Symmetry breaking bifurcations in a circular chain of N coupled logistic maps

A circular chain of N cells with logistic dynamics, coupled together with symmetric nearest neighbor coupling and periodic boundary conditions is investigated. For certain coupling parameters we observe bifurcation of a stable state into two types of period two solutions. By using the symmetry of this Coupled Map Lattice model, we show that the bifurcated system only can have periodic solutions with symmetry group corresponding to certain subgroups of the full symmetry group of the system.     

Symmetry breaking in distributed coupling of counterpropagating waves in a superradiant laser

The instability of superfluorescent decay is investigated for the case in which the sample length is greater than or comparable to the resonant wavelength. This instability can inhibit emission in the direction of the pump pulse and even cause the forward emission to be switched off. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 3, 150–154 (10 February 1996) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Model for modulated and chaotic waves in zero-Prandtl-number rotating convection

The effects of time-periodic forcing in a few-mode model for zero-Prandtl-number convection with rigid body rotation is investigated. The time-periodic modulation of the rotation rate about the vertical axis and gravity modulation are considered separately. In the presence of periodic variation of the rotation rate, the model shows modulated waves with a band of frequencies. The increase in the external forcing amplitude widens the frequency band of the modulated waves, which ultimately leads to temporally chaotic waves. The gravity modulation, on the other hand, with small frequencies, destroys the quasiperiodic waves at the onset and leads to chaos through intermittency. The spectral power density shows more power to a band of frequencies in the case of periodic modulation of the rotation rate. In the case of externally imposed vertical vibration, the spectral density has more power at lower frequencies. The two types of forcing show different routes to chaos.      

Symmetry breaking in superdense matter

A gauge theory for superdense matter is considered. It is shown that in the mean-field approximation at T = 0 °K the symmetry breaking increases with increasing density. The state of dense matter and the early Universe are shortly discussed.     

Symmetry and bifurcations of momentum mappings

The zero set of a momentum mapping is shown to have a singularity at each point with symmetry. The zero set is diffeomorphic to the product of a manifold and the zero set of a homogeneous quadratic function. The proof uses the Kuranishi theory of deformations. Among the applications, it is shown that the set of all solutions of the Yang-Mills equations on a Lorentz manifold has a singularity at any solution with symmetry, in the sense of a pure gauge symmetry. Similarly, the set of solutions of Einstein's equations has a singularity at any solution that has spacelike Killing fields, provided the spacetime has a compact Cauchy surface.This work was partially supported by the National Science Foundation. The second author was supported by a Killam Visiting fellowship at the University of Calgary during the completion of the paper     

Symmetry breaking in Heisenberg antiferromagnets

We extend Griffith's theorem on symmetry breaking in quantum spin systems to the situation where the order operator and the Hamiltonian do not commute with each other. The theorem establishes that the existence of a long range order in a symmetric (non-pure) infinite-volume state implies the existence of a symmetry breaking in the state obtained by applying an infinitesimal symmetry-breaking field. The theorem is most meaningful when applied to a class of quantum antiferromagnets where the existence of a long range order has been proved by the Dyson-Lieb-Simon method. We also present a related theorem for the ground states. It is an improvement of the theorem by Kaplan, Horsch and von der Linden. Our lower bounds on the spontaneous staggered magnetization in terms of the long range order parameter take into account the symmetry of the system properly, and are likely to be saturated in general models.     

Symmetry breaking in orbifold models

Gauge symmetry breaking to some physically interesting gauge groups is studied in the context of symmetric orbifolds.     

Symmetry breaking in dynamical spacetimes

The behaviour of scalar electrodynamics under symmetry breaking by the Higgs mechanism is studied in a class of dynamical spacetimes—those having a Bianchi type I symmetry—which includes the spatially flat Robertson-Walker spacetimes. The Einstein equations are used to obtain the effective Lagrangian, from which it is shown thateither the gauge field does not become massive during symmetry breaking (in marked contrast with the case in which the background spacetime is static),or the symmetry breaking chooses not only a direction in the phase space of the Higgs field, but also a spatial direction in the spacetime sections.     

Symmetry breaking in τ decay

In view of the recent attempts to detect theG-parity violating decay τ→πηv _τ which may have bearing on the presence of the second class current, we discuss the isospin symmetry breaking effects in the processes of τ→δv, Bv, and ηπv from a dynamical point of view. It is shown that all the symmetry breaking effects are proportional to theu?d quark mass difference. Depending on whether the current or the constituent quark masses are used, the decay τ→πηv _τ via δ is either of the same order or three orders of magnitude smaller than the upper limit set by the latest experiments. This is in agreement with the other theoretical estimates.     

Symmetry breaking,bifurcations, quasiperiodicity,and chaos due to electric fields in a coupled cell model

A model for the asymmetric coupling of two oscillatory cells is considered. The coupling between the cells is both through diffusional exchange (symmetric) and through the electromigration of ionic reactant species from one cell to the other (asymmetric) in applied electric fields. The kinetics in each cell are the same and based on the Gray-Scott scheme. Without the electric field, only simple, stable dynamics are seen. The effect of the asymmetry (applying electric fields) is to create a wide variety of stable dynamics, multistability, multiperiodic oscillations, quasiperiodicity and chaos being observed, this complexity in response being more prevalent at weaker coupling rates and at weaker field strengths. The results are obtained using a standard dynamical systems continuation program, though asymptotic results are obtained for strong coupling rates and strong electric fields. These are seen to agree well with the numerically determined values in the appropriate parameter regimes. (c) 2002 American Institute of Physics.     

