Anomalous time-reversal symmetric non-Hermitian systems

The conditions for the emergence of the non-Hermitian skin effect, as a unique physical response of non-Hermitian systems, have now become one of the hot research topics. In this paper, we study the novel physical responses of nonHermitian systems with anomalous time-reversal symmetry, in both one dimension and two dimensions. Specifically, we focus on whether the systems will exhibit a non-Hermitian skin effect. We employ the theory of generalized Brillouin zone and also numerical methods to show that the anomalous time-reversal symmetry can prevent the skin effect in onedimensional non-Hermitian systems, but is unable to exert the same effectiveness in two-dimensional cases.

Angle-resolved photoemission study of NbGeSb with non-symmorphic symmetry

We investigate the electronic structure of NbGeSb with non-symmorphic symmetry.We employ angle-resolved photoemission spectroscopy(ARPES)to observe and identify the bulk and surface states over the Brillouin zone.By utilizing high-energy photons,we identify the bulk Fermi surface and bulk nodal line along the direction X–R,while the Fermi surface of the surface state is observed by using low-energy photons.We observe the splitting of surface bands away from the high-symmetry point X.The density functional theory calculations on bulk and 1 to 5-layer slab models,as well as spin textures of NbGeSb,verify that the band splitting could be attributed to the Rashba-like spin–orbit coupling caused by space-inversion-symmetry breaking at the surface.These splitted surface bands cross with each other,forming two-dimensional Weyl-like crossings that are protected by mirror symmetry.Our findings provide insights into the two-dimensional topological and symmetry-protected band inversion of surface states.

The nonequilibrium phase transition and the symmetry revival induced by time delay in an asymmetric bistable system with correlated noises

The nonequilibrium phase transition and the symmetry revival induced by time delay in a bistable system are investigated. The stationary probability distribution function （SPDF） of the bistable system with time delay and correlated noises are calculated by an analytical method and stochastic simulation respectively. The analytical and simulative results indicate that： （1） There is a certain value of λ（λ denotes the strength of correlations between the multiplicative and additive noises） to make the SPDF symmetric under some time delay; however, above or below the given value, the symmetry will be broken; （2） With the monotonic change of λ, the unimodal peak structure of SPDF becomes bimodal at the beginning, then it becomes unimodal again; this means that there is a reentrance phenomenon in the process; （3） There is a critical value of delay time, which makes the lower peak of SPDF equal to the higher one under the critical condition. This means that the symmetry revival phenomenon emerges.

Painlevé property, local and nonlocal symmetries, and symmetry reductions for a (2+1)-dimensional integrable KdV equation

The Painlevé property for a(2+1)-dimensional Korteweg–de Vries(KdV) extension, the combined KP3(Kadomtsev–Petviashvili) and KP4(cKP3-4), is proved by using Kruskal’s simplification. The truncated Painlevé expansion is used to find the Schwartz form, the Bäcklund/Levi transformations, and the residual nonlocal symmetry. The residual symmetry is localized to find its finite Bäcklund transformation. The local point symmetries of the model constitute a centerless Kac–Moody–Virasoro algebra. The local point symmetries are used to find the related group-invariant reductions including a new Lax integrable model with a fourth-order spectral problem. The finite transformation theorem or the Lie point symmetry group is obtained by using a direct method.

THE COMPUTATION OF SYMMETRY－BREAKING BIFURCATION POINTS IN Z_2×Z_2－SYMMETRIC NONLINEAR PROBLEMS

This paper is mainly concerned with corank-2 and corank-3 symmetrybreaking bifurcation point in Z2×Z2-symmetric nonlinear problems. Regular extended systems are used to compute corank-2 and corank-3 symmetry--breaking bifurcation points. Two numerical examples are given. In addition, we show that there exist three quadratic pitchfork bifurcation point curves passing through corank-2 symmetry breaking bifurcation point.

