The anti-FPU problem

We present a detailed analysis of the modulational instability of the zone-boundary mode for one and higher-dimensional Fermi-Pasta-Ulam (FPU) lattices. Following this instability, a process of relaxation to equipartition takes place, which we have called the Anti-FPU problem because the energy is initially fed into the highest frequency part of the spectrum, at variance with the original FPU problem (low frequency excitations of the lattice). This process leads to the formation of chaotic breathers in both one and two dimensions. Finally, the system relaxes to energy equipartition on time scales which increase as the energy density is decreased. We show that breathers formed when cooling the lattice at the edges, starting from a random initial state, bear strong qualitative similarities with chaotic breathers.     

介观尺寸原子链中的等离激元：紧束缚模型

本文运用紧束缚模型对介观尺寸原子链的等离激发进行了系统的研究, 通过量子响 应理论和相无规近似得到了等离激元的本征频率方程, 通过该方程计算了系统中等离子体的激发能量, 并分别对体系的本征振荡以及外电场作用在原子链上发生共振的情况进行了研究. 结果表明, 体系在外场作用下发生共振时, 偶极矩的峰值与等离子体的激发态相对应, 说明外场此时激发了等离激元; 体系处在共振情况下, 电荷振荡的幅度远远大于非共振的情况, 相对来说体系的电荷虚部的共振更为明显. 对于体系的本征等离振荡频率, 同等长度时等离子体的激发能量总是大于同级的单电子激发能量; 等离激元的能谱与原子链的长度和电子密度以及系统的库仑关联强度都有很大关系; 在原子链长度保持不变的情况下, 等离子体的激发能量随电子数目的变化以半满为中心呈对称关系. 关键词： 纳米结构 一维原子链 等离激元     

Minigap plasmons in a two-dimensional electron gas subjected to a one-dimensional periodic potential

We investigate the plasmon excitations in a two-dimensional electron gas subjected to a one-dimensional weak periodic potential. We derive and discuss the dispersion relations for both intrasubband and intersubband excitations within the framework of Bohm-Pines' random-phase approximation. For such an anisotropic system with spatially modulated charge density, we observe a splitting of the 2D plasmon dispersion. The splitting is caused by the superlattice effect of the charge-density modulation on the collective excitation spectrum. We also discuss how the tunneling and the potential amplitude affect the plasmon excitations.     

Different kinds of discrete breathers in a Sine–Gordon lattice

We study a one-dimensional Sine–Gordon lattice of anharmonic oscillators with cubic and quartic nearest-neighbor interactions, in which discrete breathers can be explicitly constructed by an exact separation of their time and space dependence. DBs can stably exist in the one-dimensional Sine–Gordon lattice no matter whether the nonlinear interaction is cubic or quartic. When a parametric driving term is introduced in the factor multiplying the harmonic part of the on-site potential of the system, we can obtain the stable quasiperiodic discrete breathers and chaotic discrete breathers by changing the amplitude of the driver.     

Different kinds of discrete breathers in a Sine-Gordon lattice

We study a one-dimensional Sine-Gordon lattice of anharmonic oscillators with cubic and quartic nearest-neighbor interactions, in which discrete breathers can be explicitly constructed by an exact separation of their time and space dependence. DBs can stably exist in the one-dimensional Sine-Gordon lattice no matter whether the nonlinear interaction is cubic or quartic. When a parametric driving term is introduced in the factor multiplying the harmonic part of the on-site potential of the system, we can obtain the stable quasiperiodic discrete breathers and chaotic discrete breathers by changing the amplitude of the driver.     

Simulation studies of the scattering of a solitary wave by a mass impurity in a chain of nonlinear oscillators

We have simulated large amplitude motion in cyclic one-dimensional lattices of Morse potential oscillators with a mass impurity, and have observed an unexpected persistence of solitary wave behavior for which we are unable to discover a satisfactory explanation. In solitary wave motion as a function of cycle length and of initial energy, the most common feature of the dynamics is an initial energy plateau with regular oscillatory energy exchange between the solitary wave and other excitations of the lattice, followed by rapid decay. Some systems show no decay at all through 1000 impurity interactions, while others show no significant plateau before decaying. For some cycle lengths there are energy bands in which the solitary wave propagates indefinitely long, with small amplitude oscillatory exchange of energy with the lattice. No regularities were found.     

