1,720,991 research outputs found
Canonical solution of classical magnetic models with long-range couplings
No full textWe study the canonical solution of a family of classical n-vector spin models on a generic d-dimensional lattice; the couplings between two spins decay as the inverse of their distance raised to the power α, with α < d. The control of the thermodynamic limit requires the introduction of a rescaling factor in the potential energy, which makes the model extensive but not additive. A detailed analysis of the asymptotic spectral properties of the matrix of couplings was necessary to justify the saddle point method applied to the integration of functions depending on a diverging number of variables. The properties of a class of functions related to the modified Bessel functions had to be investigated. For given n, and for any α, d and lattice geometry, the solution is equivalent to that of the α = 0 model, where the dimensionality d and the geometry of the lattice are irrelevant
Vibrational properties of the amide group in acetanilide. A molecular dynamics study
No full textA simplified classical model of acetanilide crystal is built in order to study the mechanisms of vibrational energy transduction in a hydrogen-bonded solid. The intermolecular hydrogen bond is modeled by an electrostatic interaction between neighboring excess charges on hydrogen and oxygen atoms. The intramolecular interaction in the peptide group is provided by a dipole-charge interaction. Forces are calculated up to second-order terms in the atomic displacements from equilibrium positions; the model is thus a chain of nonlinear coupled oscillators. Numerical molecular-dynamics experiments are performed on chain segments of five molecules. The dynamics is ordered, at all temperatures. Energy is widely exchanged between the stretching and the bending of the N—H bond, with characteristic times of the order of 0.2 ps. Energy transduction through the H bond is somewhat slower and of smaller amplitude, and is strongly reduced when the energies of the two bound molecules are very different: This could reduce the dissipation of localized energy fluctuations
Long time behavior of quasi stationary states of the Hamiltonian mean-field model
No full textThe Hamiltonian mean-field model has been investigated, since its introduction about a decade ago, to study the equilibrium and dynamical properties of long-range interacting systems. Here we study the long-time behavior of long-lived, out-of-equilibrium, quasistationary dynamical states, whose lifetime diverges in the thermodynamic limit. The nature of these states has been the object of a lively debate in the recent past. We introduce a numerical tool, based on the fluctuations of the phase of the instantaneous magnetization of the system. Using this tool, we study the quasistationary states that arise when the system is started from different classes of initial conditions, showing that the new observable can be exploited to compute the lifetime of these states. We also show that quasistationary states are present not only below, but also above the critical temperature of the second-order magnetic phase transition of the model. We find that at supercritical temperatures the lifetime is much larger than at subcritical temperatures
Partial Lyapunov exponents in tangent space dynamics
No full textThe authors have developed a new diagnostic tool for the analysis of the order-to-chaos transition: the partial Lyapunov exponents, defined through the dynamics in the tangent space. They allow the dynamics of single variables to be analysed, and are suitable for systems with several degrees of freedom. The authors have numerically simulated the dynamics of a model of five nonlinearly coupled oscillators; the partial Lyapunov exponents have been used to compute a characteristic coherence time for each degree of freedom. These quantities give information which is complementary to the usual statistical correlation times, and show that the high-frequency degrees of freedom, while losing their correlation during the order-to-chaos transition, may keep their coherence over long times
Canonical solution of a system of long-range interacting rotators on a lattice
No full textThe canonical partition function of a system of rotators (classical X-Y spins) on a lattice, coupled by terms decaying as the inverse of their distance to the power alpha, is analytically computed. It is also shown how to compute a rescaling function that allows us to reduce the model, for any d-dimensional lattice and for any alpha<d, to the mean-field (alpha=0) model
On the unconventional amide I band in acetanilide
No full textWe developed a new model to study the molecular dynamics of the acetanilide (ACN) crystal by computer simulation. Low-frequency oscillations of the molecules as a whole were considered with high-frequency vibrations of the amidic degrees of freedom involved in hydrogen bonding. The low-temperature power spectrum has two peaks, shifted by 15 cm^-1, in the region of the amide I band: one of them corresponds to the so-called anomalous amide I band in the IR and Raman spectra of ACN. We found that this peak is due to the coupling of the low-frequency motion in the chain of molecules with the motion of the hydrogen-bonded protons, at variance with current suggestions
Metastable states in a class of long-range Hamiltonian systems
No full textWe numerically show that metastable states, similar to the quasi-stationary states found in the so-called Hamiltonian Mean Field Model, are also present in a generalized model in which N classical spins (rotators) interact through ferromagnetic couplings decaying as r(-alpha), where r is their distance over a regular lattice. Scaling laws with N are briefly discussed. (C) 2002 Elsevier Science B.V. All rights reserved
Quasisolitons on a diatomic chain at room temperature
No full textWe have studied analytically and numerically a nonlinear diatomic lattice with a cubic nearest-neighbor interaction potential. Our system is a one-dimensional chain of pairs of atoms interacting through a ‘‘hard’’ interaction, each pair being bound to the neighboring pairs by a ‘‘soft’’ interaction. This is a simple model for hydrogen-bonded molecular chains, like the spines in an α helix. We have used a multiple-scale reductive perturbative technique to transform the equations of motion, and derived a nonlinear Schrödinger equation describing the time evolution of localized solitonic excitations. We have also derived analytically, following the method introduced by Zakharov and Shabat, the thresholds for the creation of solitons when the chain is initially excited by a square wave, which is a model of a generic localized excitation. We have performed afterwards several molecular-dynamics simulations at zero temperature. We have found that localized solitonlike excitations can propagate along the chain without being significantly altered; if the initial excitation has a square-wave shape, it evolves into a solitonlike excitation also traveling along the chain. However, if the initial excitation is excessively broad it tends to disperse in a way similar to a linear system; on the other hand, if the excitation is too narrow it may become pinned at the initial position. Finally, we have repeated our simulations in presence of thermal disorder corresponding to temperatures ranging up to 300 K. We have found that the thermal vibrations not only do not destroy the solitonlike excitations, but do not even alter in any significant way their propagation along the molecular chain
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