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In this paper, we study the spectral properties of polarobreathers, that is, breathers carrying charge in a one-dimensional semiclassical model. We adapt recently developed numerical methods that preserve the charge probability at every step of time integration without using the Born–Oppenheimer approximation, which is the assumption that the electron is not at equilibrium with the atoms or ions. We develop an algorithm to obtain exact polarobreather solutions. The properties of polarobreathers, both stationary and moving ones, are deduced from the lattice and charge variable spectra in the frequency–momentum space. We consider an efficient approach to produce approximate polarobreathers with long lifespans. Their spectrum allows for the determination of the initial conditions and the necessary parameters to obtain numerically exact polarobreathers. The spectra of exact polarobreathers become extremely simple and easy to interpret. We also solve the problem that the charge frequency is not an observable, but the frequency of the charge probability certainly is an observable. [ABSTRACT FROM AUTHOR]

The Davydov model for amide I propagation in hydrogen-bonded chains of proteins is revisited. The many similarities between the mixed quantum-classical dynamical equations and those that are derived from the full quantum Davydov model while applying the so-called D2 ansatz are highlighted. The transition from a minimum energy localized amide I state to a fully delocalized state is shown to operate in four phases, one of which is abrupt and the last of which is a fast but smooth change from a very broad yet localized state to a completely delocalized one. Exploration of the dynamical phase space at zero temperature includes the well-known soliton propagation as well as double and triple discrete breathers, and dispersion of initially localized states. The uncertainties related to the question of the thermal stability of the Davydov soliton are illustrated. A solution to the seemingly endless problem of the short radiative lifetime of the amide I excitations is proposed. [ABSTRACT FROM AUTHOR]

We propose two classes of symplecticity-preserving symmetric splitting methods for semi-classical Hamiltonian dynamics of charge transfer by intrinsic localized modes in nonlinear crystal lattice models. We consider, without loss of generality, one-dimensional crystal lattice models described by classical Hamiltonian dynamics, whereas the charge (electron or hole) is modeled as a quantum particle within the tight-binding approximation. Canonical Hamiltonian equations for coupled lattice-charge dynamics are derived, and a linear analysis of linearized equations with the derivation of the dispersion relations is performed. Structure-preserving splitting methods are constructed by splitting the total Hamiltonian into the sum of Hamiltonians, for which the individual dynamics can be solved exactly. Symmetric methods are obtained with the Strang splitting of exact, symplectic flow maps leading to explicit second-order numerical integrators. Splitting methods that are symplectic and conserve exactly the charge probability are also proposed. Conveniently, they require only one solution of a linear system of equations per time step. The developed methods are computationally efficient and preserve the structure; therefore, they provide new means for qualitative numerical analysis and long-time simulations for charge transfer by nonlinear lattice excitations. The properties of the developed methods are explored and demonstrated numerically considering charge transport by mobile discrete breathers in an example model previously proposed for a layered crystal. [ABSTRACT FROM AUTHOR]

Slow energy relaxation has been observed in one-dimensional lattices with and without a nonlinear on-site potential; however, a comprehensive understanding of the detailed relaxation process remains elusive. Here we revisit this issue by introducing damping conditions at the free-end boundary of a thermalized lattice. We reveal that, in the long-cooling-time regime considered, for systems with a nonlinear on-site potential, energy relaxation exhibits a strong temperature-dependent behavior and with the increase of temperature, there is a crossover between decaying and non-decaying behaviors, around a crossover temperature point of T c ≃ 4. 2. This non-decaying behavior at higher temperature is attributed to the presence of standing multi Sievers–Takeno discrete breather (DB) states. Conversely, for systems without on-site potentials, relaxation is nearly independent of temperature but dependent on interparticle potential. Notably, we observe that the cubic anharmonicity can generate moving single Page DB states that contribute to the unusual slow energy relaxation within a specific time regime. Our results provide enhanced insights into the mechanisms governing slow energy relaxation during lattice cooling. • We study temperature-dependence of energy relaxation in systems with on-site potentials and reveal a crossover behavior between decaying and non-decaying energy. • We find in systems without on-site potentials, the cubic anharmonicity can lead to a non-decaying energy relaxation within a specific time regime. • We relate the slow energy relaxation of both systems to the presence of multi standing Sievers-Takeno and single moving Page discrete breather modes, respectively. [ABSTRACT FROM AUTHOR]

