Search results for "Exponent"
showing 10 items of 896 documents
Intermittent-Type Chaos in Nonsinusoidal Driven Oscillators
2000
The intermittent-type chaos occurring in rf- and dc- nonsinusoidal driven oscillators is investigated analytically and numerically. The attention is focused on a general class of oscillators in which the total potential VRP(,r) is the Remoissenet-Peyrard potential which has constant amplitude and is 2π-periodic in , and whose shape can be varied as a function of parameter r ( |r| < 1). A simple physical model for calculating analytically the Melnikov function is proposed. The onset of chaos is studied through an analysis of the phase space, a construction of the bifurcation diagram and a computation of the Lyapunov exponent. The parameter regions of chaotic behaviour predicted by the theore…
Collective Effects in Random Sequential Adsorption of Diffusing Hard Squares
1992
We study by Monte Carlo computer simulations random sequential adsorption (RSA) with diffusional relaxation, of lattice hard squares in two dimensions. While for RSA without diffusion the coverage approaches its maximum jamming value (large-time fractional coverage) exponentially, added diffusion allows the deposition process to proceed to the full coverage. The approach to the full coverage is consistent with the t**(-1/2) power law reminiscent of the equilibrium cluster coarsening in models with nonconserved order-parameter dynamics.
Analytical representations for relaxation functions of glasses
2002
Analytical representations in the time and frequency domains are derived for the most frequently used phenomenological fit functions for non-Debye relaxation processes. In the time domain the relaxation functions corresponding to the complex frequency dependent Cole-Cole, Cole-Davidson and Havriliak-Negami susceptibilities are also represented in terms of $H$-functions. In the frequency domain the complex frequency dependent susceptibility function corresponding to the time dependent stretched exponential relaxation function is given in terms of $H$-functions. The new representations are useful for fitting to experiment.
Surface-induced disorder in body-centered-cubic alloys
2000
We present Monte Carlo simulations of surface induced disordering in a model of a binary alloy on a bcc lattice which undergoes a first order bulk transition from the ordered DO3 phase to the disordered A2 phase. The data are analyzed in terms of an effective interface Hamiltonian for a system with several order parameters in the framework of the linear renormalization approach due to Brezin, Halperin and Leibler. We show that the model provides a good description of the system in the vicinity of the interface. In particular, we recover the logarithmic divergence of the thickness of the disordered layer as the bulk transition is approached, we calculate the critical behavior of the maxima o…
Effects of nonlinear sweep in the Landau-Zener-Stueckelberg effect
2002
We study the Landau-Zener-Stueckelberg (LZS) effect for a two-level system with a time-dependent nonlinear bias field (the sweep function) W(t). Our main concern is to investigate the influence of the nonlinearity of W(t) on the probability P to remain in the initial state. The dimensionless quantity epsilon = pi Delta ^2/(2 hbar v) depends on the coupling Delta of both levels and on the sweep rate v. For fast sweep rates, i.e., epsilon << l and monotonic, analytic sweep functions linearizable in the vicinity of the resonance we find the transition probability 1-P ~= epsilon (1+a), where a>0 is the correction to the LSZ result due to the nonlinearity of the sweep. Further increase …
Chaotic Cyclotron and Hall Trajectories Due to Spin-Orbit Coupling
2020
We demonstrate that the synergistic effect of a gauge field, Rashba spin-orbit coupling (SOC), and Zeeman splitting can generate chaotic cyclotron and Hall trajectories of particles. The physical origin of the chaotic behavior is that the SOC produces a spin-dependent (so-called anomalous) contribution to the particle velocity and the presence of Zeeman field reduces the number of integrals of motion. By using analytical and numerical arguments, we study the conditions of chaos emergence and report the dynamics both in the regular and chaotic regimes. {We observe the critical dependence of the dynamic patterns (such as the chaotic regime onset) on small variations in the initial conditions …
Finite-temperature correlations in the one-dimensional trapped and untrapped Bose gases
2003
We calculate the dynamic single-particle and many-particle correlation functions at non-zero temperature in one-dimensional trapped repulsive Bose gases. The decay for increasing distance between the points of these correlation functions is governed by a scaling exponent that has a universal expression in terms of observed quantities. This expression is valid in the weak-interaction Gross-Pitaevskii as well as in the strong-interaction Girardeau-Tonks limit, but the observed quantities involved depend on the interaction strength. The confining trap introduces a weak center-of-mass dependence in the scaling exponent. We also conjecture results for the density-density correlation function.
Ground state of the frustrated Hubbard model within DMFT: energetics of Mott insulator and metal from ePT and QMC
2004
We present a new method, ePT, for extrapolating few known coefficients of a perturbative expansion. Controlled by comparisons with numerically exact quantum Monte Carlo (QMC) results, 10th order strong-coupling perturbation theory (PT) for the Hubbard model on the Bethe lattice is reliably extrapolated to infinite order. Within dynamical mean-field theory (DMFT), we obtain continuous estimates of energy E and double occupancy D with unprecedented precision O(10^{-5}) for the Mott insulator above its stability edge U_{c1}=4.78 as well as critical exponents. In addition, we derive corresponding precise estimates for E and D in the metallic ground state from extensive low-temperature QMC simul…
Critical behaviour of coupled spin chains
1991
The authors investigate, using numerical computation of the eigenvalues of short chains, the critical behaviour of two composite spin models, which interpolate smoothly between isotropic Heisenberg chains with different values of S. For the first model which interpolates between S=1/2 and S=3/2 they find that the model is critical over the whole range and the values of the central charge and critical exponents (scaling dimensions) appear to be constant in the thermodynamic limit. In the second model, which interpolates between S=1/2 and S=1 they find that, except at S=1/2, the central charge is effectively zero, implying a non-critical behaviour.
Finite-size scaling analysis of the anisotropic critical behavior of the two-dimensional Ising model under shear
2010
The critical behavior of the two-dimensional Ising Model with non-conserved order parameter in steady-state shear is studied by large-scale Monte Carlo simulations. Studying the structure factor S(qx,qy) in the disordered phase, the ratio of correlation length exponents νx/νy in the two lattice directions (x,y) is estimated, and the critical temperature is determined as a function of the shear rate as Tc() − Tc(0) ∝ with ≈0.45. Critical exponents β≈0.37, γ≈1.1, ; ν⊥≈0.46, ν∥≈1.38 are roughly compatible with anisotropic hyperscaling.