Path-Integral Ground-State and Superfluid Hydrodynamics of a Bosonic Gas of Hard Spheres

We study a bosonic gas of hard spheres by using of the exact zero-temperature Path-Integral Ground-State (PIGS) Monte Carlo method and the equations of superfluid hydrodynamics. The PIGS method is implemented to calculate for the bulk system the energy per particle and the condensate fraction through a large range of the gas parameter $na^3$ (with $n$ the number density and $a$ the s--wave scattering length), going from the dilute gas into the solid phase. The Maxwell construction is then adopted to determine the freezing at $na^3=0.278\pm 0.001$ and the melting at $na^3=0.286\pm 0.001$. In the liquid phase, where the condensate fraction is finite, the equations of superfluid hydrodynamics, based on the PIGS equation of state, are used to find other relevant quantities as a function of the gas parameter: the chemical potential, the pressure and the sound velocity. In addition, within the Feynman's approximation, from the PIGS static structure factor we determine the full excitation spectrum, which displays a maxon-roton behavior when the gas parameter is close to the freezing value. Finally, the equations of superfluid hydrodynamics with the PIGS equation of state are solved for bosonic system under axially--symmetric harmonic confinement obtaining its collective breathing modes.Comment: 7 pages, 7 figures; improved version to be published in Phys. Rev.

Superfluid behavior of quasi-1D p-H2_2 inside carbon nanotube

We perform ab-initio Quantum Monte Carlo simulations of para-hydrogen (pH$_2$) at $T=0$ K confined in carbon nanotubes (CNT) of different radii. The radial density profiles show a strong layering of the pH$_2$ molecules which grow, with increasing number of molecules, in solid concentric cylindrical shells and eventually a central column. The central column can be considered an effective one-dimensional (1D) fluid whose properties are well captured by the Tomonaga-Luttinger liquid theory. The Luttinger parameter is explicitly computed and interestingly it shows a non-monotonic behavior with the linear density similar to what found for pure 1D $^3$He. Remarkably, for the central column in a (10,10) CNT, we found an ample linear density range in which the Luttinger liquid is (i) superfluid and (ii) stable against a weak disordered external potential, as the one expected inside realistic pores. This superfluid behavior could be experimentally revealed in bundles of carbon nanotubes, where deviations from classical inertial values associated with superfluid density could be measured via torsional oscillator techniques. In summary, our results suggest that pH$_2$ within carbon nanopores could be a practical realization of the long sought-after, elusive superfluid phase of parahydrogen.Comment: 5 pages, 3 figures accepted as PRB rapi

Supersolid structure and excitation spectrum of soft-core bosons in 3D

By means of a mean-field method, we have studied the zero temperature structure and excitation spectrum of a three-dimensional soft-core bosonic system for a value of the interaction strength that favors a crystal structure made of atomic nano-clusters arranged with FCC ordering. In addition to the longitudinal and transverse phonon branches expected for a normal crystal, the excitation spectrum shows a soft mode related to the breaking of gauge symmetry, which signals a partial superfluid character of the solid. Additional evidence of supersolidity is provided by the calculation of the superfluid fraction, which shows a first-order drop, from 1 to 0.4, at the liquid-supersolid transition and a monotonic decrease as the interaction strength parameter is increased. The conditions for the coexistence of the supersolid with the homogeneous superfluid are discussed, and the surface tension of a representative solid-liquid interface is calculated.Comment: 11 pages, 11 figure

Quantum Monte Carlo study of a vortex in superfluid 4^4He and search for a vortex state in the solid