In this paper, we study the spectral properties of polarobreathers, that is, breathers carrying charge in a one-dimensional semiclassical model. We adapt recently developed numerical methods that preserve the charge probability at every step of time integration without using the Born–Oppenheimer approximation, which is the assumption that the electron is not at equilibrium with the atoms or ions. We develop an algorithm to obtain exact polarobreather solutions. The properties of polarobreathers, both stationary and moving ones, are deduced from the lattice and charge variable spectra in the frequency–momentum space. We consider an efficient approach to produce approximate polarobreathers with long lifespans. Their spectrum allows for the determination of the initial conditions and the necessary parameters to obtain numerically exact polarobreathers. The spectra of exact polarobreathers become extremely simple and easy to interpret. We also solve the problem that the charge frequency is not an observable, but the frequency of the charge probability certainly is an observable.

• Analytical approximation for DBs of infinitely long, bi-linear FPU chain is obtained • Zones of existence of ILMs in finite chains have been established analytically • Exact analytical solutions for ILMs emerging in finite chains are derived • Stability properties of ILM solutions of finite chains are established using the Fillipov method Present study concerns the analysis of stationary intrinsically localized modes emerging in bilinear and symmetric Fermi–Pasta–Ulam chains. Each element of the chain is coupled to its nearest neighbors through identical and symmetric (tension/compression) bilinear springs. The intrinsically localized modes are the time-periodic, localized vibration states which are manifested by the extreme energy localization on one and two bonds of the chain for bond - centered and site - centered symmetries, respectively. Approximate and exact analytical solutions of intrinsic localized modes are derived for the infinite as well as the finite chains, correspondingly. The derived analytical approximations allow to describe explicitly the amplitude wave profiles of these special localized states as well as to establish their zones of existence in the space of system parameters. In the second part of the study, we derive the exact analytical solutions for the same type of site- and bond- centered intrinsically localized modes supported by the finite bilinear Fermi–Pasta–Ulam chains and analyze their stability properties using Fillipov method. [ABSTRACT FROM AUTHOR]

We investigate the spectral properties of one-dimensional spatially modulated nonlinear phononic lattices, and their evolution as a function of amplitude. In the linear regime, the stiffness modulations define a family of periodic and quasiperiodic lattices whose bandgaps host topological edge states localized at the boundaries of finite domains. With cubic nonlinearities, we show that edge states whose eigenvalue branch remains within the gap as amplitude increases remain localized, and therefore appear to be robust with respect to amplitude. In contrast, edge states whose corresponding branch approaches the bulk bands experience de-localization transitions. These transitions are predicted through continuation studies on the linear eigenmodes as a function of amplitude, and are confirmed by direct time domain simulations on finite lattices. Through our predictions, we also observe a series of amplitude-induced localization transitions as the bulk modes detach from the nonlinear bulk bands and become discrete breathers that are localized in one or more regions of the domain. Remarkably, the predicted transitions are independent of the size of the finite lattice, and exist for both periodic and quasiperiodic lattices. These results highlight the co-existence of topological edge states and discrete breathers in nonlinear modulated lattices. Their interplay may be exploited for amplitude-induced eigenstate transitions, for the assessment of the robustness of localized states, and as a strategy to induce discrete breathers through amplitude tuning.

We present a theoretical study on quantum breathers in a XXZ Heisenberg ferromagnet with the single-ion uniaxial anisotropy on a two-dimensional hexangular lattice. In our work, the full quantum and the semiclassical cases are considered, respectively. For the full quantum case, we find that some isolated two-magnon bands can exist below the free magnon band. Physically, each isolated two-magnon band correspond to a two-magnon bound state, which is the simplest quantum breather state. For the semiclassical case, the analytical form of the discrete breather solution with a line localized structure is obtained by adopting the Glauber's coherent-state representation. Furthermore, the influence of the anisotropy on the properties of quantum breathers is discussed in detail. [ABSTRACT FROM AUTHOR]

We consider a class of discrete nonlinear Schrodinger (DNLS) equations in m dimensional lattices with partially sublinear nonlinearity f. Combining variational methods and a priori estimate, we give a general sufficient condition on f for type (A), that is, a sequence of nontrivial homoclinic solutions accumulating to zero. By using a compact embedding technique, we overcome the loss of compactness due to the problem being set on the unbounded domain $\mathbb{Z}^m$. Another obstacle caused by the local definition of f is solved by using the cutoff methods to recover the global property of f. To the best of our knowledge, this is the first time to obtain infinitely many homoclinic solutions for the DNLS equations with partially sublinear nonlinearity. Moreover, we prove that if f is not sublinear, the zero solution is isolated from other homoclinic solutions. Our results show that the sublinearity and oddness of f yield type (A). Without the oddness assumption, we still can prove that this problem has at least a nontrivial homoclinic solution if f is local sublinear, which improves some existing results.

