5,317 research outputs found
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 , and
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
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
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
Transport properties of highly asymmetric hard-sphere mixtures
The static and dynamic properties of binary mixtures of hard spheres with a diameter ratio of sigma(B)/sigma(A)= 0.1 and a mass ratio of m(B)/m(A)= 0.001 are investigated using event driven molecular dynamics. The contact values of the pair correlation functions are found to compare favorably with recently proposed theoretical expressions. The transport coefficients of the mixture, determined from simulation, are compared to the predictions of the revised Enskog theory using both a third-order Sonine expansion and direct simulation Monte Carlo. Overall, the Enskog theory provides a fairly good description of the simulation data, with the exception of systems at the smallest mole fraction of larger spheres (x(A)=0.01) examined. A "fines effect" was observed at higher packing fractions, where adding smaller spheres to a system of large spheres decreases the viscosity of the mixture; this effect is not captured by the Enskog theory
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