We have performed a microscopic study of a straight quantized vortex line in three dimensions in condensed $^4$He at zero temperature using the Shadow Path Integral Ground State method and the fixed-phase approximation. We have characterized the energy and the local density profile around the vortex axis in superfluid $^4$He at several densities, ranging from below the equilibrium density up to the overpressurized regime. For the Onsager-Feynman (OF) phase our results are exact and represent a benchmark for other theories. The inclusion of backflow correlations in the phase improves the description of the vortex with respect to the OF phase by a large reduction of the core energy of the topological excitation. At all densities the phase with backflow induces a partial filling of the vortex core and this filling slightly increases with density. The core size slightly decreases for increasing density and the density profile has well defined density dependent oscillations whose wave vector is closer to the wave vector of the main peak in the static density response function rather than to the roton wave vector. Our results can be applied to vortex rings of large radius $R$ and we find good agreement with the experimental value of the energy as function of $R$ without any free parameter. We have studied also $^4$He above the melting density in the solid phase using the same functional form for the phase as in the liquid. We found that off-diagonal properties of the solid are not qualitatively affected by the velocity field induced by the vortex phase, both with and without backflow correlations. Therefore we find evidence that a perfect $^4$He crystal is not a marginally stable quantum solid in which rotation would be able to induce off-diagonal long-range coherence.Comment: 15 pages, 8 figure

Sviluppo di tecniche di monitoraggio delle prestazioni di processi chimici controllati

La tesi proposta tratta del monitoraggio delle prestazioni dei controllori in processi chimici. Diverse sono le cause di malfunzionamento: da valvole con attrito, a regolatori sintonizzati impropriamente alla propagazione di disturbi negli impianti. Con questa tesi si vuole illustrare una metodologia per individuare le cause di mancata prestazione in modo da poterle classificare ed intraprendere le necessarie contromisure. In particolare é stato approfondito il problema della sintonizzazione dei regolatori ed è stata proposta una tecnica di identificazione basata sullo studio dei disturbi, evitando quindi ulteriori sollecitazioni agli impianti per variazioni di set-point. Inoltre è stato affrontato il problema dell’attrito sulle valvole utilizzando diverse tecniche di individuazione automatica originali e già presentetate in letteratura. Il tutto è stato organizzato in un software sviluppato in ambiente Matlab

Density functional theory of a trapped Bose gas with tunable scattering length: from weak-coupling to unitarity

We study an interacting Bose gas at T=0 under isotropic harmonic confinement within Density Functional Theory in the Local Density approximation. The energy density functional, which spans the whole range of positive scattering lengths up to the unitary regime (infinite scattering length), is obtained by fitting the recently calculated Monte Carlo bulk equation of state [Phys. Rev. A 89, 041602(R) (2014)]. We compare the density profiles of the trapped gas with those obtained by MC calculations. We solve the time-dependent Density Functional equation to study the effect of increasing values of the interaction strength on the frequencies of monopole and quadrupole oscillations of the trapped gas. We find that the monopole breathing mode shows a non-monotonous behavior as a function of the scattering length. We also consider the damping effect of three-body losses on such modes.Comment: 5 pages, submitted to EP

Quenched dynamics of the momentum distribution of the unitary Bose gas

We study the quenched dynamics of the momentum distribution of a unitary Bose gas under isotropic harmonic confinement within a time-dependent density functional approach based on our recently calculated Monte Carlo (MC) bulk equation of state. In our calculations the inter-atomic s-wave scattering length of the trapped bosons is suddenly increased to a very large value and the real-time evolution of the system is studied. Prompted by the very recent experimental data of $^{85}$Rb atoms at unitarity [Nature Phys. 10, 116 (2014)] we focus on the momentum distribution as a function of time. Our results suggest that at low momenta, a quasi-stationary momentum distribution is reached after a long transient, contrary to what found experimentally for large momenta which equilibrate on a time scale shorter than the one for three body losses.Comment: 8 pages, 4 figures, submitted to a Special Issue of Few-Body Systems "Systems on the verge of the stability

Lightweight Synchronization Algorithm with Self-Calibration for Industrial LORA Sensor Networks

Wireless sensor and actuator networks are gaining momentum in the era of Industrial Internet of Things IIoT. The usage of the close-loop data from sensors in the manufacturing chain is extending the common monitoring scenario of the Wireless Sensors Networks WSN where data were just logged. In this paper we present an accurate timing synchronization for TDMA implemented on the state of art IoT radio, such as LoRa, that is a good solution in industrial environments for its high robustness. Experimental results show how it is possible to modulate the drift correction and keep the synchronization error within the requirements