Right eigenvalue equation in quaternionic quantum mechanics

We study the right eigenvalue equation for quaternionic and complex linear matrix operators defined in n-dimensional quaternionic vector spaces. For quaternionic linear operators the eigenvalue spectrum consists of n complex values. For these operators we give a necessary and sufficient condition for the diagonalization of their quaternionic matrix representations. Our discussion is also extended to complex linear operators, whose spectrum is characterized by 2n complex eigenvalues. We show that a consistent analysis of the eigenvalue problem for complex linear operators requires the choice of a complex geometry in defining inner products. Finally, we introduce some examples of the left eigenvalue equations and highlight the main difficulties in their solution.Comment: 24 pages, AMS-Te

Quaternionic eigenvalue problem

We discuss the (right) eigenvalue equation for $\mathbb{H}$, $\mathbb{C}$ and $\mathbb{R}$ linear quaternionic operators. The possibility to introduce an isomorphism between these operators and real/complex matrices allows to translate the quaternionic problem into an {\em equivalent} real or complex counterpart. Interesting applications are found in solving differential equations within quaternionic formulations of quantum mechanics.Comment: 13 pages, AMS-Te

A New Phase Time Formula for Opaque Barrier Tunneling

After a brief review of the derivation of the standard phase time formula, based on the use of the stationary phase method, we propose, in the opaque limit, an alternative method to calculate the phase time. The new formula for the phase time is in excellent agreement with the numerical simulations and shows that for wave packets whose upper limit of the momentum distribution is very close to the barrier height, the transit time is proportional to the barrier width.Comment: 9 pages, 2 figure

Quaternionic Electroweak Theory and CKM Matrix

We find in our quaternionic version of the electroweak theory an apparently hopeless problem: In going from complex to quaternions, the calculation of the real-valued parameters of the CKM matrix drastically changes. We aim to explain this quaternionic puzzle.Comment: 8, Revtex, Int. J. Theor. Phys. (to be published

Quantum coherent transport in a three-arm beam splitter and a Braess paradox

The Braess paradox encountered in classical networks is a counterintuitive phenomenon when the flow in a road network can be impeded by adding a new road or, more generally, the overall net performance can degrade after addition of an extra available choice. In this work, we discuss the possibility of a similar effect in a phase-coherent quantum transport and demonstrate it by example of a simple Y-shaped metallic fork. To reveal the Braess-like partial suppression of the charge flow in such device, it is proposed to transfer two outgoing arms into a superconducting state. We show that the differential conductance-vs-voltage spectrum of the hybrid fork structure varies considerably when the extra link between the two superconducting leads is added and it can serve as an indicator of quantum correlations which manifest themselves in the quantum Braess paradox.Comment: 9 pages, 3 figures, the author version presented at the Quantum 2017 Workshop (Torino, Italy, 7-13 May 2017) and submitted to the International Journal of Quantum Information; v2: reference 9 added and the introduction extende

Substrate induced proximity effect in superconducting niobium nanofilms

Structural and superconducting properties of high quality Niobium nanofilms with different thicknesses are investigated on silicon oxide and sapphire substrates. The role played by the different substrates and the superconducting properties of the Nb films are discussed based on the defectivity of the films and on the presence of an interfacial oxide layer between the Nb film and the substrate. The X-ray absorption spectroscopy is employed to uncover the structure of the interfacial layer. We show that this interfacial layer leads to a strong proximity effect, specially in films deposited on a SiO$_2$ substrate, altering the superconducting properties of the Nb films. Our results establish that the critical temperature is determined by an interplay between quantum-size effects, due to the reduction of the Nb film thicknesses, and proximity effects

Comparison of different techniques to study the nanostructure and the microstructure of cementitious materials with and without superabsorbent polymers

It is difficult to study the microstructural porosity in time without destroying the samples and stopping hydration. Current techniques mainly involve mercury intrusion porosimetry and microscopic analysis. These destructive techniques are able to give information on the microstructure, but the nanostructure is affected due to sample preparation. Dynamic vapour sorption is a technique which is not often used to study the nanostructure of cementitious materials and requires the application of different models. Furthermore, nuclear magnetic resonance can be applied to non-destructive study not only the total water content but also the pore size distribution by comparing the T2 relaxation times, and can be combined with cryoporometry. In this paper, these different measuring techniques are compared and linked to each other. The obtained nano- and microstructures are compared to different models found in literature. Pore sizes in the range of 1.5–2 nm and of 8–12 nm are found, reflecting the gel pores. In addition, some bigger capillary pores are found. The measuring techniques are complementary to each other as they study different pore size ranges and are based on different phenomena.</p

Dispersion processes in weakly dissipative tidal channels

We report the results of an extensive experimental campaign dedicated to the analysis of turbulent dispersion owing to the circulations in tidal environments, characterized by a tidal inlet and a channel with lateral tidal flats. We focus on weakly-convergent and weakly-dissipative estuaries or tidal embankments, where the internal waters communicate with the open sea through an inlet mouth. Tides are reproduced as single or multiple harmonics waves. Particle Image Velocimetry is employed to measure two-dimensional surface velocity fields. Large-scale macro-vortices, generated by vortex shedding during the flood phase from the inlet barrier, tend to occupy the entire tidal flats width and are completely flushed out during the ebb phase. In all experiments, an intense residual current, with shape influenced by the large-scale flood vortices, is observed. The presence of large-scale vortices and of a residual current strongly influences the Lagrangian auto-correlation functions and the corresponding absolute dispersion time evolution. Looping auto-correlations are the signature of both periodic forcing and vortices, ultimately, leading to super diffusive regimes. An asymptotic Brownian regime is always found for the investigated range of parameters allowing for an estimate of the horizontal dispersion coefficients which turn out to decrease with the friction parameter and tend to be enhanced when the semi-diurnal constituents prevail. Finally, multiple particle statistics show multiple regimes depending on particle separations, compared to a typical injection length scale that seems to coincide with the inlet mouth dimension

Dimensional crossover and incipient quantum size effects in superconducting niobium nanofilms

Superconducting and normal state properties of sputtered Niobium nanofilms have been systematically investigated, as a function of film thickness in a d=9-90 nm range, on different substrates. The width of the superconducting-to-normal transition for all films remained in few tens of mK, thus remarkably narrow, confirming their high quality. We found that the superconducting critical current density exhibits a pronounced maximum, three times larger than its bulk value, for film thickness around 25 nm, marking the 3D-to-2D crossover. The extracted magnetic penetration depth shows a sizeable enhancement for the thinnest films, aside the usual demagnetization effects. Additional amplification effects of the superconducting properties have been obtained in the case of sapphire substrates or squeezing the lateral size of the nanofilms. For thickness close to 20 nm we also measured a doubled perpendicular critical magnetic field compared to its saturation value for d>33 nm, indicating shortening of the correlation length and the formation of small Cooper pairs in the condensate. Our data analysis evidences an exciting interplay between quantum-size and proximity effects together with strong-coupling effects and importance of disorder in the thinnest films, locating the ones with optimally enhanced critical properties close to the BCS-BEC crossover regime