10,507 research outputs found
Scales for co-compact embeddings of virtually free groups
Let be a group which is virtually free of rank at least 2 and let
be the family of totally disconnected, locally
compact groups containing as a co-compact lattice.
We prove that the values of the scale function with respect to groups in
evaluated on the subset have only finitely
many prime divisors. This can be thought of as a uniform property of the family
.Comment: 12 pages; key words: uniform lattice, virtually free group, totally
disconnected group, scale function (Error in references corrected in version
2
Contraction groups and scales of automorphisms of totally disconnected locally compact groups
We study contraction groups for automorphisms of totally disconnected locally
compcat groups using the scale of the automorphism as a tool. The contraction
group is shown to be unbounded when the inverse automorphism has non-trivial
scale and this scale is shown to be the inverse value of the modular function
on the closure of the contraction group at the automorphism. The closure of the
contraction group is represented as acting on a homogenous tree and closed
contraction groups are characterised.Comment: revised version, 29 pages, to appear in Israel Journal of
Mathematics, please note that document starts on page
Andreev bound states probed in three-terminal quantum dots
We demonstrate several new electron transport phenomena mediated by Andreev
bound states (ABSs) that form on three-terminal carbon nanotube (CNT) QDs, with
one superconducting (S) contact in the center and two adjacent normal metal (N)
contacts. Three-terminal spectroscopy allows us to identify the coupling to the
N contacts as the origin of the Andreev resonance (AR) linewidths and to
determine the critical coupling strengths to S, for which a ground state
transition S-QD systems can occur. We ascribe replicas of the lowest-energy ABS
resonance to transitions between the ABS and odd-parity excited QD states, a
process called excited state ABS resonances. In the conductance between the two
N contacts we find a characteristic pattern of positive and negative
differential subgap conductance, which we explain by considering two nonlocal
processes, the creation of Cooper pairs in S by electrons from both N
terminals, and a novel mechanism called resonant ABS tunneling. In the latter,
electrons are transferred via the ABS without creating Cooper pairs in S. The
three-terminal geometry also allows spectroscopy experiments with different
boundary conditions, for example by leaving S floating. Surprisingly, we find
that, depending on the boundary conditions, the experiments either show
single-particle Coulomb blockade resonances, ABS characteristics, or both in
the same measurements, seemingly contradicting the notion of ABSs replacing the
single particle states as eigenstates of the QD. We qualitatively explain these
results as originating from the finite time scale required for the coherent
oscillations between the superposition states after a single electron tunneling
event. These experiments demonstrate that three-terminal experiments on a
single complex quantum object can also be useful to investigate charge dynamics
otherwise not accessible due to the very high frequencies.Comment: 15 pages, 16 figure
Resonant and inelastic Andreev tunneling observed on a carbon nanotube quantum dot
We report the observation of two fundamental sub-gap transport processes
through a quantum dot (QD) with a superconducting contact. The device consists
of a carbon nanotube contacted by a Nb superconducting and a normal metal
contact. First, we find a single resonance with position, shape and amplitude
consistent with the theoretically predicted resonant Andreev tunneling (AT)
through a single QD level. Second, we observe a series of discrete replicas of
resonant AT at a separation of eV, with a gate, bias and
temperature dependence characteristic for boson-assisted, inelastic AT, in
which energy is exchanged between a bosonic bath and the electrons. The
magnetic field dependence of the replica's amplitudes and energies suggest that
two different bosons couple to the tunnel process.Comment: 5 pages + 9 pages supplementary materia
Flat rank of automorphism groups of buildings
The flat rank of a totally disconnected locally compact group G, denoted
flat-rk(G), is an invariant of the topological group structure of G. It is
defined thanks to a natural distance on the space of compact open subgroups of
G. For a topological Kac-Moody group G with Weyl group W, we derive the
inequalities: alg-rk(W)\le flat-rk(G)\le rk(|W|\_0). Here, alg-rk(W) is the
maximal -rank of abelian subgroups of W, and rk(|W|\_0) is the
maximal dimension of isometrically embedded flats in the CAT0-realization
|W|\_0. We can prove these inequalities under weaker assumptions. We also show
that for any integer n \geq 1 there is a topologically simple, compactly
generated, locally compact, totally disconnected group G, with flat-rk(G)=n and
which is not linear
Scale-multiplicative semigroups and geometry: automorphism groups of trees
A scale-multiplicative semigroup in a totally disconnected, locally compact
group is one for which the restriction of the scale function on is
multiplicative. The maximal scale-multiplicative semigroups in groups acting
2-transitively on the set of ends of trees without leaves are determined in
this paper and shown to correspond to geometric features of the tree.Comment: submitted to Groups, Geometry, and Dynamic
Design study of a regenerative pump using one-dimensional and three-dimensional numerical techniques
Regenerative pumps are low cost, compact, able to deliver high heads at low flow rates. Furthermore with stable performance characteristics they can operate with very small NPSH. The complexity of the flow field is a serious challenge for any kind of mathematical modelling. This paper compares an analytical and numerical technique of resolving the performance for a new regenerative pump design. The performance characteristics computed by a CFD approach and a new one-dimensional model are compared and matched to experimental test results. The approaches of both modelling techniques are assessed as potential design tools. The approaches are shown to not only successfully resolve the complex flow field within the pump; the CFD is also capable of resolving local flow properties to conduct further refinements. The flow field is represented by the CFD as it has never been before. A new design process is suggested. The new regenerative pump design is considered with a comparable duty centrifugal pump, proving that for many high head low flow rate applications the regenerative pump is a better choice
Contact resistance dependence of crossed Andreev reflection
We show experimentally that in nanometer scaled superconductor/normal metal
hybrid devices and in a small window of contact resistances, crossed Andreev
reflection (CAR) can dominate the nonlocal transport for all energies below the
superconducting gap. Besides CAR, elastic cotunneling (EC) and nonlocal charge
imbalance (CI) can be identified as competing subgap transport mechanisms in
temperature dependent four-terminal nonlocal measurements. We demonstrate a
systematic change of the nonlocal resistance vs. bias characteristics with
increasing contact resistances, which can be varied in the fabrication process.
For samples with higher contact resistances, CAR is weakened relative to EC in
the midgap regime, possibly due to dynamical Coulomb blockade. Gaining control
of CAR is an important step towards the realization of a solid state entangler.Comment: 5 pages, 4 figures, submitted to PR
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