Asymptotic dynamics of the dual billiard transformation

Given a strictly convex plane curve, the dual billiard transformation is the transformation of its exterior defined as follows: given a pointx outside the curve, draw a support line to it from the point and reflectx at the support point. We show that the dual billiard transformation far from the curve is well approximated by the time 1 transformation of a Hamiltonian flow associated with the curve.     

Instanton interactions in dense-matter QCD

A Coulomb gas representation of dense-matter QCD is derived from a dual transformation of the low-energy effective Lagrangian. The point-like charges Q=±1 of the gas are identified with the instantons and anti-instantons of such topological charges. An instanton repels another instanton with the same force as it attracts an anti-instanton, in contrast to the semiclassical interaction.     

AdS5○×S5背景下IIB超弦的Dressing对称性及Affine可积性

在AdS5S5背景中,IIB超弦的运动方程与Maurer-Cartan方程在世界面上存在对偶对称性.通过引入扭曲对偶(twisteddual)的概念，将有限的对偶变换推广到连续的对偶变换，并给出了AdＳ5S5中IIB超弦的Lax联络及其可积的相容条件. 关键词： 扭曲对偶 κ对称性 Lax联络     

Irradiation effect of yttria-stabilized zirconia by high dose dual ion beam irradiation

Yttria-stabilized zirconia （YSZ） is irradiated with 2.0-MeV Au2＋ ions and 30-keV He＋ ions. Three types of He, Au, Au ＋ He （successively） ion irradiation are performed. The maximum damage level of a sequential dual ion beam implanted sample is smaller than single Au ion implanted sample. A comparable volume swelling is found in a sequential dual ion beam irradiated sample and it is also found in a single Au ion implanted sample. Both effects can be explained by the partial reorganization of the dislocation network into weakly damaged regions in the dual ion beam implanted YSZ. A vacancy-assisted helium trapping/diffusion mechanism in the dual ion beam irradiated condition is discussed. No phase transformation or amorphization behavior happens in all types of ion irradiated YSZ.     

Characterizing symmetry breaking patterns in a lattice by dual degrees of freedom

A duality transformation in quantum field theory is usually established first through partition functions. It is always important to explore the dual relations between various correlation functions in the transformation. Here, we explore such a dual relation to study quantum phases and phase transitions in an extended boson Hubbard model at 1/3 (2/3) filling on a triangular lattice. We develop systematically a simple and effective way to use the vortex degrees of freedom on dual lattices to characterize both the density wave and valence bond symmetry breaking patterns of the boson insulating states in the direct lattices. In addition to a checkerboard charge density wave (X-CDW) and a stripe CDW, we find a novel CDW-VBS phase which has both local CDW and local valence bond solid (VBS) orders. Implications for Quantum Monte Carlo simulations are addressed. The possible experimental realizations of cold atoms loaded on optical lattices are discussed.     

Nonuniversal quantities from dual renormalization group transformations

Using a simplified version of the renormalization group (RG) transformation of Dyson's hierarchical model, we show that one can calculate all the nonuniversal quantities entering into the scaling laws by combining an expansion about the high-temperature fixed point with a dual expansion about the critical point. The magnetic susceptibility is expressed in terms of two dual quantities transforming covariantly under an RG transformation and has a smooth behavior in the high-temperature limit. Using the analogy with Hamiltonian mechanics, the simplified example discussed here is similar to the anharmonic oscillator, while more realistic examples can be thought of as coupled oscillators, allowing resonance phenomena.     

On the Dual Symrnetry in Two-dimensional Field Theory

Discrete and continuous dual symmetry is analysed and explained in its geometrical origin. Linear eigenvalue equations of the dual transforming operators U are deduced in different forms in a suitable gauge, under the gauge transformation. Different dual parameters are compared too.     

Duality and Self-Duality (Energy Reflection Symmetry) of Quasi-Exactly Solvable Periodic Potentials

A class of spectral problems with a hidden Lie-algebraic structure is considered. We define a duality transformation which maps the spectrum of one quasi-exactly solvable (QES) periodic potential to that of another QES periodic potential. The self-dual point of this transformation corresponds to the energy-reflection symmetry found previously for certain QES systems. The duality transformation interchanges bands at the bottom (top) of the spectrum of one potential with gaps at the top (bottom) of the spectrum of the other, dual, potential. Thus, the duality transformation provides an exact mapping between the weak coupling (perturbative) and semiclassical (nonperturbative) sectors.     

Nahm's transformation for instantons

We describe in mathematical detail the Nahm transformation which maps anti-self dual connections on the four-torus (S ¹)⁴ onto anti-self-dual connections on the dual torus. This transformation induces a map between the relevant instanton moduli spaces and we show that this map is a (hyperKähler) isometry.     

Magnetic fluid behavior in uniform DC,AC, and rotating magnetic fields

New flows and instabilities are demonstrated for magnetic fluids and by dual analogy to dielectric fluids. If a fluid drop is contained in a thin gap between two glass plates (Hele–Shaw cell) with a simultaneously applied in-plane rotating field and a DC axial field, smooth spirals or an abrupt transformation to many small droplets can occur. A preliminary minimum magnetization and surface energy analysis is presented to model the abrupt transformation in ferrofluids. An analysis of effective DC magnetoviscosity is also presented for planar Couette flow with an applied uniform DC field transverse to a duct axis with the effective magnetoviscosity and flow spin velocity calculated as a function of field strength. Related Couette viscometer measurements of ferrofluid viscosity show zero and negative magnetoviscosity values for rotating magnetic fields.     

