Dynamical properties of an harmonic oscillator impacting a vibrating wall

The dynamics of a spring-mass system under repeated impact with a vibrating wall is investigated using the static wall approximation. The evolution of the harmonic oscillator is described by two coupled difference equations. These equations are solved numerically, and in some cases exact analytical expressions have also been found. For a periodically vibrating wall, Fermi acceleration is only found at resonance. There, the average rebounding velocity increases linearly with the number of collisions. Near resonance, the average rebounding velocity grows initially with the number of collisions and eventually reaches a plateau. In the vicinity of resonance, the motion of the oscillator exhibits scaling properties over a range of frequency ratios. The presence of dissipation at resonance destroys the Fermi-acceleration process and induces scaling behavior similar to that at near resonance. For a moving wall with a random amplitude at collisions, Fermi acceleration is observed independently of the ratio between the wall and oscillator frequencies. In this case the average rebounding velocity grows with the square root of the number of collisions with the wall. Also, in this latter case, dissipation suppresses the Fermi-acceleration mechanism and induces a scaling behavior with the same universality class as that of the dissipative bouncing ball model with random external perturbations

Quantum fidelity approach to the ground state properties of the 1D ANNNI model in a transverse field

In this work we analyze the ground-state properties of the $s=1/2$ one-dimensional ANNNI model in a transverse field using the quantum fidelity approach. We numerically determined the fidelity susceptibility as a function of the transverse field $B_x$ and the strength of the next-nearest-neighbor interaction $J_2$, for systems of up to 24 spins. We also examine the ground-state vector with respect to the spatial ordering of the spins. The ground-state phase diagram shows ferromagnetic, paramagnetic, floating, $\Braket{2,2}$ phases, and we predict an infinite number of modulated phases in the thermodynamic limit ($L \rightarrow \infty$). The transition lines separating the modulated phases seem to be of second-order, whereas the line between the floating and the $\Braket{2,2}$ phases is possibly of first-order.Comment: 10 pages, 20 figure

Corrections to scaling for diffusion in disordered media

We study the diffusion of a particle in a d-dimensional lattice where disorder arises from a random distribution of waiting times associated with each site of the lattice. Using scaling arguments we derive, in addition to the leading asymptotic behaviour, the correction-to-scaling terms for the mean square displacement. We also perform detailed Monte Carlo simulations for one, two and three dimensions which give results in substantial agreement with the scaling argument predictions

Comment on Long-Time Dynamics via Direct Summation of Infinite Continued Fractions

A Comment on the Letter by Z.-X. Cai et al., Phys. Rev. Lett. 68, 1637 (1992)

Breakdown of Hydrodynamics in the Classical ID Heisenberg Model

Extensive spin‐dynamics simulations have been performed to study the dynamical behavior of the classical Heisenberg chain at infinite temperatures and long wavelengths. We find that the energy and spin show distinctly different dynamics in the isotropic system. The energy correlation function follows the classical diffusion theory prediction, namely, it decays exponentially with q 2 t. In contrast, the spin correlation function is found to decay exponentially as q 2.12 t ln t implying a logarithmically divergent diffusion constant and the failure of the usual hydrodynamic assumptions

Critical behavior of the one-dimensional \u3ci\u3eS\u3c/i\u3e = 1 \u3ci\u3eXY\u3c/i\u3e model with single-ion anisotropy

We study the quantum critical behavior of the one-dimensional, S = 1 XY model in the presence of a single-ion anisotropy. Using a path-integral approach, we obtain, at T = 0 and for a positive anisotropy constant, a classical free-energy functional that allows discussion of the critical properties. The rescaling of frequencies is governed by the critical exponent z = 1. Renormalization-group arguments reveal that at criticality the system belongs to the same universality class as the isotropic 2-d XY model

Quantum phase transitions in the transverse one-dimensional Ising model with four-spin interactions

In this work we investigate the quantum phase transitions at zero temperature of the one-dimensional transverse Ising model with an extra term containing four-spin interactions. The competition between the energy couplings of the model leads to an interesting zero-temperature phase diagram. We use a modified Lanczos method to determine the ground state and the first excited state energies of the system, with sizes of up to 20 spins. We apply finite size scaling to the energy gap to obtain the boundary region where ferromagnetic to paramagnetic transition takes place. We also find the critical exponent associated with the correlation length. We find a degenerate ⟨3,1⟩ phase region. The first-order transition boundary between this phase and the paramagnetic phase is determined by analyzing the behavior of the transverse spin susceptibility as the system moves from one region to the other