Entanglement entropy and macroscopic quantum states with dipolar bosons in a triple-well potential

We study interacting dipolar atomic bosons in a triple-well potential within a ring geometry. This system is shown to be equivalent to a three-site Bose-Hubbard model. We analyze the ground state of dipolar bosons by varying the effective on-site interaction. This analysis is performed both numerically and analytically by using suitable coherent-state representations of the ground state. The latter exhibits a variety of forms ranging from the su(3) coherent state in the delocalization regime to a macroscopic cat-like state with fully localized populations, passing for a coexistence regime where the ground state displays a mixed character. We characterize the quantum correlations of the ground state from the bi-partition perspective. We calculate both numerically and analytically (within the previous coherent-state representation) the single-site entanglement entropy which, among various interesting properties, exhibits a maximum value in correspondence to the transition from the cat-like to the coexistence regime. In the latter case, we show that the ground-state mixed form corresponds, semiclassically, to an energy exhibiting two almost-degenerate minima.Comment: 9 pages, 2 figure

Violation of cluster decomposition and absence of light cones in local integer and half-integer spin chains

We compute the ground-state correlation functions of an exactly solvable chain of integer spins, recently introduced in [R. Movassagh and P. W. Shor, arXiv:1408.1657], whose ground state can be expressed in terms of a uniform superposition of all colored Motzkin paths. Our analytical results show that for spin s≥2 there is a violation of the cluster decomposition property. This has to be contrasted with s=1, where the cluster property holds. Correspondingly, for s=1 one gets a light-cone profile in the propagation of excitations after a local quench, while the cone is absent for s=2, as shown by time dependent density-matrix renormalization group. Moreover, we introduce an original solvable model of half-integer spins, which we refer to as Fredkin spin chain, whose ground state can be expressed in terms of superposition of all Dyck paths. For this model we exactly calculate the magnetization and correlation functions, finding that for s=1/2, a conelike propagation occurs, while for higher spins, s≥3/2, the colors prevent any cone formation and clustering is violated, together with square root deviation from the area law for the entanglement entropy

Dynamics and energy spectra of aperiodic discrete-time quantum walks

We investigate the role of different aperiodic sequences in the dynamics of single quantum particles in discrete space and time. For this we consider three aperiodic sequences, namely, the Fibonacci, Thue-Morse, and Rudin-Shapiro sequences, as examples of tilings the diffraction spectra of which have pure point, singular continuous, and absolutely continuous support, respectively. Our interest is to understand how the order, intrinsically introduced by the deterministic rule used to generate the aperiodic sequences, is reflected in the dynamical properties of the quantum system. For this system we consider a single particle undergoing a discrete-time quantum walk (DTQW), where the aperiodic sequences are used to distribute the coin operations at different lattice positions (inhomogeneous DTQW) or by applying the same coin operation at all lattice sites at a given time but choosing different coin operation at each time step according to the chosen aperiodic sequence (time dependent DTQW). We study the energy spectra and the spreading of an initially localized wave packet for different cases, finding that in the case of Fibonacci and Thue-Morse tilings the system is superdiffusive, whereas in the Rudin-Shapiro case it is strongly subdiffusive. Trying to understand this behavior in terms of the energy spectra, we look at the survival amplitude as a function of time. By means of the echo we present strong evidence that, although the three orderings are very different as evidenced by their diffraction spectra, the energy spectra are all singular continuous except for the inhomogeneous DTQW with the Rudin-Shapiro sequence where it is discrete. This is in agreement with the observed strong localization both in real space and in the Hilbert space. Our paper is particularly interesting because quantum walks can be engineered in laboratories by means of ultracold gases or in optical waveguides, and therefore would be a perfect playground to study singular continuous energy spectra in a completely controlled quantum setup

Violation of Cluster Decomposition and Absence of Light-Cones in Local Integer and Half-Integer Spin Chains

We compute the ground-state correlation functions of an exactly solvable chain of integer spins, recently introduced in [R. Movassagh and P. W. Shor, arXiv: 1408.1657], whose ground state can be expressed in terms of a uniform superposition of all colored Motzkin paths. Our analytical results show that for spin s >= 2 there is a violation of the cluster decomposition property. This has to be contrasted with s = 1, where the cluster property holds. Correspondingly, for s = 1 one gets a light-cone profile in the propagation of excitations after a local quench, while the cone is absent for s = 2, as shown by time dependent density-matrix renormalization group. Moreover, we introduce an original solvable model of half-integer spins, which we refer to as Fredkin spin chain, whose ground state can be expressed in terms of superposition of all Dyck paths. For this model we exactly calculate the magnetization and correlation functions, finding that for s = 1/2, a conelike propagation occurs, while for higher spins, s >= 3/2, the colors prevent any cone formation and clustering is violated, together with square root deviation from the area law for the entanglement entropy. \ua9 2016 American Physical Society