Symmetry breaking in tunnel junctions between partially dielectrized metals with charge or spin density waves

Tunnel current-voltage characteristics are calculated for symmetric junctions between metals waves of with charge or spin density that have equal absolute values |Σ| of the dielectric order parameter. The possibility of different signs for Σ on opposite sides of the junction is considered. As a result, the current-voltage characteristics are highly asymmetric. The predicted effect is a new example of symmetry breaking in many particle systems and makes it possible to explain some experimental data for symmetric URu₂Si₂-URu₂Si₂ microjunctions. Fiz. Tverd. Tela (St. Petersburg) 40, 385–388 (March 1998)     

Symmetry breaking by instantons in supergravity

The non-zero modes of different spin operators on the background of a self-dual gravitational instanton are all related by global supersymmetry transformations and completely cancel in the one-loop term, which is determined entirely by the zero modes. We derive the number of zero modes of each spin. In an asymptotically locally Euclidean self-dual instanton there are 2τ $\text{spin}\text{-}\text{3}\text{2}$ zero modes and 3τ spin-2 zero modes, where τ is the Hirzebruch signature. Up to 3 of the spin-2 zero modes (depending on boundary conditions) may correspond to global rotations. The $\text{spin}\text{-}\text{3}\text{2}$ zero modes break the U(1) chiral symmetry and give rise to helicity-changing amplitudes. Together with the spin-2 zero modes they determine the trace anomaly or scaling behaviour. We can compare our results with the perturbation theory predictions for the axial vector current and trace anomalies in K3, the unique compact self-dual gravitational instanton, because in this case there are no boundary terms. We obtain agreement.     

Symmetry breaking in honeycomb photonic lattices

We study the phenomena associated with symmetry breaking in honeycomb photonic lattices. As the honeycomb structure is gradually deformed, conical diffraction around its diabolic points becomes elliptic and eventually no longer occurs. As the deformation is further increased, a gap opens between the first two bands, and the lattice can support a gap soliton. The existence of the gap soliton serves as a means to detect the symmetry breaking and provide an estimate of the size of the gap.     

Symmetry breaking in boron nitride nanotubes

We have imaged boron nitride nanotubes with atomic scale resolution using scanning tunneling microscopy. While some nanotubes show the expected triangular lattice pattern, the majority of the nanotubes show unusual stripe patterns which break the underlying symmetry of the boron nitride lattice. We identify the origin of the symmetry breaking and demonstrate that conventional STM imaging analysis is inadequate for boron nitride nanotubes.     

Symmetry breaking in quantum chaotic systems

We show, using semiclassical methods, that as a symmetry is broken, the transition between universality classes for the spectral correlations of quantum chaotic systems is governed by the same parametrization as in the theory of random matrices. The theory is quantitatively verified for the kicked rotor quantum map. We also provide an explicit substantiation of the random matrix hypothesis, namely that in the symmetry-adapted basis the symmetry-violating operator is random.     

Symmetry breaking patterns in superfluid He

By means of the time reversal operator a general form of the Landau free energy functional of superfluid ³He is investigated. Various possible phase diagrams of superfluid ³He in a magnetic field are discussed in the context of group theory. Both the cases of neglible and strong spin-orbit coupling are treated.     

混沌吸引子的对称破缺激变

许多非线性动力系统都有某种对称性,在不同情形下可有不同的表现形式,但始终保持其对称的特点.不同对称形式间的转变导致对称破缺分岔或激变.关于非线性动力系统中相空间运动轨道的对称破缺分岔,已有大量研究工作,但绝大多数是指周期或拟周期相轨的对称破缺,偶尔提到对称系统中的混沌相轨也存在“对偶性”.最近,在简谐外激Duffing系统周期轨道对称破缺引发鞍-结分岔的研究中,得到了分岔后由Poincaré映射点间断流构成的图像,其中包括两个稳定周期结点、一个周期鞍点,及其稳定流形与不稳定流形,均较规则.本工作研究了正弦 关键词： 对称破缺 混沌 激变 分形吸引域     

Symmetry breaking in La2-xBaxCuO4

When La in body-centered-tetragonal La₂CuO₄ is substituted by Ba only tetragonal symmetry remains with two formula units per unit cell. Assuming an ordered La₃BaCu₂O₈ structure the effect of substitution on the energy bands is studied by electronic-structure calculations employing the augmented-spherical-wave (ASW) method. It is found that Cu-d O-p interactions not only in the xy plane are important, but also in the z direction when oxygen atoms are involved which are near Ba. The stabilizing electrostatic effect of Ba²⁺ ions is reduced in comparison to La³⁺ ions and cause the oxygen states near Ba²⁺ to be raised in energy. This mechanism effectively reduces the coordination of Cu to essentially fivefold (as found in YBa₂Cu₃O₇. The two inequivalent Cu atoms differ such that the symmetry breaking could support valence fluctuations.