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.

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.

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.

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.

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.

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.

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.

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.

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.

New γ-soft rotation in the interacting boson model with SU(3) higher-order interactions

The interacting boson model with S U(3) higher-order interactions offers a new route to enhance our understanding onγ-soft rotation.In this paper, U(5) -like and O(6) -like newγ-softness are observed,in which the corresponding energy levels in the ground and quasi-γbands can be exactly degenerate and have a partial O(5) dynamical symmetry.The spherical-likeγ-softness is not related to the classical O(6) dynamical symmetry.The transitional behaviors of B(E2) values of the low-lying levels and quadrupole moment of the 2^(+)_(1) state are also discussed.Spherical-likeγ-softness can be used to explain the low-lying spectra and B(E2) values in ^(110)Cd normal states.

Coupling Vibration of Simply-Supported Damping Beam Carrying a Moving Mass

The coupling dynamic problems,such as the vehicle-bridge interaction problem,are difficult to be analyzed.In this paper,the generalized multi-symplectic approach is employed to investigate the coupling dynamic behaviors in the vehicle-bridge interaction system.A simply-supported damping beam model carrying a moving mass is considered and the generalized multi-symplectic form with the dynamical symmetry breaking factors is deduced firstly.And then,Preissmann’s scheme is employed to discretize the generalized multi-symplectic form,and the discrete structure-preserving condition for the numerical scheme is presented.According to the discrete structure-preserving condition,the permitted moving speed of the mass with different damping factors and different time step lengths is obtained to ensure the structure-preserving properties of the numerical scheme.Finally,the effects of the damping factor of the beam and the moving speed of the mass on the vibration of the beam are investigated by Preissmann’s scheme.The main contribution of this work is to provide a structure-preserving analysis approach for the vehicle-bridge interaction problem.

Exploring the light-quark interaction

Two basic motivations for an upgraded JLab facility are the needs： to determine the essential nature of light-quark confinement and dynamical chiral symmetry breaking （DCSB）; and to understand nucleon structure and spectroscopy in terms of QCD＇s elementary degrees of freedom. During the next ten years a programme of experiment and theory will be conducted that can address these questions. We present a Dyson- Schwinger equation perspective on this effort with numerous illustrations, amongst them： an interpretation of string^breaking; a symmetry-preserving truncation for mesons; the nucleon＇s strangeness σ-term; and the neutron＇s charge distribution.

Temperature dependence of quarks and gluon vacuum condensate in the Dyson-Schwinger Equations at finite temperature

Based on the Dyson-Schwinger Equations （DSEs）, the two-quark vacuum condensate, the four-quark vacuum condensate, and the quark gluon mixed vacuum condensate in the non-perturbative QCD vacuum state are investigated by solving the DSEs with rainbow truncation at zero- and finite- temperature, respectively. These condensates are important input parameters in QCD sum rule with zero and finite temperature, and in studying hadron physics, as well as predicting the quark mean squared momentum rn02- also called quark virtuality in the QCD vacuum state. The present calculated results show that these physical quantities are almost independent of the temperature below the critical point temperature Tc=131 MeV, and above Tc the chiral symmetry is restored. For comparison we calculate the temperature dependence of the ＂in-hadron condensate＂ for pion. At the same time, we also calculate the ratio of the quark gluon mixed vacuum condensate to the two-quark vacuum condensate by using these condensates, and the unknown quark mean squared momentum in the QCD vacuum state has been obtained. The results show that the ratio m2/0（T） is almost fiat in the temperature region from 0 to To, although there are drastic changes of the quark vacuum condensate and the quark gluon mixed vacuum condensate at the region. Our predicted ratio comes out to be m2/0（T）=2.41 GeV2 at the Chiral limit, which is consistent with other theory model predictions, and strongly indicates the significance that the quark gluon mixed vacuum condensate has played in the virtuality calculations.