Effect of orbital symmetry on atomic ionization in near-infrared laser fields

We have performed a comparative study of the photoelectron spectra adopting different initial states(2s or 2_(p0))of hydrogen atoms in a near-infrared laser pulse by using the full three-dimensional time-dependent Schr?dinger equation.It is demonstrated that the atomic photoelectron spectra oscillate out of step as a function of electron kinetic energies for different initial states(2s or 2_(p0)),which is well reproduced by the simulations based on strong field approximation,and the above distinct feature is ascribed to the different interferences from the partial electron wave packets detached by positive and negative electric fields for different initial states of 2s and 2_(p0).

Relaxation model for a homogeneous plasmas with spherically symmetric velocity space

We derive the transport equations from the Vlasov–Fokker–Planck equation when the velocity space is spherically symmetric.The Shkarofsky's form of Fokker–Planck–Rosenbluth collision operator is employed in the Vlasov–Fokker–Planck equation.A closed-form relaxation model for homogeneous plasmas could be presented in terms of Gauss hypergeometric2F1functions.This has been accomplished based on the Maxwellian mixture model.Furthermore,we demonstrate that classic models such as two-temperature thermal equilibrium model and thermodynamic equilibrium model are special cases of our relaxation model and the zeroth-order Braginskii heat transfer model can also be derived.The present relaxation model is a nonequilibrium model based on the hypothesis that the plasmas system possesses finitely distinguishable independent features,without relying on the conventional near-equilibrium assumption.

Conserved quantities from Lie symmetries for nonholonomic systems

This paper presents a new method to seek the conserved quantity from a Lie symmetry without using either Lagrangians or Hamiltonians for nonholonomic systems. The differential equations of motion of the systems are established. The definition of the Lie symmetrical transformations of the systems is given, which only depends upon the infinitesimal transformations of groups for the generalized coordinates. The conserved quantity is directly constructed in terms of the Lie symmetry of the systems. The condition under which the Lie symmetry can lead to the conserved quantity and the form of the conserved quantity are obtained. Finally, an example is given to illustrate the application of the result.

On the Lie Symmetries of the NonholonomicMechanical Systems

The Lie symmetries of nonholonomic mechanical systems are corsidered. Some defmi tions and criteria on the Lie symmetries, and the conservation laws of the systems are given.And some examples to illustrate the application of the results are provided.

Polarization properties of elliptical core non-hexagonal symmetry polymer photonic crystal fibre

In this paper, polarization properties and propagation characteristics of polymer photonic crystal fibres with elliptical core and non-hexagonal symmetry structure are investigated by using the full vectorial plane wave method. The results show that the birefringence of the fibre is induced by asymmetries of both the cladding and the core. Moreover, by adjusting the non-symmetrical ratio factor of cladding η from 0.4 to 1 in step 0.1, we find the optimized design parameters of the fibre with high birefringence and limited polarization mode dispersion, operating in a single mode regime at an appropriate wavelength range. The range of wavelength approaches the visible and near-infrared which is consistent with the communication windows of polymer optical fibres.

Noether symmetry and conserved quantity for dynamical system with non-standard Lagrangians on time scales

This paper focuses on studying the Noether symmetry and the conserved quantity with non-standard Lagrangians, namely exponential Lagrangians and power-law Lagrangians on time scales. Firstly, for each case, the Hamilton prin- ciple based on the action with non-standard Lagrangians on time scales is established, with which the corresponding Euler-Lagrange equation is given. Secondly, according to the invariance of the Hamilton action under the infinitesimal transformation, the Noether theorem for the dynamical system with non-standard Lagrangians on time scales is established. The proof of the theorem consists of two steps. First, it is proved under the infinitesimal transformations of a special one-parameter group without transforming time. Second, utilizing the technique of time-re-parameterization, the Noether theorem in a general form is obtained. The Noether-type conserved quantities with non-standard Lagrangians in both clas- sical and discrete cases are given. Finally, an example in Friedmann-Robertson-Walker spacetime and an example about second order Duffing equation are given to illustrate the application of the results.

Classical and nonclassical symmetry classifications of nonlinear wave equation with dissipation

A complete classical symmetry classification and a nonclassical symmetry classification of a class of nonlinear wave equations are given with three arbitrary parameter functions. The obtained results show that such nonlinear wave equations admit richer classical and nonclassical symmetries, leading to the conservation laws and the reduction of the wave equations. Some exact solutions of the considered wave equations for particular cases are derived.

