QUASIPERIODICITY OF TRANSCENDENTAL MEROMORPHIC FUNCTIONS

This paper is devoted to considering the quasiperiodicity of complex differential polynomials,complex difference polynomials and complex delay-differential polynomials of certain types,and to studying the similarities and differences of quasiperiodicity compared to the corresponding properties of periodicity.

Mobility edges and localization characteristics in one-dimensional quasiperiodic quantum walk

We construct a one-dimensional quasiperiodic quantum walk to investigate the localization–delocalization transition.The inverse participation ratio and Lyapunov exponent are employed as two indexes to determine the mobility edge, a critical energy to distinguish the energy regions of extended and localized states. The analytical solution of mobility edge is obtained by the Lyapunov exponents in global theory, and the consistency of the two indexes is confirmed. We further study the dynamic characteristics of the quantum walk and show that the probabilities are localized to some specific lattice sites with time evolution. This phenomenon is explained by the effective potential of the Hamiltonian which corresponds to the phase in the coin operator of the quantum walk.

The Problem of Quasiperiodic Photonic Structures Solved by Considering the Cut of 2D Periodic Structure

The physical objective of solving for eigen-modes of a 1D quasiperiodic structure in photonics has been achieved. This was achieved thru considering this structure as a 1D projection or cut of a 2D periodic structure. And the problem is solved in a manner similar to 2D periodic photonic structures. A mechanical analogy (quasiperiodic orbits) helps to bring conceptual clarity.

Invariable mobility edge in a quasiperiodic lattice

We analytically and numerically study a 1 D tight-binding model with tunable incommensurate potentials.We utilize the self-dual relation to obtain the critical energy,namely,the mobility edge.Interestingly,we analytically demonstrate that this critical energy is a constant independent of strength of potentials.Then we numerically verify the analytical results by analyzing the spatial distributions of wave functions,the inverse participation rate and the multifractal theory.All numerical results are in excellent agreement with the analytical results.Finally,we give a brief discussion on the possible experimental observation of the invariable mobility edge in the system of ultracold atoms in optical lattices.

Quantum diffusion in semi-infinite periodic and quasiperiodic systems

This paper studies quantum diffusion in semi-infinite one-dimensional periodic lattice and quasiperiodic Fibonacci lattice. It finds that the quantum diffusion in the semi-infinite periodic lattice shows the same properties as that for the infinite periodic lattice. Different behaviour is found for the semi-infinite Fibonacci lattice. In this case, there are still C（t） - t^-δ and d（t） - t^β. However, it finds that 0 〈δ 〈 1 for smaller time, and δ = 0 for larger time due to the influence of surface localized states. Moreover, β for the semi-infinite Fibonacci lattice is much smaller than that for the infinite Fibonacci lattice. Effects of disorder on the quantum diffusion are also discussed.

Periodic, quasiperiodic, and chaotic breathers in two-dimensional discrete β-Fermi-Pasta-Ulam lattice

Using numerical method, we investigate whether periodic, quasiperiodic, and chaotic breathers are supported by the two-dimensional discrete Fermi-Pasta-Ulam （FPU） lattice with linear dispersion term. The spatial profile and time evolution of the two-dimensional discrete fl-FPU lattice are segregated by the method of separation of variables, and the numerical simulations suggest that the discrete breathers （DBs） are supported by the system. By introducing a periodic interaction into the linear interaction between the atoms, we achieve the coupling of two incommensurate frequencies for a single DB, and the numerical simulations suggest that the quasiperiodic and chaotic breathers are supported by the system, too.

Monte Carlo Simulation of the Potts Model on a Dodecagonal Quasiperiodic Structure

By means of a Monte Carlo simulation,we study the three-state Potts model on a two-dimensional quasiperiodic structure based on a dodecagonal cluster covering pattern.The critical temperature and exponents are obtained from finite-size scaling analysis.It is shown that the Potts model on the quasiperiodic lattice belongs to the same universal class as those on periodic ones.