Condensed matter is thermodynamically unstable in a vacuum. That is what thermodynamics tells us through the relation showing that condensed matter at temperatures above absolute zero always has non-zero vapour pressure. This instability implies that at low temperatures energy must not be distributed equally among atoms in the crystal lattice but must be concentrated. In dynamical systems such concentrations of energy in localized excitations are well known in the form of discrete breathers, solitons and related nonlinear phenomena. It follows that to satisfy thermodynamics such localized excitations must exist in systems of condensed matter at arbitrarily low temperature and as such the nonlinear dynamics of condensed matter is crucial for its thermodynamics. This article is part of the theme issue 'Stokes at 200 (Part 1)'. [ABSTRACT FROM AUTHOR]

This study explores the nonlinear dynamics of helical compression valve springs. To this end, the spring is mathematically modeled as a finite nonhomogenous one-dimensional mass–spring–damper discrete chain. Periodic displacement, which mimics the actual camshaft profile, is assumed at the upper end of the chain, while the other end is fixed. For the linear dynamics, the amplitudes of the periodic response are determined directly; they decrease toward the fixed end of the spring. Then, in order to meet more realistic conditions, the displacement of the upper mass is assumed to be nonnegative. This condition is realized by introducing an appropriate impact constraint. We assume that the impact is described by Newton impact law with restitution coefficient less than unity. For the case of one impact per period (1IPP) of excitation, exact periodic solutions are derived. The interplay between the nonhomogenous structure, multi-frequency excitation and nonlinearity leads to two qualitatively different states of the periodic responses; we refer to them as propagating states and edge states. The propagating states are characterized by weak localization, and the edge states—by strong localization at the forced edge. The stability of the system is analyzed using Floquet theory. Generic pitchfork and Neimark–Sacker bifurcations are observed. Analytical solutions conform to numerical simulations and experimental tests conducted on real valve springs. [ABSTRACT FROM AUTHOR]

The modulational instability associated with discrete breathers in 2D quantum ultracold atoms is studied by using the Glauber's coherent state combined with a semi-discrete approximation and multiple-scale methods. The linear stability analysis exhibits an intriguing threshold amplitude and instability regions associated with modulational growth rate. In addition, we demonstrate a coexistence of two bright intrinsic localized modes namely, the radial symmetric and bilateral symmetric modes, at the center and at the edges of the Brillouin zone, respectively, by alternating the on-site parameter interaction. Numerical investigations reveal a good agreement with the theoretical analysis. [ABSTRACT FROM AUTHOR]

Abstract Graphane is a fully hydrogenated graphene which is practically interesting for application in electronics, hydrogen storage and transportation, in nanoscale devices. As it was previously shown, the energy of a discrete breather (nonlinear localized mode) in graphane close to the value of the energy barrier at which the dehydrogenation of graphene occurs. In the present work, molecular dynamics simulation is used to investigate the possibility of energy exchange between discrete breathers in graphane in thermal equilibrium at 400 K and 600 K. In thermally equilibrated graphane, hydrogen atoms are spontaneously excited and can be considered as discrete breathers. Comparison of the kinetic energy per atom as the function of time for the selected hydrogen atoms with their displacements along the z axis showed that there is an energy exchange between the discrete breathers at evaluated temperatures. Hydrogen atom, transmitting its energy to the neighboring atom no longer exists as discrete breather. At high temperatures (600 K) the energy exchange between closely located discrete breathers also take place but strong thermo-oscillations of atoms at high temperatures (above 400 K) considerably affect the process. Highlights • Discrete breathers (DBs) are spontaneously excited in thermally equilibrated graphane. • DBs moves from one excited hydrogen atom to another until the total energy loss. • Thermo-oscillations of atoms at 600 K considerably affect the energy exchange between DBs. • Data on the study of DBs in graphane can be used to hydrogen storage and transportation. [ABSTRACT FROM AUTHOR]

By method of molecular dynamics investigated the interaction of nonlinear localized modes with bivacancies Pt crystal Pt3Al. Identified dependences of the lifetime of the nonlinear localized modes from the initial temperature of the crystal model, the initial atom Al deviation from its equilibrium position, as well as the distance to the introduced bivacancy Pt in (111) plane of the crystal.

