Mass Generation by Weyl Symmetry Breaking

A massless electroweak theory for leptons is formulated in a Weyl space, W₄, yielding a Weyl invariant dynamics of a scalar field , chiral Dirac fermion fields _L and _R, and the gauge fields , A, Z, W, and W , allowing for conformal rescalings of the metric g and all fields with nonvanishing Weyl weight together with the corresponding transformations of the Weyl vector fields, , representing the D(1) or dilatation gauge fields. The local group structure of this Weyl electroweak (WEW) theory is given by —or its universal coverging group for the fermions—with denoting the electroweak gauge group SU(2)_W × U(1)_Y. In order to investigate the appearance of nonzero masses in the theory the Weyl symmetry is explicitly broken by a term in the Lagrangean constructed with the curvature scalar R of the W₄ and a mass term for the scalar field. Thereby also the Z and W gauge fields as well as the charged fermion field (electron) acquire a mass as in the standard electroweak theory. The symmetry breaking is governed by the relation D ² = 0, where is the modulus of the scalar field and D denotes the Weyl-covariant derivative. This true symmetry reduction, establishing a scale of length in the theory by breaking the D(1) gauge symmetry, is compared to the so-called spontaneous symmetry breaking in the standard electroweak theory, which is, actually, the choice of a particular (nonlinear ) gauge obtained by adopting an origin, , in the coset space representing , with being invariant under the electromagnetic, gauge group U(1)_e.m.. Particular attention is devoted to the appearance of Einstein's equations for the metric after the Weyl symmetry breaking, yielding a pseudo-Riemannian space, V₄, from a W₄ and a scalar field with a constant modulus . The quantity affects Einstein's gravitational constant in a manner comparable to the Brans-Dicke theory. The consequences of the broken WEW theory are worked out and the determination of the parameters of the theory is discussed.     

Biased Motion in a Symmetric Periodic Potential by Breaking Temporal Symmetry

Unidirectional transport of a particle in a spatially periodic and symmetric potential under a periodic force with broken temporal symmetry is studied.With a collaboration of the potential field and the asymmetric ac force,a dc current can be observed.Resonant current steps are found for a finite period of the ac force.A phase diagram of these resonant steps is given.Stochastic-resonance-like directional transport induced by thermal nonises is revealed.     

Chirality and Symmetry Breaking in a Discrete Internal Space

In previous papers the permutation group S ₄ has been suggested as an ordering scheme for quarks and leptons, and the appearance of this finite symmetry group was taken as indication for the existence of a discrete inner symmetry space underlying elementary particle interactions. Here it is pointed out that a more suitable choice than the tetrahedral group S ₄ is the pyritohedral group A ₄×Z ₂ because its vibrational spectrum exhibits exactly the mass multiplet structure of the 3 fermion generations. Furthermore it is noted that the same structure can also be obtained from a primordial symmetry breaking S ₄→A ₄. Since A ₄ is a chiral group, while S ₄ is achiral, an argument can be given why the chirality of the inner pyritohedral symmetry leads to parity violation of the weak interactions.     

Fano Resonance Effect in CO-Adsorbed Zigzag Graphene Nanoribbons

Quantum interference plays an important role in tuning the transport property of nano-devices. Using the non-equilibrium Green's Function method in combination with density functional theory, we investigate the influence to the transport property of a CO molecule adsorbed on one edge of a zigzag graphene nanoribbon device. Our results show that the CO molecule-adsorbed zigzag graphene nanoribbon devices can exhibit the Fano resonance phenomenon. Moreover, the distance between CO molecules and zigzag graphene nanoribbons is closely related to the energy sites of the Fano resonance. Our theoretical analyses indicate that the Fano resonance would be attributed to the interaction between CO molecules and the edge of the zigzag graphene nanoribbon device, which results in the localization of electrons and significantly changes the transmission spectrum.     

