显示图形符号,传递信息。     

CORE: Frustrated Magnets, Charge Fractionalization, and QCD

I explain how to use a simple method to extract the physics of lattice Hamiltonian systems which are not easily analyzed by exact or other numerical methods. I will then use this method to establish the relationship between QCD and a special class of generalized, highly frustrated anti-ferromagnets.     

H定理的一个补充

一.引言 统计力学中研究一个力学体系的平衡态通常所用的基本出发点,便是将体系的平衡态看作为它的态对于一个极长的时间的平均。由此推论在平衡态中体系的相空间占有相同体积的各部份有同样的几率,再由此推广到量子统计学中的“力学体系的各个量子态有同样几率”的假定。自这里起,Fowler讨论了一个含有许多近独立子系的力学体系(子系的所谓“近独立”,乃是指在计算整个体系     

远看物理之美——北京大学非物理学科物理教学体会

作者在北京大学讲授非物理学科学生的课程《今日物理》的6年中,慢慢体会到讲授的特点,那就是从高处和远处看物理.对学生讲清楚物理学的基本轮廓、基本要点和发展脉络.从重要物理事件的发展看科学家如何处理问题,从科学家的言行看如何做研究.通过这些,让学生明白什么才是科学上重要的东西,培养学生创造性思维的方式.作者谨以文中的这些浅...     

在解决物理问题过程中培养学生“去理想化”思维习惯——以一个有趣的静电场问题为例

物理教学离不开理想化模型的建构,简化的理想模型能够帮助中学生在现有知识层面的基础上,更好地理解相关知识并解决问题.但是在实际物理问题中,如果不充分考虑理想化条件,学生在解决问题时就容易产生认知矛盾,不知所措.以一个有趣的静电场问题为例,揭示理想化模型的局限性,强调"去理想化"思维习惯的重要性.探讨分析了教师如何帮助学生打破思维定势,让其对已掌握的物理知识活学活用,培养学生严谨的科学思维.     

“STELLA 2011 — School for Training in Experiments with Lasers and Laser Applications”: Short-term evaluation by quantitative methods

STELLA School is an advanced education program in laser physics for PhD and postdoctoral students in which highly qualified training in experimental techniques was delivered directly by using top-level research equipment. Its basic idea is born from the very idea which has seeded the birth of universities in the Middle Age: the inherent unity between research and education. This paper describes a study of a short-term survey that investigates the agreement of the students with some core ideas of the School as well as their general satisfaction as a marker of the robustness of the School method.     

Optical Bragg,atomic Bragg and cavity QED detections of quantum phases and excitation spectra of ultracold atoms in bipartite and frustrated optical lattices

Ultracold atoms loaded on optical lattices can provide unprecedented experimental systems for the quantum simulations and manipulations of many quantum phases and quantum phase transitions between these phases. However, so far, how to detect these quantum phases and phase transitions effectively remains an outstanding challenge. In this paper, we will develop a systematic and unified theory of using the optical Bragg scattering, atomic Bragg scattering or cavity QED to detect the ground state and the excitation spectrum of many quantum phases of interacting bosons loaded in bipartite and frustrated optical lattices. The physically measurable quantities of the three experiments are the light scattering cross sections, the atom scattered clouds and the cavity leaking photons respectively. We show that the two photon Raman transition processes in the three detection methods not only couple to the density order parameter, but also the valence bond order parameter due to the hopping of the bosons on the lattice. This valence bond order coupling is very sensitive to any superfluid order or any valence bond (VB) order in the quantum phases to be probed. These quantum phases include not only the well-known superfluid and Mott insulating phases, but also other important phases such as various kinds of charge density waves (CDW), valence bond solids (VBS), and CDW-VBS phases with both CDW and VBS orders unique to frustrated lattices, and also various kinds of supersolids. We analyze respectively the experimental conditions of the three detection methods to probe these various quantum phases and their corresponding excitation spectra. We also address the effects of a finite temperature and a harmonic trap. We contrast the three scattering methods with recent in situ measurements inside a harmonic trap and argue that the two kinds of measurements are complementary to each other. The combination of both kinds of detection methods could be used to match the combination of Scanning tunneling microscopy (STM), the Angle Resolved Photo Emission spectroscopy (ARPES) and neutron scattering in condensed matter systems, therefore achieve the putative goals of quantum simulations     

Correlated spin networks in frustrated systems

We introduce a network model for frustrated spin systems based on highly correlated spin fluctuations, to quantify and visualize their ordering. This model shows that networks of strongly correlated but non-contiguous spins exist at low temperatures on a triangular Ising lattice with competing nearest-neighbor interactions. This finding is consistent with chaotic renormalization-group trajectories previously reported for frustrated hierarchical lattices.     