Energy spreading,equipartition, and chaos in lattices with non-central forces

We numerically study a one-dimensional,nonlinear lattice model which in the linear limit is relevant to the study of bending(flexural)waves.In contrast with the classic one-dimensional mass-spring system,the linear dispersion relation of the considered model has different characteristics in the low frequency limit.By introducing disorder in the masses of the lattice particles,we investigate how different nonlinearities in the potential(cubic,quadratic,and their combination)lead to energy delocalization,equipartition,and chaotic dynamics.We excite the lattice using single site initial momentum excitations corresponding to a strongly localized linear mode and increase the initial energy of excitation.Beyond a certain energy threshold,when the cubic nonlinearity is present,the system is found to reach energy equipartition and total delocalization.On the other hand,when only the quartic nonlinearity is activated,the system remains localized and away from equipartition at least for the energies and evolution times considered here.However,for large enough energies for all types of nonlinearities we observe chaos.This chaotic behavior is combined with energy delocalization when cubic nonlinearities are present,while the appearance of only quadratic nonlinearity leads to energy localization.Our results reveal a rich dynamical behavior and show differences with the relevant Fermi–Pasta–Ulam–Tsingou model.Our findings pave the way for the study of models relevant to bending(flexural)waves in the presence of nonlinearity and disorder,anticipating different energy transport behaviors.     

Discrete breathers

Nonlinear classical Hamiltonian lattices exhibit generic solutions in the form of discrete breathers. These solutions are time-periodic and (typically exponentially) localized in space. The lattices exhibit discrete translational symmetry. Discrete breathers are not confined to certain lattice dimensions. Necessary ingredients for their occurrence are the existence of upper bounds on the phonon spectrum (of small fluctuations around the groundstate) of the system as well as the nonlinearity in the differential equations. We will present existence proofs, formulate necessary existence conditions, and discuss structural stability of discrete breathers. The following results will be also discussed: the creation of breathers through tangent bifurcation of band edge plane waves; dynamical stability; details of the spatial decay; numerical methods of obtaining breathers; interaction of breathers with phonons and electrons; movability; influence of the lattice dimension on discrete breather properties; quantum lattices — quantum breathers.Finally we will formulate a new conceptual approach capable of predicting whether discrete breathers exist for a given system or not, without actually solving for the breather. We discuss potential applications in lattice dynamics of solids (especially molecular crystals), selective bond excitations in large molecules, dynamical properties of coupled arrays of Josephson junctions, and localization of electromagnetic waves in photonic crystals with nonlinear response.     

Scale invariant characteristic energy of the one-dimensional electron gas with backward scattering

The characteristic energy scale for a one-dimensional electron gas is obtained through the scaling equations for the invariant couplings in next leading order divergence renormalization. This characteristic energy is proportional to the gap of the spin density excitations spectrum.     

Quantum breathers in a finite Heisenberg spin chain with antisymmetric interactions

A study of the likelihood of quantum breathers in a quantum Heisenberg spin system including a Dzyaloshinsky-Moriya interaction (DMI) is done through an extended Bose-Hubbard model while using the scheme of few body physics. The energy spectrum of the resulting Bose-Hubbard Hamiltonian, on a periodic one-dimensional lattice containing more than two quanta shows interesting detailed band structures. From a non degenerate, and a degenerate perturbation theory in addition to a numerical diagonalization, a careful investigation of these fine structures is set up. The attention is focussed on the effects of various interactions that are; the DMI, the Heisenberg in-plane (X, Y) as well as the out of plane exchange interaction on the energy spectrum of such a system. The outcome displays a possibility of an energy self-compensation in the system. We also computed the weight function of the eigenstates in direct space and in the space of normal modes. From a perturbation theory it is shown that the interaction between the quanta leads to an algebraic localization of the modified extended states in the normal-mode space of the non-interacting system that are coined quantum q-breathers excitations.     

Ultracold atoms in a disordered crystal of light: towards a bose glass

We use a bichromatic optical lattice to experimentally realize a disordered system of ultracold strongly interacting 87Rb bosons. In the absence of disorder, the atoms are pinned by repulsive interactions in the sites of an ideal optical crystal, forming one-dimensional Mott-insulator states. We measure the excitation spectrum of the system as a function of disorder strength and characterize its phase-coherence properties with a time-of-flight technique. Increasing disorder, we observe a broadening of the Mott-insulator resonances and the transition to a state with vanishing long-range phase coherence and a flat density of excitations, which suggest the formation of a Bose-glass phase.     

Discrete breathers in a model with Morse potentials

Under harmonic approximation, this paper discusses the linear dispersion relation of the one-dimensional chain. The existence and evolution of discrete breathers in a general one-dimensional chain are analysed for two particular examples of soft (Morse) and hard (quartic) on-site potentials. The existence of discrete breathers in one-dimensional and two-dimensional Morse lattices is proved by using rotating wave approximation, local anharmonic approximation and a numerical method. The localization and amplitude of discrete breathers in the two-dimensional Morse lattice with on-site harmonic potentials correlate closely to the Morse parameter a and the on-site parameter к.     

Quantum Breathers in Anisotropy Ferromagnetic Chains with Second-Order Coupling

Under considering the next-nearest-neighbor interaction, quantum breathers in one-dimensional anisotropy ferromagnetic chains are theortically studied. By introducing the Dyson-Maleev transformation for spin operators, a map to a Heisenberg ferromagnetic spin lattice into an extended Bose–Hubbard model can be established. In the case of a small number of bosons, by means of the numerical diagonalization technique, the energy spectrum of the corresponding extended Bose–Hubbard model containing two bosons is calculated. When the strength of the single-ion anisotropy is enough large, a isolated single band appears. This isolated single band corresponds to two-boson bound state, which is the simplest quantum breather state. It is shown that the introduction of the next-nearest-neighbor interaction will lead to interesting band structures. In the case of a large number of bosons, by applying the time-dependent Hartree approximation, quantum breather states for the system is constructed. In this case, the effect of the next-nearest-neighbor interaction on quantum breathers is also analyzed.     