We explore the dynamics of localized periodic solutions (discrete solitons, or discrete breathers) in a finite one-dimensional chain of asymmetric vibro-impact oscillators. The model is intended to simulate dynamical responses of crack arrays, motion of rigid elements between obstacles, as well as the behavior of arrays of microscopic vibro-impact oscillators. The explored chain involves a parabolic on-site potential with asymmetric rigid constraints (the displacement domain of each particle is finite and asymmetric with respect to its equilibrium position) and a linear nearest-neighbor coupling. When the particle approaches the constraint, it undergoes an impact that satisfies the Newton impact law. The restitution coeffcient may be less than unity, and it is the only source of damping in the model. Nonlinearity of the system stems from the impact interactions. We demonstrate that this vibro-impact model allows derivation of exact analytical solutions for the asymmetric discrete breathers, in both conservative and forced-damped settings. The asymmetry makes two types of breathers possible: breathers that impact both constraints or only one constraint. Transition between these two types of breathers occurs through a grazing bifurcation. Special character of the nonlinearity permits explicit derivation of the monodromy matrix. Therefore, the stability of the obtained breather solutions can be studied with the desired accuracy in the framework of simple methods of linear algebra, and with rather moderate computational efforts. All three generic scenarios of loss of stability (pitchfork, Neimark{Sacker, and period doubling bifurcations) are observed. [ABSTRACT FROM AUTHOR]

We have used deep level transient spectroscopy (DLTS) and Laplace DLTS (L-DLTS) to characterize the electrically active point defects introduced in n -type gallium arsenide by electron beam exposure prior to Schottky metallization. The GaAs crystals were exposed to incident electrons at sub-threshold energies which are deemed low and insufficient to form defects through ion solid interactions. DLTS revealed a set of electron traps different from those commonly observed in n -GaAs after particle irradiation. These different signatures from the same radiation type suggest that different mechanisms are responsible for defect formation in the two electron irradiation processes. An analysis of the conditions under which the defects were formed was done to distil a number of possible defect formation mechanisms using the experimental evidence obtained. [ABSTRACT FROM AUTHOR]

Nonlinear dynamics of graphane (hydrogenated graphene) as well as some other properties of this new promising material are of high interest nowadays. One of the main challenges is the explanation of hydrogenation/dehydrogenation process of graphane at finite temperatures and the understanding of the underlying mechanisms. In present work, the hypothesis of discrete breathers working as the activators of the dehydrogenation is presented. Molecular dynamics simulation is conducted to study the discrete breathers in graphane in thermal equilibrium for temperature range 50–600 K. With the temperature increase the possibility of atom separation decreases because of thermal oscillations while the critical amplitude of the atom separation increase. It is shown that nonlinear localized modes or discrete breathers can be found in graphane at thermal equilibrium at temperature range of 400–600 K. The lifetime of discrete breather increases with the increase of its initial amplitude while temperature decrease leads to the increase of lifetime. It is concluded, that discrete breathers can facilitate the process of graphene dehydrogenation, because of their high energy. [ABSTRACT FROM AUTHOR]

We numerically investigate out-of-equilibrium stationary processes emerging in a Discrete Nonlinear Schrödinger chain in contact with a heat reservoir (a bath) at temperature TL and a pure dissipator (a sink) acting on opposite edges. Long-time molecular-dynamics simulations are performed by evolving the equations of motion within a symplectic integration scheme. Mass and energy are steadily transported through the chain from the heat bath to the sink. We observe two different regimes. For small heat-bath temperatures TL and chemical-potentials, temperature profiles across the chain display a non-monotonous shape, remain remarkably smooth and even enter the region of negative absolute temperatures. For larger temperatures TL, the transport of energy is strongly inhibited by the spontaneous emergence of discrete breathers, which act as a thermal wall. A strongly intermittent energy flux is also observed, due to the irregular birth and death of breathers. The corresponding statistics exhibit the typical signature of rare events of processes with large deviations. In particular, the breather lifetime is found to be ruled by a stretched-exponential law. [ABSTRACT FROM AUTHOR]

