Dynamic symmetry breaking and structure-preserving analysis on thelongitudinal wave in an elastic rod with a variable cross-section

The longitudinal wave propagating in an elastic rod with a variable cross-section owns wide engineering background,in which the longitudinal wave dissipation determines some important performances of the slender structure.To reproduce the longitudinal wave dissipation effects on an elastic rod with a variable cross-section,a structure-preserving approach is developed based on the dynamic symmetry breaking theory.For the dynamic model controlling the longitudinal wave propagating in the elastic rod with the variable cross-section,the approximate multi-symplectic form is deduced based on the multi-symplectic method,and the expression of the local energy dissipation for the longitudinal wave propagating in the rod is presented,referring to the dynamic symmetry breaking theory.A structure-preserving method focusing on the residual of the multi-symplectic structure and the local energy dissipation of the dynamic model is constructed by using the midpoint difference discrete method.The longitudinal wave propagating in an elastic rod fixed at one end is simulated,and the local/total energy dissipations of the longitudinal wave are investigated by the constructed structure-preserving scheme in two typical cases in detail.

Dynamical Symmetry Breaking of Maximally Generalized Yang-Mills Model and Its Restoration at Finite Temperatures

In terms of the Nambu-Jona-Lasinio mechanism, dynamical breaking of gauge symmetry for the maximally generalized Vang-Mills model is investigated. The gauge symmetry behavior at finite temperature is also investigated and it is shown that the gauge symmetry broken dynamically at zero temperature can be restored at finite temperatures.

A Generalized Yang-Mills Model and Dynamical Breaking of Gauge Symmetry

A generalized Yang-Mills model, which contains, besides the vector part Vμ, also a scalar part S, is constructed and the dynamical breaking of gauge symmetry in the model is also discussed. It is shown, in terms of Nambu-Jona-Lasinio (NJL) mechanism, that the gauge symmetry breaking can be realized dynamically in the generalized Yang-Mills model. The combination of the generalized Yang-Mills model and the NJL mechanism provides a way to overcome the difficulties related to the Higgs field and the Higgs mechanism in the usual spontaneous symmetry breaking theory.

Critical Behavior of Dynamical Chiral Symmetry Breaking with Gauge Boson Mass in QED3

Since the massless quantum electrodynamics in 2＋1 dimensions （QEDa） with nonzero gauge boson mass ζ can be used to explain some important traits of high-Tc superconductivity in planar cuprates, it is worthwhile to apply this model to analyze the nature of chiral phase transition at the critical value ζ. Based on the feature of chiral susceptibility, we show that the system at ζ exhibits a second-order phase transition which accords with the nature of appearance of the high-To superconductivity, and the estimated critical exponents around ζ are illustrated.

Dynamical Evolution of an Effective Two-Level System with PT Symmetry

We investigate the dynamics of parity-and time-reversal（PT） symmetric two-energy-level atoms in the presence of two optical and one radio-frequency fields. The strength and relative phase of fields can drive the system from the unbroken to the broken PT symmetric regions. Compared with the Hermitian model, Rabi-type oscillation is still observed, and the oscillation characteristics are also adjusted by the strength and relative phase in the region of the unbroken symmetry. At the exception point, the oscillation breaks down. To better understand the underlying properties we study the effective Bloch dynamics and find that the emergence of the PT components of the fixed points is the feature of the PT symmetry breaking and the projections in the x–y plane can be controlled with high flexibility compared with the standard two-level system with the PT symmetry. It helps to study the dynamic behavior of the complex PT symmetric model.

Dynamic Similarity of Six Bar Ball Tensegrity Structure in Compression and Expansion Processes

Tensegrity structures have identical members in an orientation that have correlated dynamics under external force.To study this interdependent dynamics in different members in compression and expansion processes,it is vital to analyze the dynamics of the whole structure.In this study,six bar tensegrity structure was studied under compression and expansion,and interdependent movement of different members of the structure in both processes was obtained.First,the relationship between external force and members force densities was analytically developed based on the assumption that each bar moves with the same distance when an external force is applied on the six bar tensegrity ball structure along one plane that either compresses or expands the structure.Then,two individual simulations were carried out to analyze the movement of each bar in compression and expansion under the effect of external force,and elongation in all strings was studied in both processes.Finally,comparative dynamic study of different members in compression and expansion of the structure with the effect of external force was performed,which were categorized according to dynamic symmetry.