Exact solutions of discrete master equations in terms of continued fractions

We present the continued fraction solution for the stationary probability of discrete master equations of one-variable processes. After we elucidate the method for simple birth and death processes we focus the study on processes which introduce at least two-particle jumps. Consequently, these processes do in general not obey a detailed balance condition. The outlined method applies as well to solutions of eigenmodes of the stochastic operator. Further we derive explicit continued fraction solutions for the Laplace transform of conditional probabilities. All the various continued fraction coefficients are given directly in terms of the transition rates and they obey recursion relations. The method is illustrated for the stationary solution of a simple nonlinear chemical reaction scheme originated by Nicolis.     

Atomic quantum gases in Kagomé lattices

We demonstrate the possibility of creating and controlling an ideal and trimerized optical Kagomé lattice, and study the low temperature physics of various atomic gases in such lattices. In the trimerized Kagomé lattice, a Bose gas exhibits a Mott transition with fractional filling factors, whereas a spinless interacting Fermi gas at 2/3 filling behaves as a quantum magnet on a triangular lattice. Finally, a Fermi-Fermi mixture at half-filling for both components represents a frustrated quantum antiferromagnet with a resonating-valence-bond ground state and quantum spin liquid behavior dominated by a continuous spectrum of singlet and triplet excitations. We discuss the method of preparing and observing such a quantum spin liquid employing molecular Bose condensates.     

Geometry effect on the magnetic ordering of geometrically frustrated rectangular and triangular magnets

We investigate the effect of geometry on the ground-state ordering of artificially frustrated magnetic rectangular and triangular lattices by Monte Carlo method. By varying the vertical lattice spacing while keeping the horizontal one fixed, we show that when the ratio of vertical to horizontal lattice spacing, labeled by η, is less than 1.82, the ground state of the rectangular lattice presents long-range antiferromagnetic order and for η?1.82 the ground state changes to long-range mixed ferromagnetic and antiferromagnetic order. For the frustrated triangular lattice, the short-range ordered state as well as two long-range ordered ground states occurs transiently at η=0.87 and 2, where the energies of the two ground states with long-range order are approximately equal. In addition, the level of frustration of both frustrated lattices is found to be largely relevant to the ratio η.     

Pair (Bethe) approximation applied to a frustrated Ising model

It is argued that a macroscopic number of spins in a frustrated Ising model are not polarized to +1 or -1 in the low-temperature limit in the pair (Bethe) approximation. It is conjectured that the low-temperature phase of a frustrated Ising model is always paramagnetic in the pair (Bethe) approximation.     

Optical mapping of pressures in tyre contact areas

An optical method of measuring the pressure distribution in an automobile tyre contact area is reported. The method relies on the phenomenon of frustrated total internal reflection to produce a video image in which the brightness is a measurement of the pressure at any point. Conversion of this monochrome picture via a colour synthesizer allows the contact area to be displayed as a colour contour map of pressure.     

Metrics for ergodicity and design of ergodic dynamics for multi-agent systems

In this paper we propose a metric that quantifies how far trajectories are from being ergodic with respect to a given probability measure. This metric is based on comparing the fraction of time spent by the trajectories in spherical sets to the measure of the spherical sets. This metric is shown to be equivalent to a metric obtained as a distance between a certain delta-like distribution on the trajectories and the desired probability distribution. Using this metric, we formulate centralized feedback control laws for multi-agent systems so that agents trajectories sample a given probability distribution as uniformly as possible. The feedback controls we derive are essentially model predictive controls in the limit as the receding horizon goes to zero and the agents move with constant speed or constant forcing (in the case of second-order dynamics). We numerically analyze the closed-loop dynamics of the multi-agents systems in various scenarios. The algorithm presented in this paper for the design of ergodic dynamics will be referred to as Spectral Multiscale Coverage (SMC).