Surprises in the suddenly-expanded infinite well

I study the time-evolution of a particle prepared in the ground state of an infinite well after the latter is suddenly expanded. It turns out that the probability density $|\Psi(x, t)|^{2}$ shows up quite a surprising behaviour: for definite times, {\it plateaux} appear for which $|\Psi(x, t)|^{2}$ is constant on finite intervals for $x$. Elements of theoretical explanation are given by analyzing the singular component of the second derivative $\partial_{xx}\Psi(x, t)$. Analytical closed expressions are obtained for some specific times, which easily allow to show that, at these times, the density organizes itself into regular patterns provided the size of the box in large enough; more, above some critical time-dependent size, the density patterns are independent of the expansion parameter. It is seen how the density at these times simply results from a construction game with definite rules acting on the pieces of the initial density.Comment: 24 pages, 14 figure

Geometric phase effects for wavepacket revivals

The study of wavepacket revivals is extended to the case of Hamiltonians which are made time-dependent through the adiabatic cycling of some parameters. It is shown that the quantal geometric phase (Berry's phase) causes the revived packet to be displaced along the classical trajectory, by an amount equal to the classical geometric phase (Hannay's angle), in one degree of freedom. A physical example illustrating this effect in three degrees of freedom is mentioned.Comment: Revtex, 11 pages, no figures

Superrevivals in the quantum dynamics of a particle confined in a finite square well potential

We examine the revival features in wave packet dynamics of a particle confined in a finite square well potential. The possibility of tunneling modifies the revival pattern as compared to an infinite square well potential. We study the dependence of the revival times on the depth of the square well and predict the existence of superrevivals. The nature of these superrevivals is compared with similar features seen in the dynamics of wavepackets in an anharmonic oscillator potential.Comment: 8 pages in Latex two-column format with 5 figures (eps). To appear in Physical Review

NMR experiment factors numbers with Gauss sums

We factor the number 157573 using an NMR implementation of Gauss sums.Comment: 4 pages 5 figure

Resonance Phenomenon Related to Spectral Singularities, Complex Barrier Potential, and Resonating Waveguides

A peculiar property of complex scattering potentials is the appearance of spectral singularities. These are energy eigenvalues for certain scattering states that similarly to resonance states have infinite reflection and transmission coefficients. This property reveals an interesting resonance effect with possible applications in waveguide physics. We study the spectral singularities of a complex barrier potential and explore their application in designing a waveguide that functions as a resonator. We show that for the easily accessible sizes of the waveguide and its gain region, we can realize the spectral singularity-related resonance phenomenon at almost every wavelength within the visible spectrum or outside it.Comment: Published version, 20 pages, 2 tables, 7 figure

Oxidative stress in the brain and arterial hypertension

Universidade Federal de São Paulo, Dept Physiol, BR-04023060 São Paulo, BrazilUniversidade Federal de São Paulo, Dept Physiol, BR-04023060 São Paulo, BrazilWeb of Scienc

Triggered optical coherence tomography for capturing rapid periodic motion

Quantitative cross-sectional imaging of vocal folds during phonation is potentially useful for diagnosis and treatments of laryngeal disorders. Optical coherence tomography (OCT) is a powerful technique, but its relatively low frame rates makes it challenging to visualize rapidly vibrating tissues. Here, we demonstrate a novel method based on triggered laser scanning to capture 4-dimensional (4D) images of samples in motu at audio frequencies over 100 Hz. As proof-of-concept experiments, we applied this technique to imaging the oscillations of biopolymer gels on acoustic vibrators and aerodynamically driven vibrations of the vocal fold in an ex vivo calf larynx model. Our results suggest that triggered 4D OCT may be useful in understanding and assessing the function of vocal folds and developing novel treatments in research and clinical settings

Quantum Revivals in Periodically Driven Systems close to nonlinear resonance

We calculate the quantum revival time for a wave-packet initially well localized in a one-dimensional potential in the presence of an external periodic modulating field. The dependence of the revival time on various parameters of the driven system is shown analytically. As an example of application of our approach, we compare the analytically obtained values of the revival time for various modulation strengths with the numerically computed ones in the case of a driven gravitational cavity. We show that they are in very good agreement.Comment: 14 pages, 1 figur