Search results for "harmonic"
showing 10 items of 984 documents
Anyons and transmutation of statistics via vacuum induced Berry phase
2004
We show that bosonic fields may present anyonic behavior when interacting with a fermion in a Jaynes-Cummings-like model. The proposal is accomplished via the interaction of a two-level system with two quantized modes of a harmonic oscillator; under suitable conditions, the system acquires a fractional geometric phase. A crucial role is played by the entanglement of the system eigenstates, which provides a two-dimensional confinement in the effective evolution of the system, leading to the anyonic behavior. For a particular choice of parameters, we show that it is possible to transmute the statistics of the system continually from fermions to bosons. We also present an experimental proposal…
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.
Harmonic Vibrational Excitations in Disordered Solids and the "Boson Peak"
1998
We consider a system of coupled classical harmonic oscillators with spatially fluctuating nearest-neighbor force constants on a simple cubic lattice. The model is solved both by numerically diagonalizing the Hamiltonian and by applying the single-bond coherent potential approximation. The results for the density of states $g(\omega)$ are in excellent agreement with each other. As the degree of disorder is increased the system becomes unstable due to the presence of negative force constants. If the system is near the borderline of stability a low-frequency peak appears in the reduced density of states $g(\omega)/\omega^2$ as a precursor of the instability. We argue that this peak is the anal…
On the anomalous Stark effect in a thin disc-shaped quantum dot
2010
The effect of a lateral external electric field F on an exciton ground state in an InAs disc-shaped quantum dot has been studied using a variational method within the effective mass approximation. We consider that the radial dimension of the disc is very large compared to its height. This situation leads to separating the excitonic Hamiltonian into two independent parts: the lateral confinement which corresponds to a two-dimensional harmonic oscillator and an infinite square well in the growth direction. Our calculations show that the complete description of the lateral Stark shift requires both the linear and quadratic terms in F which explains that the exciton possess nonzero lateral dipo…
Effective field analysis using the full angular spin-orbit torque magnetometry dependence
2017
Spin-orbit torques promise ultra-efficient magnetization switching used for advanced devices based on emergent quasi-particles such as domain walls and skyrmions. Recently, the spin structure dynamics, materials and systems with tailored spin-orbit torques are being developed. A method, which allows one to detect the acting torques in a given system as a function of the magnetization direction is the torque-magnetometry method based on a higher harmonics analysis of the anomalous Hall-effect. Here we show that the effective fields acting on magnetic domain walls that govern the efficiency of their dynamics require a sophisticated analysis taking into account the full angular dependence of t…
Propagation and localisation of vibrational modes in 3–dimensional disordered systems: the binary force constant model
1999
We consider a system of coupled harmonic oscillators on a cubic lattice. The force constants are supposed to take two distinct values at random according to a bond concentration x. The density of states (DOS) is evaluated both by numerical diagonalisation and in coherent-potential approximation (CPA). There is excellent agreement between the results of the two methods. Near the concentration, where the bonds with the larger force constants percolate, the DOS differs appreciably from the crystalline one and is anomalously enhanced at low frequencies as compared to Debye's ω2 law (“boson peak”). These features are shared with models with continuous distributions of force constants. The mean f…
Model calculations for vibrational properties of disordered solids and the “boson peak”
1999
Abstract It is demonstrated that a disordered system of coupled classical harmonic oscillators with a continuous distribution of coupling parameters exhibits generally a low-frequency enhancement (“boson peak”) of the density of states, as compared with the Debye law. This phenomenon is most pronounced if the system is close to an instability. This is shown by means of a scalar model on a simple cubic lattice. The force constants are assumed to fluctuate from bond to bond according to a Gaussian distribution which is truncated at its lower end. The model is solved for the density of states and the one-phonon dynamic structure factor S(q, ω) by applying the two-site coherent potential approx…
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 $…