Stochastic resonance and nonequilibrium dynamic phase transition of Ising spin system driven by a joint external field

The dynamic response and stochastic resonance of a kinetic Ising spin system （ISS） subject to the joint action of an external field of weak sinusoidal modulation and stochastic white-nolse are studied by solving the mean-field equation of motion based on Glauber dynamics. The periodically driven stochastic ISS shows that the characteristic stochastic resonance as well as nonequilibrium dynamic phase transition （NDPT） occurs when the frequency ω and amplitude h0 of driving field, the temperature t of the system and noise intensity D are all specifically in accordance with each other in quantity. There exist in the system two typical dynamic phases, referred to as dynamic disordered paramagnetic and ordered ferromagnetic phases respectively, corresponding to a zero- and a unit-dynamic order parameter. The NDPT boundary surface of the system which separates the dynamic paramagnetic phase from the dynamic ferromagnetic phase in the 3D parameter space of ho-t-D is also investigated. An interesting dynamical ferromagnetic phase with an intermediate order parameter of 0.66 is revealed for the first time in the ISS subject to the perturbation of a joint determinant and stochastic field. The intermediate order dynamical ferromagnetic phase is dynamically metastable in nature and owns a peculiar characteristic in its stability as well as the response to external driving field as compared with a fully order dynamic ferromagnetic phase.

Nonlinear dynamical symmetries of Smorodinsky-Winternitz and and Fokas-Lagerstorm systems

General solutions of the Smorodinsky-Winternitz system and the Fokas-Lagerstorm system, which are superintegrable in two-dimensional Euclidean space, are obtained using the algebraic method （structure function）. Their dynamical symmetries, which are governed by deformed angular momentum algebras, are revealed.

Quark Loop Effects on Dressed Gluon Propagator in Framework of Global Color Symmetry Model

Based on the global color symmetry mode/ （GCM）, a method for obtaining the quark loop effects on the dressed gluon propagator in GCM is developed. In the chiral limit, it is found that the dressed gluon propagator containing the quark loop effects in the Nambu-Goldstone and Wigner phases are quite different. In solving the quark self-energy functions in the two different phases and subsequent study of bag constant one shouM use the above dressed gluon propagator as input. The above approach for obtaining the current quark mass effects on the dressed gluon propagator is quite general and can also be used to calculate the chemical potential dependence of the dressed gluon propagator.

Spectral observation of symmetry-protected selection rules for dynamical high-dimensional parity in alignment magnetic resonance

Multidimensional Floquet-driven alignment systems with dynamical symmetry present various exotic phenomena and applications.However,there are challenges in directly characterizing large-spin dynamical symmetry from spectra.Here,we first observe the symmetry-protected selection rules of dynamical high-dimensional parity in a large-spin(F=4)system.We theoretically construct a Floquet-driven alignment system that can be used to reveal high-dimensional spatiotemporal symmetry.In the experiment,the system is implemented in Cs atomic gas subjected to two-dimensional Floquet-modulated magnetic resonance driving.By developing Floquet detection protocols of alignment double-sided spectra,we directly verify symmetry-protected selection rules of dynamical high-dimensional parity for large-spin systems.This work advances the exploration of dynamical symmetry to large spins,and unravels a universal Floquet scheme for the investigation of symmetry-protected selection rules.

Optimal control of quantum systems with SU(1,1)dynamical symmetry

SU（1,1） dynamical symmetry is of fundamental importance in analyzing unbounded quantum systems in theoretical and applied physics. In this paper, we study the control of generalized coherent states associated with quantum systems with SU（1,1） dynamical symmetry. Based on a pseudo Riemannian metric on the SU（1,1） group, we obtain necessary conditions for minimizing the field fluence of controls that steer the system to the desired final state. Further analyses show that the candidate optimal control solutions can be classified into normal and abnormal extremals. The abnormal extremals can only be constant functions when the control Hamiltonian is non-parabolic, while the normal extremals can be expressed by Weierstrass elliptic functions according to the parabolicity of the control Hamiltonian. As a special case, the optimal control solution that maximally squeezes a generalized coherent state is a sinusoidal field, which is consistent with what is used in the laboratory.

Critical Mass of Gauge Boson in Rainbow QED3

In three-dimensional quantum electrodynamics (QED3) with a massive gauge boson, we investigate the coupled Dyson-Schwinger equations for the fermion and photon propagators in the rainbow approximation, and obtain the critical gauge boson mass for various numbers of the fermion flavors. A comparision with the previous results is presented.