The Raman coupling function in amorphous silica and the nature of the long wavelength excitations in disordered systems

New Raman and incoherent neutron scattering data at various temperatures and molecular dynamic simulations in amorphous silica, are compared to obtain the Raman coupling coefficient $C(\omega)$ and, in particular, its low frequency limit. This study indicates that in the $\omega \to 0$ limit $C(\omega)$ extrapolates to a non vanishing value, giving important indications on the characteristics of the vibrational modes in disordered materials; in particular our results indicate that even in the limit of very long wavelength the local disorder implies non-regular local atomic displacements.Comment: Revtex, 4 ps figure

Elastic constant dishomogeneity and Q2Q^2 dependence of the broadening of the dynamical structure factor in disordered systems

We propose an explanation for the quadratic dependence on the momentum $Q$, of the broadening of the acoustic excitation peak recently found in the study of the dynamic structure factor of many real and simulated glasses. We ascribe the observed $Q^2$ law to the spatial fluctuations of the local wavelength of the collective vibrational modes, in turn produced by the dishomegeneity of the inter-particle elastic constants. This explanation is analitically shown to hold for 1-dimensional disordered chains and satisfatorily numerically tested in both 1 and 3 dimensions.Comment: 4 pages, RevTeX, 5 postscript figure

High frequency sound waves in vitreous silica

We report a molecular dynamics simulation study of the sound waves in vitreous silica in the mesoscopic exchanged momentum range. The calculated dynamical structure factors are in quantitative agreement with recent experimental inelastic neutron and x-ray scattering data. The analysis of the longitudinal and transverse current spectra allows to discriminate between opposite interpretations of the existing experimental data in favour of the propagating nature of the high frequency sound waves.Comment: 4 pages, Revtex, 4 ps figures; to be published in Phys. Rev. Lett., February 198

Vibrational spectrum of topologically disordered systems

The topological nature of the disorder of glasses and supercooled liquids strongly affects their high-frequency dynamics. In order to understand its main features, we analytically studied a simple topologically disordered model, where the particles oscillate around randomly distributed centers, interacting through a generic pair potential. We present results of a resummation of the perturbative expansion in the inverse particle density for the dynamic structure factor and density of states. This gives accurate results for the range of densities found in real systems.Comment: Completely rewritten version, accepted in Physical Review Letter

Relaxation processes in harmonic glasses?

A relaxation process, with the associated phenomenology of sound attenuation and sound velocity dispersion, is found in a simulated harmonic Lennard-Jones glass. We propose to identify this process with the so called microscopic (or instantaneous) relaxation process observed in real glasses and supercooled liquids. A model based on the memory function approach accounts for the observation, and allows to relate to each others: 1) the characteristic time and strength of this process, 2) the low frequency limit of the dynamic structure factor of the glass, and 3) the high frequency sound attenuation coefficient, with its observed quadratic dependence on the momentum transfer.Comment: 11 pages, 3 figure

Severe Aortic Stenosis and Myocardial Function: Diagnostic and Prognostic Usefulness of Ultrasonic Integrated Backscatter Analysis

Background— The aim of this study was to assess the myocardial reflectivity pattern in severe aortic valve stenosis through the use of integrated backscatter (IBS) analysis. Patients with aortic stenosis (AS) were carefully selected in the Department of Cardiology. Methods and Results— Thirty-five subjects (AS: valve orifice ≤1 cm2; 12 female; mean age, 71.8±6.2 years) and 25 healthy subjects were studied. All subjects of the study had conventional 2D-Doppler echocardiography and IBS. Backscatter signal was sampled at the septum and posterior wall levels. Patients with AS were divided into 2 groups: 16 patients with initial signs of congestive heart failure and a depressed left ventricular systolic function (DSF) (ejection fraction [EF] range, 35% to 50%) and 19 asymptomatic patients with normal left ventricular systolic function (NSF) (EF >50%). Myocardial echo intensity (pericardium related) was significantly higher at the septum and posterior wall levels in DSF than in NSF and in control subjects. IBS variation, as an expression of variation of the signal, appeared to be significantly lower in AS with DSF than in NSF and in control subjects, at both the septum and posterior wall levels. Patients with DSF underwent aortic valve replacement, and, during surgical intervention, a septal myocardial biopsy was made for evaluation of myocardium/fibrosis ratio. Abnormally increased echo intensity was detected in left ventricular pressure overload by severe aortic stenosis and correlated with increase of myocardial collagen content (operating biopsy). Conclusions— One year after aortic valve replacement, we observed a significant reduction of left ventricular mass, and, only if pericardial indexed IBS value (reduction of interstitial fibrosis) decreased, it was possible to observe an improvement of EF and of IBS variation