等离子体纳米结构中的Fano共振效应及其应用

Fano共振效应是一种具有非对称线型的共振散射现象,起源于共振过程和非共振过程的量子干涉效应。近年来,在等离子体纳米结构中Fano共振现象也被发现,并成为纳米光子学的一个研究热点。等离子体Fano共振通常具有较窄的光谱线宽,且不能直接与入射光耦合,只能局域在近场,强的近场局域特性可以获得巨大的表面电磁场增强。由于等离子体Fano共振独特的光学特性,已经被应用到单分子探测、高灵敏度传感、增强光谱、完美吸收、电磁诱导透明和慢光光子学器件等众多领域当中。     

How a Fano Resonance Crosses the Mobility Edge in Quantum Waveguides

new scenario for the occurrence of a Fano resonance in the transmission probability of electron waveguides is investigated using a coupled-channel theory. Both a quantum dot and an antidot with either short- or finite-range interaction are embedded in the electron waveguide. Particularly, when the Fano resonance occurs close to the mobility edge (channel threshold), it is shown that Γ~U ₁₂ ^4/3 , where Γ is the resonance width and U₁₂ is the coupling strength between bound state and continuum. This is in contrast to the usual result Γ ~U ₁₂ ² , which is valid when the resonance occurs far from the mobility edge. Furthermore, it is shown that increasing the size of both dot and antidot leads to larger resonance width.     

Fano Resonance in Landau Fermi and Luttinger Liquids

With a two-channel model, we study the influence of temperature, external voltage and magnetic flux on the line shape of the Fano resonance, and show that in the Luttinger liquid case, the background transmittance and the asymmetric parameter depend strongly on the temperature and external voltage, while for the Landau Fermi liquid case they are nearly independent of these parameters in the low energy region. Moreover, we demonstrate that the asymmetric parameter changes periodically with an external magnetic flux, which is consistent with the recent experimental data.     

Heat Generation by Electrical Current in Quantum Dot System with Fano Resonance

We study the heat generation in quantum dot system with Fano resonance by nonequilibrium Green's functions method. The Fano resonance influences the heat generation significantly. As ξ increases, the heat generation decreases gradually. From the study of Q-eV curves, we find that the linewidth function Γ has huge influence on the heat generation. The Q-eV curves display obvious steps when the linewidth function Γ is small. However, these steps disappear with Γ increasing. As the source-drain bias eV increases, the Q-eV g curves also display interesting behaviors.     

Heat Generation by Electrical Current in Quantum Dot System with Fano Resonance

We study the heat generation in quantum dot system with Fano resonance by nonequilibrium Green's functions method. The Fano resonance influences the heat generation significantly. As ξ increases, the heat generation decreases gradually. From the study of Q-eV curves, we find that the linewidth function Γ has huge influence on the heat generation. The Q-eV curves display obvious steps when the linewidth function Γ is small. However, these steps disappear with Γ increasing. As the source-drain bias eV increases, the Q-eV_g curves also display interesting behaviors.     

基于半圆形与矩形谐振腔耦合结构的Fano共振

设计了一种基于金属-介质-金属波导的半圆形谐振腔与矩形谐振腔的耦合结构,采用有限元方法研究了该结构的传播特性.结果表明:透射光谱中产生一个类似Fano共振线型的共振谷,该Fano共振由半圆形谐振腔的宽谱共振和矩形谐振腔的窄谱共振相互耦合所导致.变化谐振腔的结构参量,发现该Fano共振谷位置依赖于矩形谐振腔的几何参量,而对两谐振腔相对位置的微小移动不敏感;同时,改变两谐振腔的并联方式,研究了两种衍生结构的传播特性,发现这些结构均可产生明显的Fano共振.此外,通过在谐振腔中填充不同折射率的介质材料,研究了三种结构基于Fano共振效应的折射率传感特性,其折射率敏感度最高达到750 nm/RIU.研究结果可为未来芯片上基于表面等离极化激元波导的高灵敏折射率传感器的设计提供理论依据.     

Modeling of Fano Resonance in High-Contrast Resonant Grating Structures

A new model is presented for Fano resonance in resonant grating structure based on the temporal coupled mode theory. By using this model, the reflection spectrum can be reproduced with the information of eigenmode of the structure, which can be numerically calculated by the finite element method. Therefore, the eigenmode plays a key role in determining the profile of the line shape of the Fano resonance in the resonant grating structure. When the space of two grating modulations is decreased, the line shape experiences a significant change. Such a drastic change can be attributed to the increase of quality factor of the eigenmodes. Thus, our model not only provides a simple and intuitive understanding on the mechanism of Fano resonance, but it also offers a convenient way to engineer the line shape of the Fano resonance. The proposed model can be used in many applications, such as biosensors, optical filters, and optical switchers.     