The properties of discrete breathers and modulational instability in a discrete $$\phi ^{4}$$ nonlinear lattice which includes the next-nearest-neighbor coupling interaction are investigated analytically. By using the method of multiple scales combined with a quasi-discreteness approximation, we get a dark-type and a bright-type discrete breather solutions and analyze the existence conditions for such discrete breathers. It is found that the introduction of the next-nearest-neighbor coupling interactions will influence the existence condition for the bright discrete breather. Considering that the existence of bright discrete breather solutions is intimately linked to the modulational instability of plane waves, we will analytically study the regions of discrete modulational instability of plane carrier waves. It is shown that the shape of the region of modulational instability changes significantly when the strength of the next-nearest-neighbor coupling is sufficiently large. In addition, we calculate the instability growth rates of the $$q=\pi $$ plane wave for different values of the strength of the next-nearest-neighbor coupling in order to better understand the appearance of the bright discrete breather. [ABSTRACT FROM AUTHOR]

Locally resonant metamaterials have recently drawn the attention of many researchers due to their capability in controlling low-frequency waves by forming a bandgap resulting from mode hybridization. Although linear acoustics of these metamaterials have been extensively explored, only a little is known about their nonlinear acoustics. This work investigates the nonlinear acoustics of a 1D discrete strongly nonlinear locally resonant metamaterial under impulsive force excitation. The metamaterial is modeled as a chain of linearly grounded masses connected by essential strong nonlinearity (purely cubic nonlinearity), and embedded by linear local resonators. Numerical investigations demonstrate the existence of different families of traveling breathers that depend on the coupling coefficient between the local resonator and its holding cell. One of these families is reported for the first time in the current work due to the existence of multiple fast frequencies in its profile. Although the investigated system is undamped, numerical simulations demonstrate that the breather arrest is controlled by certain parameters of the system. In the limit of small energy levels, the complexification averaging method (CX-A) is utilized with the help of numerical observations to demonstrate some aspects of the nonlinear acoustics of the system. Particularly, analytical analysis is used to determine the nonlinear band structure of the system. The outcome indicates the presence of two energy-dependent nonlinear propagation zones (PZs) (i.e., acoustics and optical) and three complementary attenuation zones (AZs) for the infinite lattice case. In addition, the different families of traveling breathers in the semi-infinite lattice are investigated analytically and compared to their corresponding numerical results. [ABSTRACT FROM AUTHOR]

We analyze the existence and properties of discrete localized excitations in a Bose–Einstein condensate loaded into a periodic two-dimensional optical lattice, when a dipolar interaction between atoms is present. The dependence of the Number of Atoms (Norm) on the energy of solutions is studied, along with their stability. Two important features of the system are shown, namely, the absence of the Norm threshold required for localized solutions to exist in finite 2D systems, and the existence of regions in the parameter space where two fundamental solutions are simultaneously unstable. This feature enables mobility of localized solutions, which is an uncommon feature in 2D discrete nonlinear systems. With attractive dipolar interaction, a non-trivial behavior of the Norm dependence is obtained, which is well described by an analytical model. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

By means of the semidiscrete multiple-scale method, we study the existence and properties of high-order envelope solitons and discrete breathers in a homogeneous DNA chain model that is based on pairing enthalpies and site-dependent finite stacking. We obtain the analytical solutions for an envelope soliton, and find that at the Brillouin zone center, discrete breather solutions can appear below the bottom of the phonon band. The behavior of two solitons in collisions and the stability of discrete breathers are confirmed by numerical simulations of the exact equations of the system. [ABSTRACT FROM AUTHOR]

We consider a chain of torsionally-coupled, planar pendula shaken horizontally by an external sinusoidal driver. It has been known that in such a system, theoretically modeled by the discrete sine-Gordon equation, intrinsic localized modes, also known as discrete breathers, can exist. Recently, the existence of multifrequency breathers via subharmonic driving has been theoretically proposed and numerically illustrated by Xu et al. (2014) [21] . In this paper, we verify this prediction experimentally. Comparison of the experimental results to numerical simulations with realistic system parameters (including a Floquet stability analysis), and wherever possible to analytical results (e.g. for the subharmonic response of the single driven–damped pendulum), yields good agreement. Finally, we report the period-1 and multifrequency edge breathers which are localized at the open boundaries of the chain, for which we have again found good agreement between experiments and numerical computations. [ABSTRACT FROM AUTHOR]