Fermion dynamical symmetry and strongly-correlated electrons:A comprehensive model of high-temperature superconductivity

We review application of the SU(4)model of strongly-correlated electrons to cuprate and iron-based superconductors.A minimal self-consistent generalization of BCS theory to incorporate antiferromag-netism on an equal footing with pairing and strong Coulomb repulsion is found to account system-atically for the major features of high-temperature superconductivity,with microscopic details of the parent compounds entering only parametrically.This provides a systematic procedure to separate es-sential from peripheral,suggesting that many features exhibited by the high-Te data set are of interest in their own right but are not central to the superconducting mechanism.More generally,we propose that the surprisingly broad range of conventional and unconventional superconducting and superfluid behavior observed across many fields of physics results from the systemnatic appearance of similar al-gebraic structures for the emergent ffoctive Harmiltonians,even though the microscopic Harmiltonians of the corresponding parent states may differ radically from each other.

Small Current Quark Mass Effects on Dressed-Quark Propagator in an Effective Quark-Quark Interaction Model

A method for obtaining the small current quark mass dependence of the dressed quark propagator from an effective quark-quark interaction model is developed. Within this approach the small current quark mass effects on dressed-quark propagator have been studied. A comparison with previous results is given.

Scalar Susceptibility of QCD from Dyson-Schwinger Approach

In quantum chromodynamics （QCD）, the scalar susceptibility represents the modification of the quark condensate, to a small perturbation of the parameter responsible for the explicit breaking of the symmetry, i.e., the current quark mass. By studying the linear response of the dressed quark propagator to the presence of a nonzero quark mass, we derive a model-independent formula for the scalar susceptibility, which contains the dressed quark propagator G（p） and the dressed scalar vertex F（p, 0）. The numerical values of the scalar susceptibility Xs are calculated within the framework of the rainbow-ladder approximation of the Dyson-Schwinger approach by employing two typical forms of model gluon propagator.

An SU(3) Electroweak Unified Model Using Generalized Yang-Mills Theory

Generalized Yang-Mills theory has a covariant derivative which contains both vector and scalar gauge bosons. Based on this theory, we construct an SU(3) unified model of electromagnetic and weak interactions to simplify the Weinberg-Salam model. By using the Nambu-Jona-Lasinio mechanism, the symmetry breaking can be realized dynamically. The masses of W±, Z0 are obtained and interactions between various particles are the same as that of the Weinberg-Salam model. At the same time, sin2 θw =1/4 can be given.

Higgs Algebraic Symmetry of Screened System in a Spherical Geometry

The orbits and the dynamical symmetries for the screened Coulomb potentials and isotropic harmonic oscillators have been studied by Wu and Zeng [Z.B. Wund J.Y. Zeng, Phys. Rev. A 62 （2000） 032509]. We find similar properties in the corresponding systems in a sphericM space, whose dynamical symmetries are described by Higgs algebra. There exist extended Runge-Lenz vector for screened Coulomb potentials and extended quadruple tensor for screened harmonic oscillators. They, together with angular momentum, constitute the generators of the geometrical symmetry group. Moreover, there exist an infinite number of dosed orbits for suitable angular momentum values, and we give the equations of the classical orbits. The eigenenergy spectrum and corresponding eigenstates in these systems are derived.

Dynamical CP violation of the generalized Yang-Mills model

Starting from the generalized Yang-Mills model which contains, besides the vector part Vμ, also a scalar part S and a pseudoscalar part P. It is shown, in terms of the Nambu-Jona-Lasinio （NJL） mechanism, that CP violation can be realized dynamically. The combination of the generalized Yang-Mills model and the NJL mechanism provides a new way to explain CP violation.

Dynamical CP violation at finite temperature

By using the generalized Yang-Mills model, CP violation behavior at finite temperature is investigated, and it is shown that dynamical CP violation of the generalized Yang-Mills model at zero temperature can be restored at finite temperature.

Flavor mixing and solution structures in Dyson–Schwinger equations for a two-flavor system

We solved the Dyson–Schwinger(DS)equations for a two-flavor system with symmetry to study its flavor mixing effects.Initially,we employed the point interaction model and bare vertex approximation to reveal the structure of the solutions.Using the point interaction model,the DS equations can be solved analytically,and we found that these solutions can be classified into three groups,each forming an ellipse.These solutions exhibit SO(2)symmetry,while the original SU(2)symmetry at the Lagrangian level is dynamically broken to SO(2),corresponding to the emergence of flavor mixing effects.However,this flavor mixing effect does not manifest in the final physical state.By utilizing the system's SO(2)symmetry,we can diagonalize the propagators of the DS equations,eliminating the flavor mixing effect but causing the originally degenerate masses at the Lagrangian level to split.These mass eigenstates have identical quantum numbers but different masses.If we can correspond these to quark particles of different generations,we can explain why the three generations of quarks have different masses and obtain the corresponding quark mass spectrum.Finally,we provide the corresponding numerical results using a more realistic interaction model.