Discrete breathers in classical ferromagnetic lattices with easy-plane anisotropy

Discrete breathers (nonlinear localized modes) have been shown to exist in various nonlinear Hamiltonian lattice systems. This paper is devoted to the investigation of a classical d-dimensional ferromagnetic lattice with easy plane anisotropy. Its dynamics is described via the Heisenberg model. Discrete breathers exist in such a model and represent excitations with locally tilted magnetization. They possess energy thresholds and have no analogs in the continuum limit. We are going to review the previous results on such solutions and also to report new results. Among the new results we show the existence of a big variety of these breather solutions, depending on the respective orientation of the tilted spins. Floquet stability analysis has been used to classify the stable solutions depending on their spatial structure, their frequency, and other system parameters, such as exchange interaction and local (single-ion) anisotropy.     

Charge transfer, double and bond-breaking excitations with time-dependent density matrix functional theory

Time-dependent density functional theory (TDDFT) in its current adiabatic implementations exhibits three remarkable failures: (a) completely wrong behavior of the excited state surface along a bond-breaking coordinate; (b) lack of doubly excited configurations; (c) much too low charge transfer excitation energies. These TDDFT failure cases are all strikingly exhibited by prototype two-electron systems such as dissociating H2 and HeH+. We find for these systems with time-dependent density matrix functional theory that: (a) Within previously formulated simple adiabatic approximations, the bonding-to-antibonding excited state surface as well as charge transfer excitations are described without problems, but not the double excitations; (b) An adiabatic approximation is formulated in which also the double excitations are fully accounted for.     

Quantum Solitons and Breathers in an Anisotropic Ferromagnet with Octupole-Dipole Interaction

By using a full quantum approach based on the time-dependent Hartree approximation and the semidiscrete multiple-scale method, we study quantum nonlinear excitations in a one-dimensional ferromagnetic chain with octupole-dipole interaction and on-site uniaxial anisotropy. We find that quantum solitons and breathers can exist in the ferromagnetic chain, and analyze existence conditions of these excitations. Since the system states corresponding to quantum breathers are stationary states, we can get the energy level formula of such quantum breathers.     

Measures of chaos and equipartition in integrable and nonintegrable lattices

We have simulated numerically the behavior of the one-dimensional, periodic FPU-alpha and Toda lattices to optical and acoustic initial excitations of small--but finite and large amplitudes. For the small-through-intermediate amplitudes (small initial energy per particle) we find nearly recurrent solutions, where the acoustic result is due to the appearance of solitons and where the optical result is due to the appearance of localized breather-like packets. For large amplitudes, we find complex-but-regular behavior for the Toda lattice and "stochastic" or chaotic behaviors for the alpha lattice. We have used the well-known diagnostics: Localization parameter; Lyapounov exponent, and slope of a linear fit to linear normal mode energy spectra. Space-time diagrams of local particle energy and a wave-related quantity, a discretized Riemann invariant are also shown. The discretized Riemann invariants of the alpha lattice reveal soliton and near-soliton properties for acoustic excitations. Except for the localization parameter, there is a clear separation in behaviors at long-time between integrable and nonintegrable systems.     

Discrete gap breathers in a two-dimensional diatomic face-centered square lattice

In this paper we study the existence and stability of two-dimensional discrete gap breathers in a two-dimensional diatomic face-centered square lattice consisting of alternating light and heavy atoms, with on-site potential and coupling potential. This study is focused on two-dimensional breathers with their frequency in the gap that separates the acoustic and optical bands of the phonon spectrum. We demonstrate the possibility of the existence of two-dimensional gap breathers by using a numerical method. Six types of two-dimensional gap breathers are obtained, i.e., symmetric, mirror-symmetric and asymmetric, whether the center of the breather is on a light or a heavy atom. The difference between one-dimensional discrete gap breathers and two-dimensional discrete gap breathers is also discussed. We use Aubry's theory to analyze the stability of discrete gap breathers in the two-dimensional diatomic face-centered square lattice.     

Excitation of lattice motion by interaction with large amplitude electron plasma oscillations

Fast heavy-ion bombardment on solids in which a “free-electron”-limit for high excitations exists, generates plasma oscillations with very large amplitudes, as found in no other process. This should uniquely enable the observation of their coupling with other degrees of freedom such as phonons. The frequency spectrum of phonons excited by second-order coupling with plasmons and the respective energy loss to the lattice are calculated, using a simple two-fluid-model and the Lagrangian formalism as appropriate for high coherent excitations.