Search results for "anharmonicity"
showing 10 items of 118 documents
Analysis of the transition from normal modes to local modes in a system of two harmonically coupled Morse oscillators
1992
The system consisting of two Morse oscillators coupled via either a potential or a kinetic quadratic term is considered. The corresponding classical equations of motion have been numerically integrated and the initial conditions have been systematically analyzed in the regime of low total excitation energy of the system. Particular attention was paid to the full characterization of an intermediate type of motion, herein called transition mode, which appears at total energy values in between those typical of normal modes and those where local and normal modes coexist. A previously proposed perturbative approach (Jaffe C, Brumer P (1980) J Chem Phys 73:5646) is reanalyzed and compared with th…
Frenkel-Kontorova model with anharmonic interactions
1986
It is shown that consideration of more realistic interatomic potentials (with limited tensile strength) within the framework of the Frenkel-Kontorova model may lead to a breakdown of the soliton picture in systems with competing periodicities. Closed analytical expressions for the form of a single soliton in an anharmonic chain reveal discontinuities which indicate a disintegration of the entire system beyond some critical values of the misfit, and/or of the height of the periodic substrate potential. The length of anharmonic solitons depends essentially on both the sign and the magnitude of the misfit. The influence of misfit on the pinning-unpinning transition is also investigated.
Delocalization-Localization Transition due to Anharmonicity
2008
Analytical and numerical calculations for a reduced Fermi-Pasta-Ulam chain demonstrate that energy localization does not require more than one conserved quantity. Clear evidence for the existence of a sharp delocalization-localization transition at a critical amplitude is given. Approaching the critical amplitude from above and below, diverging time scales occur. Above the critical amplitude, the energy packet converges towards a discrete breather. Nevertheless, ballistic energy transportation is present, demonstrating that its existence does not necessarily imply delocalization.
Magnetopolaron in a weakly elliptical InAs/GaAs quantum dot
2003
We study theoretically the properties of a polaron formed in a shallow, weakly elliptical, disk-shaped InAs/GaAs quantum dot in the presence of a magnetic field by using the Davydov's canonical transformation. Special attention is paid to the energy-level splitting due to the Frohlich interaction of an electron in a quantum dot with optical phonons near resonance. The polaron relaxation rates, including the anharmonicity induced channel, are analyzed for various confinement energies and magnetic field magnitudes, taking into account coherent polaronic effects.
Some comments on fluctuating-elasticity and local oscillator models for anomalous vibrational excitations in glasses
2011
Abstract An overview is given on the present status of the theoretical description of vibrational spectra of glasses, as seen by inelastic neutron, X-ray and light (Raman) scattering. Using the language of Green's/response functions the merits and shortcomings of a local oscillator and a generalized elasticity-theory point of view are discussed. It is pointed out that in both cases the interaction of phonons with disorder-induced irregularities leads to Rayleigh scattering (mean free path l ∝ ω − 4 ) at low enough frequencies and temperatures. In disordered solids at ambient temperature the Rayleigh scattering is usually masqued by Akhiezer-like anharmonic scattering l ∝ ω − 2 , but it can …
Long lifetime of the E1u in-plane infrared-active modes of h -BN
2020
We present an infrared reflectivity study of the ${E}_{1u}$ in-plane phonons of hexagonal BN as a function of temperature in the 40--680 K range. The infrared reflectance spectra of high-quality lamellar single crystals are accurately fitted using Lowndes' factorized form of the dielectric response, where the longitudinal-optic (LO) frequency is an independent adjustable parameter. From this analysis we obtain reliable values for the phonon damping of the IR-active ${E}_{1u}$ phonons which couple to light and give rise to the phonon-polariton excitations in this hyperbolic material. Anharmonic coupling potentials are estimated from the temperature dependence of the damping parameters. The $…
Total free energy of a spin-crossover molecular system
2004
The free energy of spin-crossover molecular systems studied so far deal with the inner degrees of freedom of the spin-crossover molecules and a variety of interaction schemes between the molecules in the high spin (HS) and low spin (LS) states. Different types of transition curves, gradual, abrupt, hysteresis, and also two step transitions have been simulated or even satisfactorily fitted to experimental data. However, in the last decade spin transition curves were measured, especially under pressure, which could not be explained within these theoretical models. In this contribution the total free energy of an anharmonic lattice incorporating spin-crossover molecules which have a certain mi…
Number of metastable states of a chain with competing and anharmonicΦ4−like interactions
1993
We investigate the number of metastable configurations of a Φ 4 -like model with competing and anharmonic interactions as a function of an effective coupling constant η. The model has piecewise harmonic nearest-neighbor and harmonic next-nearerst-neighbor interactions. The number M of metastable states in the configuration space increases exponentially with the number N of particles: M∞exp(vN). It is shown numerically that, outside the previously considered range |η|<1/3, v is approximately linearly decreasing with η for |η|<1 and that v=0 for η≥1. These findings can be understood by describing the metastable configurations as an arrangement of kink solitons whose width creases with η
Convergent Strong-Coupling Expansions from Divergent Weak-Coupling Perturbation Theory
1995
Divergent weak-coupling perturbation expansions for physical quantities can be converted into sequences of uniformly and exponentially fast converging approximations. This is possible with the help of an additional variational parameter to be optimized order by order. The uniformity of the convergence for any coupling strength allows us to take all expressions directly to the strong-coupling limit, yielding a simple calculation scheme for the coefficients of convergent strong-coupling expansions. As an example, we determine these coefficients for the ground state energy of the anharmonic oscillator up to 22nd order with a precision of about 20 digits.
STATISTICAL MECHANICS OF NONCLASSIC SOLITONIC STRUCTURES-BEARING DNA SYSTEM
2011
We theoretically investigate the thermodynamic properties of modified oscillator chain proposed by Peyrard and Bishop. This model obtained by adding the quartic anharmonicity term to the coupling in the Peyrard–Bishop model is useful to model the coexistence of various phases of the molecule during the denaturation phenomenon. Within the model, the negative anharmonicity is responsible for the sharpness of calculated melting curves. We perform the transfer integral calculations to demonstrate that the model leads to a good agreement with known experimental results for DNA.