Discrete breathers in dissipative lattices

Marín, J. L.; Falo, Fernando; Martínez, Pedro J.; Floría, L. M.

doi:10.1103/physreve.63.066603

Cited by 76 publications

(107 citation statements)

References 27 publications

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“…Crucially, our rigorous quantitative results establish prerequisites for the existence of discrete breathers in general damped and driven nonlinear lattices beyond the validity of the continuation process starting from the anti-continuum limit. 8,[18][19][20][21] Our results are generic as they hold not only for any coupling strength but also for any on-site potential, any type of attractive interaction, any degree of attractive interaction, general driving fields and arbitrary dimension of the system. We study the dynamics of general driven and damped nonlinear lattice systems of dimension d given by the following system…”

mentioning

confidence: 86%

“…Compared to their Hamiltonian (conservative) counterparts breathers in dissipative and driven lattice systems do not occur in families of localised solutions as they are provided by discrete sets of attractors for appropriate initial conditions contained in the corresponding basin(s) of attraction. [18][19][20][21][22][23][24][25] The aim of this work is to establish quantitative conditions in parameter space for the existence respectively non-existence of discrete breathers in general damped and driven anharmonic lattice systems. To this end we show that there exist parameter ranges such that for any launched localised state the difference between the maximal amplitude and the minimal amplitude of the oscillators decays exponentially fast.…”

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confidence: 99%

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Existence and non-existence of breather solutions in damped and driven nonlinear lattices

Hennig

2013

AIP Advances

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We investigate the existence of spatially localised solutions, in the form of discrete breathers, in general damped and driven nonlinear lattice systems of coupled oscillators. Conditions for the exponential decay of the difference between the maximal and minimal amplitudes of the oscillators are provided which proves that initial non-uniform spatial patterns representing breathers attain exponentially fast a spatially uniform state preventing the formation and/or preservation of any breather solution at all. Strikingly our results are generic in the sense that they hold for arbitrary dimension of the system, any attractive interaction, coupling strength and on-site potential and general driving fields. Furthermore, our rigorous quantitative results establish conditions under which discrete breathers in general damped and driven nonlinear lattices can exist at all and open the way for further research on the emergent dynamical scenarios, in particular features of pattern formation, localisation and synchronisation, in coupled cell networks

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confidence: 86%

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confidence: 99%

Existence and non-existence of breather solutions in damped and driven nonlinear lattices

Hennig

2013

AIP Advances

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“…In Josephson junction systems, this is actually even implemented experimentally. Let us mention the basic new features one is faced with when studying dissipative breathers and their properties [22,33,34].…”

Section: Dissipative Discrete Breathersmentioning

confidence: 99%

“…2.2, we may introduce a (quasi-symplectic) matrix R which maps the phase space of the perturbations onto itself by integration of (36) over one breather period [34]. By using the transformation…”

Section: Perturbing Dissipative Breathersmentioning

confidence: 99%

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Discrete Breathers with Dissipation

Flach

Gorbach

2008

Lecture Notes in Physics

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The interplay between discreteness and nonlinearity leads to the emergence of a new class of nonlinear excitations, viz. discrete breathers. These time-periodic and spatially localized excitations correspond to generic exact solutions of the underlying nonlinear lattice models. Discrete breathers are not confined to certain lattice dimensions, nor are they sensitive to the particular type of nonlinearity in the system. They are usually dynamically and structurally stable and emerge in a variety of physical systems, ranging from lattice vibrations and magnetic excitations in crystals to light propagation in photonic structures and cold atom dynamics in periodic optical traps. Basic properties of discrete breathers, including spatial localization and stability, are briefly discussed in this chapter. Special focus is placed on a subclass of dissipative discrete breathers. Dissipation eliminates extended waves and allows for various resonances of discrete breathers with damped cavity modes. We discuss applications of the discrete breather concept in systems where dissipation is not only unavoidable but essential in order to observe and manipulate discrete breathers, and in order to use them for spectroscopic tools, amongst others.

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Model of temperature dependent crystal relaxation

Mihóková

Schulman

2006

Phys. Status Solidi (c)

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Anomalous decay of the slow emission component in certain doped alkali halides was explained by the creation of a discrete breather in the immediate neighborhood of the impurity. It was experimentally observed that with rising temperature the decay anomaly becomes less pronounced, finally disappearing in the range 100 K to150 K (depending on the substance). In view of the breather explanation, this temperature dependence should be a consequence of the effect of temperature on breathers. We present an improved model of the dissipative effects of temperature on lattice breathers so as to compare it to the observed experimental temperature behavior. Introduction Luminescence of various alkali halides doped by heavy ns2 ions excited in the Aabsorption band displays an anomaly in the decay of the slow component [1,2]. The initial part of the decay, up to several milliseconds, is nonexponential. This anomaly was explained by assuming extremely slow relaxation of the crystal lattice as a response to the Jahn-Teller effect acting on the emission center in its excited state [3]. The slowness of the lattice relaxation was later ascribed to the creation of a discrete breather in the immediate neighborhood of the impurity [4]. As experimentally observed, the anomaly is most pronounced at the lowest temperatures. As the temperature increases the anomaly weakens and is finally extinguished around 100-150 K, depending on the lattice substance. In view of the breather explanation the temperature dependence of the anomaly should be the consequence of temperature effects on the breather. Such effects are under investigation; however, so far they are still not fully understood. Thermal relaxation of the breather in a monatomic nonlinear chain shows [5][6][7] that breathers are likely to be spontaneously created if the initial temperature is sufficiently high. Thermal background can also set the breather in motion [7,8] and cause the breather to collide with other excitations and chain boundaries. Stability of the breather in thermal equilibrium for one and two-dimensional monatomic lattices is studied in [9,10].In the case of the decay anomaly due to breather creation, experimental data on the anomaly's temperature dependence suggest that increasing temperature causes the breather to decay, ultimately leading to its destruction, together with the disappearance of the decay anomaly. We now provide a model of finite temperature effects on the decay of the breather in a diatomic non-linear chain. The model confirms the expected tendency consistent with experimental data on the decay anomaly: the higher the temperature, the faster the decay of the breather.

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Discrete breathers in dissipative lattices

Cited by 76 publications

References 27 publications

Existence and non-existence of breather solutions in damped and driven nonlinear lattices

Existence and non-existence of breather solutions in damped and driven nonlinear lattices

Discrete Breathers with Dissipation

Model of temperature dependent crystal relaxation

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