Mobility edges and reentrant localization in one-dimensional dimerized non-Hermitian quasiperiodic lattice

The mobility edges and reentrant localization transitions are studied in one-dimensional dimerized lattice with non-Hermitian either uniform or staggered quasiperiodic potentials.We find that the non-Hermitian uniform quasiperiodic disorder can induce an intermediate phase where the extended states coexist with the localized ones,which implies that the system has mobility edges.The localization transition is accompanied by the PT symmetry breaking transition.While if the non-Hermitian quasiperiodic disorder is staggered,we demonstrate the existence of multiple intermediate phases and multiple reentrant localization transitions based on the finite size scaling analysis.Interestingly,some already localized states will become extended states and can also be localized again for certain non-Hermitian parameters.The reentrant localization transitions are associated with the intermediate phases hosting mobility edges.Besides,we also find that the non-Hermiticity can break the reentrant localization transition where only one intermediate phase survives.More detailed information about the mobility edges and reentrant localization transitions are presented by analyzing the eigenenergy spectrum,inverse participation ratio,and normalized participation ratio.

Quantum phase transition and von Neumann entropy of quasiperiodic Hubbard chains

The half-filled Hubbard chains with the Fibonacci and Harper modulating site potentials are studied in a selfconsistent mean-field approximation. A new order parameter is introduced to describe a charge density order. We also calculate the von Neumann entropy of the ground state. The results show that the von Neumann entropy can identify a CDW/SDW （charge density wave/spin density wave） transition for quasiperiodic models.

Design and Optimization of Omnidirectional Band Gap for One-Dimensional Periodic and Quasiperiodic Phononic Heterostructures

A new kind of one-dimensional multilayer phononie heterostructure is constructed to obtain a broad acoustic omnidirectional reflection （ODR） band. The heterostructure is formed by combining finite periodic phononic crystals （PnCs） and Fibonacci （or Thue-Morse） quasiperiodic PnCs. From the numerical results performed by the transfer matrix method, it is found that the ODR bands can be enlarged obviously by using the combination of periodic and quasi-periodic PnCs. Moreover, an application of particle swarm optimization in designing and optimizing acoustic ODR bands is reported. With regards to different thickness ratios and periodic numbers in the heterostructure, we give some optimization examples and finally achieve phononic heterostructure with a very broad ODR bandwidth. The result provides a new approach to achieve broad acoustic ODR bandwidth, and will be applied in design of omnidirectional acoustic mirrors.

KAM-type Theorem for Nearly Integrable Hamiltonian with a Quasiperiodic Perturbation

In this paper we consider the persistence of invariant tori of an integrable Hamiltonian system with a quasiperiodic perturbation. It is proved that if the unperturbed system satisfies the Rtissmann non-degenerate condition and the perturbed system satisfies the co-linked non-resonant condition, then the majority of invariant tori is persistent under the perturbation.

Subdiffusion of Dipolar Gas in One-Dimensional Quasiperiodic Potentials

Considering the discrete nonlinear Schrodinger model with dipole-dipole interactions （DDIs）, we comparatively and numerically study the effects of contact interaction, DDI and disorder on the properties of diffusion of dipolar condensate in one-dimensional quasi-periodic potentials. Due to the coupled effects of the contact interaction and the DDI, some new and interesting mechanisms are found： both the DDI and the contact interaction can destroy localization and lead to a subdiffusive growth of the second moment of the wave packet. However, compared with the contact interaction, the effect of DDI on the subdiffusion is stronger. Furthermore and interestingly, we find that when the contact interaction （λ1） and DDI （A2） satisfy λ1 ≥ 2λ2, the property of the subdiffusion depends only on contact interaction; when λ1 ≤ 2λ2, the property of the subdiffusion is completely determined by DDI. Remarkably, we numerically give the critical value of disorder strength v＊ for different values of contact interaction and DDI. When the disorder strength v ≥ v＊, the wave packet is localized. On the contrary, when the disorder strength v ≤ v＊, the wave packet is subdiffusive.

