Stationary and moving intrinsic localized modes in one-dimensional monatomic lattices with cubic and quartic anharmonicity

Bickham, S. R.; Kiselev, S. A.; Sievers, A. J.

doi:10.1103/physrevb.47.14206

Cited by 141 publications

(71 citation statements)

References 13 publications

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“…In the chains with 2-4 and 2-3-4 potentials, discrete breathers are observed in agreement with [1][2][3][4][5][6]. After the breathers decay, thermal equilibrium is achieved and kink-like solitons also appear in these chains.…”

Section: Discussionsupporting

confidence: 70%

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Spontaneously Appearing Discrete Moving Kinks in Nonlinear Acoustic Chain With Realistic Potential

Metlov¹,

Eremeichenkova²

2003

Condens. Matter Phys.

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Molecular dynamic simulations are performed to investigate a long-time evolution of different initial signals in nonlinear acoustic chains with realistic Exp-6 potential and with power potentials. First, in the chain with realistic potential, long-lifetime kink-shaped excitations are found in the system in thermodynamic equilibrium. They give sharp peaks on high-energy tile of Gibbs distribution. Travelling along the chain, each kink collects the energy from the background atoms, and, consequently, transfers it to smallamplitude phonons. Dynamic equilibrium is observed between the processes of growth and decay of the kinks.

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Section: Discussionsupporting

confidence: 70%

“…Power expansions of interatomic potentials (taking into account anharmonisms up to fourth order) are frequently used in order to investigate strongly nonlinear phenomena [1][2][3][4][5][6]. However, for soliton-like excitations with large amplitudes one cannot be sure that high-order anharmonisms may be omitted.…”

Section: Introductionmentioning

confidence: 99%

Spontaneously Appearing Discrete Moving Kinks in Nonlinear Acoustic Chain With Realistic Potential

Metlov¹,

Eremeichenkova²

2003

Condens. Matter Phys.

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“…For a classical nonlinear oscillator array, there are a number of characteristic ILM properties, probed theoretically, such as their interaction with an ac driver, 14,34 -36 their propagation 5,[37][38][39][40] and amplitude dependent mobility 4,6,[40][41][42] in a discrete lattice potential, 43,44 as well as their interactions with impurities, [45][46][47][48][49][50] that still need to be examined experimentally. Note that strongly excited ILMs 42 can be trapped anywhere in the lattice, so they also could approach impurity mode behavior.…”

Section: Introductionmentioning

confidence: 99%

Study of intrinsic localized vibrational modes in micromechanical oscillator arrays

Satō

Hubbard

English

et al. 2003

Chaos: An Interdisciplinary Journal of Nonlinear Science

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103

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Intrinsic localized modes ͑ILMs͒ have been observed in micromechanical cantilever arrays, and their creation, locking, interaction, and relaxation dynamics in the presence of a driver have been studied. The micromechanical array is fabricated in a 300 nm thick silicon-nitride film on a silicon substrate, and consists of up to 248 cantilevers of two alternating lengths. To observe the ILMs in this experimental system a line-shaped laser beam is focused on the 1D cantilever array, and the reflected beam is captured with a fast charge coupled device camera. The array is driven near its highest frequency mode with a piezoelectric transducer. Numerical simulations of the nonlinear Klein-Gordon lattice have been carried out to assist with the detailed interpretation of the experimental results. These include pinning and locking of the ILMs when the driver is on, collisions between ILMs, low frequency excitation modes of the locked ILMs and their relaxation behavior after the driver is turned off. © 2003 American Institute of Physics. ͓DOI: 10.1063/1.1540771͔An advance of the theory of nonlinear excitations in discrete lattices was the discovery that some localized vibrations in perfectly periodic but nonintegrable lattices could be stabilized by lattice discreteness. The modulational instability of extended large amplitude vibrational modes has been proposed as a mechanism for the realization of dynamical localization on the scale of the lattice constant. Although theoretically a variety of methods to excite the instability of a homogeneous vibrational mode have been proposed, these ideas have yet to be tested experimentally. Since the observation of nanoscale localized vibrational modes still cannot be achieved there is definite advantage to examining a macroscopic array, which is small enough so that the entire time dependence of the instability dynamics occurs in a practical measurement interval. This has been accomplished by using micromechanical silicon technology to fabricate up to 248 identical cantilevers with a 40 micron lattice constant. Optical techniques have been used to track the motion of individual cantilevers in the presence of an inertial driver. In addition to experimentally characterizing the modulational instability and identifying the best method for producing intrinsic localized modes a new discovery is the locking of the local mode amplitude with the driver frequency. Numerical simulations have been used to better understand the nature of this synchronization effect.