Spontaneous Symmetry Breaking of a Hyperbolic Sigma Model in Three Dimensions

Non-linear sigma models that arise from the supersymmetric approach to disordered electron systems contain a non-compact bosonic sector. We study the model with target space H², the two-hyperboloid with isometry group SU(1,1), and prove that in three dimensions moments of the fields are finite in the thermodynamic limit. Thus the non-compact symmetry SU(1,1) is spontaneously broken. The bound on moments is compatible with the presence of extended states.Dedicated to Freeman Dyson on the Occasion of his eightieth birthdayAcknowledgement T. Spencer would like to thank M. Disertori, K. Gawedzki, G. Papanicolau and S.R.S. Varadhan for helpful comments.     

Collective Directional Transport in Symmetric Periodic Potentials by Breaking the Coupling Symmetry

Collective unidirectional motion of an asymmetrically coupled array of oscillators in symmetric periodic potentials is studied. A directed current is observed when the drift coupling is presented, while no external biased force is applied. Negative directed current is found when varying system parameters. An addition of a periodic rocking force may enhance the efficiency of directed transport. Resonant steps of the current are found and interpreted as the mode locking between the array and the ac force. Noise-assisted transport is observed, and an optimal noise intensity can give rise to a most efficient transport. The directed transport thus can be optimized and furthermore controlled by suitably adjusting the parameters of the system.     

Acceleration of the Universe in Matter Dominant Era by Conformal Symmetry Breaking

We introduce a scenario in which the breakdown of conformal symmetry is responsible for the acceleration of universe in the matter dominant era. In this regard, we consider a self interacting scalar field non-minimally coupled to the Ricci scalar and the trace of energy-momentum tensor. For a traceless energy-momentum tensor in radiation dominant era, the coupling to matter vanishes and we are left with a conformal invariant gravitational action of Deser, where the universe may experience a decelerating phase in agreement with observations. In matter dominant era, the coupling to matter no longer vanishes, the conformal symmetry is broken down, and the matter inevitably becomes pressureless. The corresponding field equations are obtained and it is shown that the universe may have an accelerating phase in this era, provided that the value of self interaction coupling constant satisfies an specific lower bound. Moreover, we provide a reasonable solution to the coincidence problem.     

Rigorous Results on Spontaneous Symmetry Breaking in a One-Dimensional Driven Particle System

We study spontaneous symmetry breaking in a one-dimensional driven two-species stochastic cellular automaton with parallel sublattice update and open boundaries. The dynamics are symmetric with respect to interchange of particles. Starting from an empty initial lattice, the system enters a symmetry broken state after some time T ₁ through an amplification loop of initial fluctuations. It remains in the symmetry broken state for a time T ₂ through a traffic jam effect. Applying a simple martingale argument, we obtain rigorous asymptotic estimates for the expected times 〈 T ₁〉 ∝ Lln L and ln 〈 T ₂〉 ∝ L, where L is the system size. The actual value of T ₁ depends strongly on the initial fluctuation in the amplification loop. Numerical simulations suggest that T ₂ is exponentially distributed with a mean that grows exponentially in system size. For the phase transition line we argue and confirm by simulations that the flipping time between sign changes of the difference of particle numbers approaches an algebraic distribution as the system size tends to infinity.     

Chiral Symmetry Breaking as a Phase Transition in QED Plus NJL Model

The chiral symmetry breaking (CSB) of massless &ED is studied analytically and then numerically by introducing a Nambu-Jona-Lasinio (NJL) term. We use the method of relativistic canonical transformation and random phase approximation to find the criterion for CSB (i.e., the condensation in vacuum) and the accompanying elementary excitations. The role played by NJL term, the scale anomaly and the meaning of critical point (α_c≈1.5) are discussed.     

Symmetry and Resonance in Periodic FPU Chains

The symmetry and resonance properties of the Fermi Pasta Ulam chain with periodic boundary conditions are exploited to construct a near-identity transformation bringing this Hamiltonian system into a particularly simple form. This “Birkhoff–Gustavson normal form” retains the symmetries of the original system and we show that in most cases this allows us to view the periodic FPU Hamiltonian as a perturbation of a nondegenerate Liouville integrable Hamiltonian. According to the KAM theorem this proves the existence of many invariant tori on which motion is quasiperiodic. Experiments confirm this qualitative behaviour. We note that one can not expect this in lower-order resonant Hamiltonian systems. So the periodic FPU chain is an exception and its special features are caused by a combination of special resonances and symmetries. Received: 25 July 2000 / Accepted: 20 December 2000