A chiral elastic metamaterial beam for broadband vibration suppression

Quantum Chaos and Thermalization in Isolated Systems of Interacting Particles.

By means of full exact diagonalization, we study level statistics and the structure of the eigenvectors of one-dimensional gapless bosonic and fermionic systems across the transition from integrability to quantum chaos. These systems are integrable in the presence of only nearest-neighbor terms, whereas the addition of next-nearest-neighbor hopping and interaction may lead to the onset of chaos. We show that the strength of the next-nearest-neighbor terms required to observe clear signatures of nonintegrability is inversely proportional to the system size. Interestingly, the transition to chaos is also seen to depend on particle statistics, with bosons responding first to the integrability breaking terms. In addition, we discuss the use of delocalization measures as main indicators for the crossover from integrability to chaos and the consequent viability of quantum thermalization in isolated systems.

Onset of quantum chaos in one-dimensional bosonic and fermionic systems and its relation to thermalization.

Dynamics of quantum systems embedded in a continuum

Wave Motion in Periodic Flexural Beams and Characterization of the Transition Between Bragg Scattering and Local Resonance

The destruction caused by the earthquake of 19 September 1985 in Mexico City shows three remarkable features1. First, a (concentration of damage in the former lake bed; second, a peculiar distribution of high- and low-damage areas alternating within a few city blocks, and third, a selectivity for buildings between five and fifteen storeys high. While the last point is understood by civil engineers2 and the first confirms the relevance of the soft ground, the second feature is the most puzzling. To a physicist such a pattern evokes the idea of a standing wave, with low- and high-damage areas corresponding to nodes and antinodes. This suggests a resonance phenomenon of the waterlogged ground moving collectively. From the Navier equations of classical elasticity, it is known3 that a transfer of the incoming seismic-wave energy to longitudinal waves takes place if a sharp change from hard to soft ground exists. Solving then the two-dimensional Poisson equation for the longitudinal waves within the ancient lake boundaries, we show that for the observed seismic wave period of 2 s, a standing-wave solution exists which explains qualitatively the damage distribution pattern.

Possible resonance effect in the distribution of earthquake damage in Mexico City

Using longer spectra we reanalyze spectral properties of the two-body random ensemble studied 30 years ago. At the center of the spectra the old results are largely confirmed, and we show that the nonergodicity is essentially due to the variance of the lowest moments of the spectra. The longer spectra allow us to test and reach the limits of validity of French's correction for the number variance. At the edge of the spectra we discuss the problems of unfolding in more detail. With a Gaussian unfolding of each spectrum the nearest-neighbor spacing distribution between ground state and first exited state is shown to be stable. Using such an unfolding the distribution tends toward a semi-Poisson distribution for longer spectra. For comparison with the nuclear table ensemble we could use such unfolding obtaining similar results as in the early papers, but an ensemble with realistic splitting gives reasonable results if we just normalize the spacings in accordance with the procedure used for the data.

Spectral statistics of the two-body random ensemble revisited.

To measure and detect elastic waves in metallic rods a low-frequency electromagnetic-acoustic transducer has been developed. Frequencies range from a few hertz up to hundreds of kilohertz. With appropriate configuration of the transducer, compressional or torsional waves can be selectively excited or detected. Although the transducer can be used in many different situations, it has been tested and applied to a locally periodic rod, which consists of a finite number of unit cells. The measured wave amplitudes are compared with theoretical ones, obtained with the one-dimensional transfer matrix method, and excellent agreement is obtained.

Compressional and torsional wave amplitudes in rods with periodic structures.

The optical analogues of Bloch oscillations and their associated Wannier-Stark ladders have been recently analyzed. In this Letter we propose an elastic realization of these ladders, employing for this purpose the torsional vibrations of specially designed one-dimensional elastic systems. We have measured, for the first time, the ladder wave amplitudes, which are not directly accessible either in the quantum-mechanical or optical cases. The wave amplitudes are spatially localized and coincide rather well with theoretically predicted amplitudes. The rods we analyze can be used to localize different frequencies in different parts of the elastic systems and vice versa.

https://arxiv.org/pdf/cond-mat/0608343.pdf

J. Flores

Papers

Possible resonance effect in the distribution of earthquake damage in Mexico City

Spectral statistics of the two-body random ensemble revisited.

Compressional and torsional wave amplitudes in rods with periodic structures.

Wannier-stark ladders in one-dimensional elastic systems.

Experimental study of the Timoshenko beam theory predictions