Geometry and duality in supersymmetric σ-models

The Supersymmetric Dual Sigma Model (SDSM) is a local field theory introduced to be nonlocally equivalent to the Supersymmetric Chiral nonlinear σ-Model (SCM), this dual equivalence being proven by explicit canonical transformation in tangent space. This model is here reconstructed in superspace and identified as a chiral-entwined supersymmetrization of the Dual Sigma Model (DSM). This analysis sheds light on the boson fermion symphysis of the dual transition, and on the new geometry of the DSM.     

Homology in Abelian Lattice Models

We study Abelian lattice gauge theory defined on a simplicial complex with arbitrary topology. The use of dual objects allows one to reformulate the theory in terms of different dynamical variables; however, we avoid entirely the use of the dual cell complex. Topological modes which are present in the transformation now appear as homology classes, in contrast to the cohomology modes found in the dual cell picture. Irregularities of dual cell complexes do not arise in this approach. We treat the two and three-dimensional cases in detail, and prove a general vanishing theorem for Wilson line correlators.     

The Duality Transformation for an n-Species Ising Model Interacting with Z2 Gauge Fields on a Random Surface

The duality transformation is carried out for an n-species Ising spin system interacting with Z₂ gauge fields. For n > 1, we find that the dual model has topological terms when the surface is topologically nontrivial. The plaquette interaction of the gauge fields is dual to an n-spin coupling in the dual model.     

离散余弦变换域抗二次打印-扫描鲁棒零水印算法

由于现有的抵抗打印-扫描攻击的鲁棒数字水印算法缺乏抵抗二次打印-扫描的能力.本文利用子块的离散余弦变换域直流系数与所有子块直流系数的均值之间的大小关系稳定性,提出一种抗二次打印-扫描鲁棒零水印算法.通过对图像进行分块离散余弦变换,计算所有子块直流系数的均值;通过比较各个子块的直流系数与所有子块直流系数的均值之间的大小关...     

Double Bäcklund transformations and fission solutions of axisymmetric gravitational equations

The results of Kyriakopoulos are extended to a double-complex form, and a double Bäcklund transformation of the Ernst equation is derived concretely. By using the noncommutative relation between this double Bäcklund transformation and the dual mapping, a fission-type generation process of new solutions is discussed.     

Kitaev模型与拓扑量子相变

文章通过在一种准一维路径上引入自旋算符的约当-维格纳（Jordan—Wigner）变换，证明了Kitaev自旋模型完全等价于一个不含任何非物理自由度的自由Majorana费米子模型。通过对偶变换，进一步证明了这个系统中存在的量子相变可用非定域的拓扑序参量来描述；并且，这些非定域的拓扑序参量在对偶空间变成为定域的朗道类型的序参量。文章作者的工作揭示了传统的量子相变和拓扑量子相变的内在关系，扩展了朗道二级相变理论的适用范围。     

Four-dimensional singular oscillator and generalized MIC-Kepler system

It is shown that the generalized MIC-Kepler system and four-dimensional singular oscillator are dual to each other and the duality transformation is the generalized version of the Kustaanheimo-Stiefel transformation. The text was submitted by the authors in English.     

A non-lorentzian form of the principle of relativistic invariance

A linear quasistochastic representation of the hyperbolic tangent semigroup is described which acts in dual space-time and which is a semigroup of relativistic endomorphisms. Some of its properties are described, and its relationship with the Lorentz group is discussed. This transformation semigroup permits a novel approach to space-time concepts and a discussion of the representations of the quasistochastic semigroup of relativistic endomorphisms and the associated invariants.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, Vol. 12, No. 4, pp. 121–127, April, 1969.The authors thank D. D. Ivanenko for discussion and useful advice.     

Enhanced optoelectronic properties of UV-light-induced photodegraded TPD

We report UV-light-induced photodegradation of N,N’-diphenyl-N,N’-bis(3-methylphenyl)-1,1’-biphenyl-4,4’ diamine (TPD) dye. When a halomethane solution of TPD is exposed to UV light it first oxidizes TPD and subsequently with further exposure leads to irreversible transformation of TPD to an acridine derivative as photoproduct. Exclusive use of halomethane solvents like chloroform and dichloromethane suggests solvent radical initiated photochemical transformation of TPD to a stable acridine-based photoproduct. The resultant photoproduct of TPD showed broad-band dual (both blue and green) emissions in various solvents and also from the sublimed thin film. Based on solvent- and concentration-dependent photoluminescence (PL) of the photoproduct, PL excitation and lifetimes of blue and green bands, the origin of emission in the green region is due to an intermolecular excimer/aggregate of acridine-based photoproduct. A film of acridine-based photoproduct dispersed in polystyrene also showed substantial improvement in electrical conductivity compared to the parent compound TPD. The technique of UV-light-induced molecule structure transformation and material processing under specific environmental conditions may be considered as an efficient means of obtaining materials with enhanced optoelectronic properties. PACS 61.82.Pv; 72.80.Le; 82.50.-m; 82.30.Lp; 33.50.-j