Real eigenvalues determined by recursion of eigenstates

Quantum physics is primarily concerned with real eigenvalues,stemming from the unitarity of time evolutions.With the introduction of PT symmetry,a widely accepted consensus is that,even if the Hamiltonian of the system is not Hermitian,the eigenvalues can still be purely real under specific symmetry.Hence,great enthusiasm has been devoted to exploring the eigenvalue problem of non-Hermitian systems.In this work,from a distinct perspective,we demonstrate that real eigenvalues can also emerge under the appropriate recursive condition of eigenstates.Consequently,our findings provide another path to extract the real energy spectrum of non-Hermitian systems,which guarantees the conservation of probability and stimulates future experimental observations.

Quasiperiodic Motions for Asymmetric Oscillators

We prove the existence of quasiperiodic solutions and Lagrange stability for a class of differential equations with jumping nonlinearity x+ax^+-bx^-+φ(x)=p(t), where a, b】0, p(t)∈ C(R/2πZ) and φ: R→R is an unbounded function.

Quasiperiodic Solutions for Nonlinear Differential Equations of Second Order with Symmetry

In this paper,we study the existence of quasi-periodic solutions and the bound- edness of solutions for a wide class nonlinear differential equations of second order.Using the KAM theorem of reversible systems and the theory of transformations,we obtain the existence of quasi-periodic solutions and the boundedness of solutions under some reasonable conditions.

Spatiotemporal quasiperiodicity transition to chaos in the one-way coupled bistability lattice system

One-way coupled optical bnstability lattice (OCBL) system for open flow is investigated. By using numerical simulations spatiotemporal quasiperiodicity is found. A rough phase diagram indicating the main spatiotemporal dynamic behavior in weakly coupled lattice is given. The transitions between spatiotemporal quasiperiodicity and chaos are observed. This result is important for the understanding of turbulence.

ON THE REDUCIBILITY OF LINEAR DIFFERENTIAL EQUATIONS WITH QUASIPERIODIC COEFFICIENTS WHICH IS FINITELY DIFFERENTIABLE

We show that, for most values of the frequencies, the system x = (A + εQ(t))x is reducible, where A is a constant matrix whose eigenvalues are not necessarily simple and Q is a quasiperiodic finitely differentiable matrix.

Absence of eigenvalues for quasiperiodic Schrodinger type operators

We obtain the matrix-valued Schrodinger-type operators [Hα,θ] with Lipschitz potentials having no eigenvalues on the set {E : L ( E )<δ)C,d(α,θ),where δ is an explicit function depending on the sampling function C(θ), dimension d, phase θ, and frequency a, and L ( E ) is the Lyapunov exponent.

Wave-vector-dependent Tunneling Transmission Characteristics in Periodic and Quasiperiodic Semiconductor Superlattices

Wave vector dependent tunneling transmission in periodic and quasiperiodic semiconductor superlattices is investigated while the coupling between longitudinal and transverse momentums is taken into account. It is shown that: (1) there exists a transition from tunneling through effective multiple barriers to transport above effective multiple wells with increasing transverse wave number k xy ;(2) the transmission spectrum for periodic superlattices exhibits resonant domains separated by nonresonant gaps, and the resonance splitting is regular;(3) the transmission spectrum for quasiperiodic superlattices exhibits complicated oscillations and selective suppressions, both singlet and doublet resonances exist in the considered quasiperiodic systems, and there exist more doublet resonances in high order generations of the Thue Morse sequence; (4) complete resonant tunneling can occur in the quasiperiodic superlattice.

Effective Reducibility of a Class of Linear Differential Equations with Quasiperiodic Coefficients

In this paper we consider the effective reducibility of the following linear differential equation: , where A is a constant matrix, Q(t,?) is quasiperiodic in t, and ? is a small perturbation parameter. We prove that if the eigenvalues of A and the basic frequencies of Q satisfy some non-resonant conditions, the linear differential equation can be reduced to , where R* is exponentially small in ?.