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“…A great deal of progress studying ILMs had now occurred both theoretically and experimentally and a number of reviews had appeared [33][34][35][36][37]. An important step forward in crystal lattice dynamics was the recognition that the odd terms in the two body intersite potentials removed the high frequency local mode as a possibility [38,39]. These terms produced a local dc distortion at the ILM site that theoretically insured, at least for ionic crystals, a soft anharmonic potential so ILMs could only appear in the gap between the optic and acoustic phonon branches or as resonances in the acoustic spectrum [40].…”

Section: Two Elastic Configurations In Ki:ag + Without Ilmsmentioning

confidence: 99%

Shozo Takeno and intrinsic localized modes

Sievers

2012

NOLTA

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Abstract:Research into defect lattice dynamics played an important roll in the development of our work on the local mode properties of anharmonic lattices. Using a historical perspective I show that the different theoretical and experimental studies of the impurity-induced absorption associated with the low frequency resonances in alkali halide crystals provided the kernel for our breakout into a new area.Key Words: defect induced absorption, anharmonicity, intrinsic localized modes, two elastic configurations 1. Some research at the laboratory of atomic and solid state physics in 1965When Shozo Takeno arrived at Cornell in 1965 the properties of localized vibrational modes in the acoustic spectrum of ionic crystals were being uncovered and represented one of the main laboratory thrusts. The experimental discovery by Schaefer in 1958 that a hydrogen ion substituted into a KCl crystal generated a sharp IR absorption line associated with a vibrational mode far above the plane wave phonon spectrum [1] illuminated the pathway for experimentalists to enter a field where there had been a great deal of theoretical work over the years but no experiments. This mode was strongly localized in space because of its large frequency separation from the plane wave spectrum, a result expected from the dynamical theory of lattices [2,3]. It quickly became apparent that there were very few different kinds of impurities that produced local modes so attention turned to the question of how impurities might alter the acoustic spectrum. Thermal conductivity was the experimental probe of choice at Cornell since theory suggested that impurities would scatter acoustic waves. By measuring the temperature dependence of the thermal conductivity over a large temperature interval it was discovered that, in addition to the expected Rayleigh-type scattering from the impurities, there was another contribution indicating the presence of a phonon active impurity mode that produced resonance scattering in some defect-lattice combinations [4]. Since it had been assumed that such resonances observed in the thermal conductivity temperature dependence were not IR active a complete surprise occurred when, with a far infrared (FIR) spectroscopic technique, it was discovered that KI:Ag + had a sharp absorption line at 17.3 cm −1 , far down in the acoustic spectrum [5]. Unlike the H − ion impurity mode found by Schaefer this impurity-induced vibration was in direct contact with the crystal phonon modes and such resonant 2

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Stationary and moving intrinsic localized modes in one-dimensional monatomic lattices with cubic and quartic anharmonicity

Cited by 141 publications

References 13 publications

Spontaneously Appearing Discrete Moving Kinks in Nonlinear Acoustic Chain With Realistic Potential

Spontaneously Appearing Discrete Moving Kinks in Nonlinear Acoustic Chain With Realistic Potential

Study of intrinsic localized vibrational modes in micromechanical oscillator arrays

Shozo Takeno and intrinsic localized modes

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