Symmetry of Lagrangians of nonholonomic systems of non-Chetaev's type

This paper studies the symmetry of Lagrangians of nonholonomic systems of non-Chetaev＇s type. First, the definition and the criterion of the symmetry of the system are given. Secondly, it obtains the condition under which there exists a conserved quantity and the form of the conserved quantity. Finally, an example is shown to illustrate the application of the result.

Unified symmetry of nonholonomic mechanical systems with variable mass

Based on the total time derivative along the trajectory of the system the definition and the criterion for a unified symmetry of nonholonomic mechanical system with variable mass are presented in this paper. A new conserved quantity, as well as the Noether conserved quantity and the Hojman conserved quantity, deduced from the unified symmetry, are also obtained, An example is given to illustrate the application of the results.

Mei symmetry and Mei conserved quantity of nonholonomic systems with unilateral Chetaev type in Nielsen style

This paper studies the Mei symmetry and Mei conserved quantity for nonholonomic systems of unilateral Chetaev type in Nielsen style. The differential equations of motion of the system above are established. The definition and the criteria of Mei symmetry, loosely Mei symmetry, strictly Mei symmetry for the system are given in this paper. The existence condition and the expression of Mei conserved quantity are deduced directly by using Mei symmetry. An example is given to illustrate the application of the results.

Noether symmetry and non-Noether conserved quantity of the relativistic holonomic nonconservative systems in general Lie transformations

For a relativistic holonomic nonconservative system, by using the Noether symmetry, a new non-Noether conserved quantity is given under general infinitesimal transformations of groups. On the basis of tile theory of invariance of differential equations of motion under general infinitesimal transformations, we construct the relativistic Noether symmetry, Lie symmetry and the condition under which the Noether symmetry is a Lie symmetry under general infinitesimal transformations. By using the Noether symmetry, a new relativistic non-Noether conserved quantity is given which only depends on the variables t, qs and qs. An example is given to illustrate the application of the results.

Mei symmetries and Mei conserved quantities for higher-order nonholonomic constraint systems

This paper presents the Mei symmetries and new types of non-Noether conserved quantities for a higher-order nonholonomic constraint mechanical system. On the basis of the form invariance of differential equations of motion for dynamical functions under general infinitesimal transformation, the determining equations, the constraint restriction equations and the additional restriction equations of Mei symmetries of the system are constructed. The criterions of Mei symmetries, weak Mei symmetries and strong Mei symmetries of the system are given. New types of conserved quantities, i.e. the Mei symmetrical conserved quantities, the weak Mei symmetrical conserved quantities and the strong Mei symmetrical conserved quantities of a higher-order nonholonomic system, are obtained. Then, a deduction of the first-order nonholonomic system is discussed. Finally, two examples are given to illustrate the application of the method and then the results.

Approximate Generalized Conditional Symmetries for the Perturbed Nonlinear Diffusion-Convection Equations

The concept of approximate generalized conditional symmetry （A GCS） as a generalization to both approximate Lie point symmetry and generalized conditional symmetry is introduced, and it is applied to study the perturbed nonlinear diffusion-convection equations. Complete classification of those perturbed equations which admit cerrain types of AGCSs is derived. Some approximate solutions to the resulting equations can be obtained via the AGCS and the corresponding unperturbed equations.

Symmetries and Mei Conserved Quantities of Nonholonomic Controllable Mechanical Systems

This paper concentrates on studying the symmetries and a new type of conserved quantities called Mei conserved quantity. The criterions of the Mei symmetry, the Noether symmetry and the Lie symmetry are given. The conditions and the forms of the Mei conserved quantities deduced from these three symmetries are obtained. An example is given to illustrate the application of the result.

A series of non-Noether conservative quantities and Mei symmetries of nonconservative systems

In this paper Mei symmetry is introduced for a nonconservative system. The necessary and sufficient condition for a Mei symmetry to be also a Lie symmetry is derived. It is proved that the Mei symmetry leads to a non-Noether conservative quantity via a Lie symmetry, and deduces a Lutzky conservative quantity via a Lie point symmetry.