3,391 research outputs found
On C*-algebras generated by pairs of q-commuting isometries
We consider the C*-algebras O_2^q and A_2^q generated, respectively, by
isometries s_1, s_2 satisfying the relation s_1^* s_2 = q s_2 s_1^* with |q| <
1 (the deformed Cuntz relation), and by isometries s_1, s_2 satisfying the
relation s_2 s_1 = q s_1 s_2 with |q| = 1. We show that O_2^q is isomorphic to
the Cuntz-Toeplitz C*-algebra O_2^0 for any |q| < 1. We further prove that
A_2^{q_1} is isomorphic to A_2^{q_2} if and only if either q_1 = q_2 or q_1 =
complex conjugate of q_2. In the second part of our paper, we discuss the
complexity of the representation theory of A_2^q. We show that A_2^q is *-wild
for any q in the circle |q| = 1, and hence that A_2^q is not nuclear for any q
in the circle.Comment: 18 pages, LaTeX2e "article" document class; submitted. V2 clarifies
the relationships between the various deformation systems treate
Critical Current 0- Transition in Designed Josephson Quantum Dot Junctions
We report on quantum dot based Josephson junctions designed specifically for
measuring the supercurrent. From high-accuracy fitting of the current-voltage
characteristics we determine the full magnitude of the supercurrent (critical
current). Strong gate modulation of the critical current is observed through
several consecutive Coulomb blockade oscillations. The critical current crosses
zero close to, but not at, resonance due to the so-called 0- transition in
agreement with a simple theoretical model.Comment: 5 pages, 4 figures, (Supplementary information available at
http://www.fys.ku.dk/~hij/public/nl_supp.pdf
Electron transport in single wall carbon nanotube weak links in the Fabry-Perot regime
We fabricated reproducible high transparency superconducting contacts
consisting of superconducting Ti/Al/Ti trilayers to gated single-walled carbon
nanotubes (SWCNTs). The reported semiconducting SWCNT have normal state
differential conductance up to and exhibit clear Fabry-Perot
interference patterns in the bias spectroscopy plot. We observed subharmonic
gap structure in the differential conductance and a distinct peak in the
conductance at zero bias which is interpreted as a manifestation of a
supercurrent. The gate dependence of this supercurrent as well as the excess
current are examined and compared to a coherent theory of superconducting point
contacts with good agreement.Comment: 10 pages, 4 figure
Convex optimization problem prototyping for image reconstruction in computed tomography with the Chambolle-Pock algorithm
The primal-dual optimization algorithm developed in Chambolle and Pock (CP),
2011 is applied to various convex optimization problems of interest in computed
tomography (CT) image reconstruction. This algorithm allows for rapid
prototyping of optimization problems for the purpose of designing iterative
image reconstruction algorithms for CT. The primal-dual algorithm is briefly
summarized in the article, and its potential for prototyping is demonstrated by
explicitly deriving CP algorithm instances for many optimization problems
relevant to CT. An example application modeling breast CT with low-intensity
X-ray illumination is presented.Comment: Resubmitted to Physics in Medicine and Biology. Text has been
modified according to referee comments, and typos in the equations have been
correcte
Superconductivity-enhanced bias spectroscopy in carbon nanotube quantum dots
We study low-temperature transport through carbon nanotube quantum dots in
the Coulomb blockade regime coupled to niobium-based superconducting leads. We
observe pronounced conductance peaks at finite source-drain bias, which we
ascribe to elastic and inelastic cotunneling processes enhanced by the
coherence peaks in the density of states of the superconducting leads. The
inelastic cotunneling lines display a marked dependence on the applied gate
voltage which we relate to different tunneling-renormalizations of the two
subbands in the nanotube. Finally, we discuss the origin of an especially
pronounced sub-gap structure observed in every fourth Coulomb diamond
A triple quantum dot in a single wall carbon nanotube
A top-gated single wall carbon nanotube is used to define three coupled
quantum dots in series between two electrodes. The additional electron number
on each quantum dot is controlled by top-gate voltages allowing for current
measurements of single, double and triple quantum dot stability diagrams.
Simulations using a capacitor model including tunnel coupling between
neighboring dots captures the observed behavior with good agreement.
Furthermore, anti-crossings between indirectly coupled levels and higher order
cotunneling are discussed.Comment: Supporting Information is available at Nano Lett. website (see link
below
On boson algebras as Hopf algebras
Certain types of generalized undeformed and deformed boson algebras which
admit a Hopf algebra structure are introduced, together with their Fock-type
representations and their corresponding -matrices. It is also shown that a
class of generalized Heisenberg algebras including those algebras including
those underlying physical models such as that of Calogero-Sutherland, is
isomorphic with one of the types of boson algebra proposed, and can be
formulated as a Hopf algebra.Comment: LaTex, 18 page
The tunnel magnetoresistance in chains of quantum dots weakly coupled to external leads
We analyze numerically the spin-dependent transport through coherent chains
of three coupled quantum dots weakly connected to external magnetic leads. In
particular, using the diagrammatic technique on the Keldysh contour, we
calculate the conductance, shot noise and tunnel magnetoresistance (TMR) in the
sequential and cotunneling regimes. We show that transport characteristics
greatly depend on the strength of the interdot Coulomb correlations, which
determines the spacial distribution of electron wave function in the chain.
When the correlations are relatively strong, depending on the transport regime,
we find both negative TMR as well as TMR enhanced above the Julliere value,
accompanied with negative differential conductance (NDC) and super-Poissonian
shot noise. This nontrivial behavior of tunnel magnetoresistance is associated
with selection rules that govern tunneling processes and various high-spin
states of the chain that are relevant for transport. For weak interdot
correlations, on the other hand, the TMR is always positive and not larger than
the Julliere TMR, although super-Poissonian shot noise and NDC can still be
observed
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