8,490 research outputs found
Electronic Hong-Ou-Mandel interferometry in two-dimensional topological insulators
The edge states of a two-dimensional topological insulator are characterized
by their helicity, a very remarkable property which is related to the
time-reversal symmetry and the topology of the underlying system. We
theoretically investigate a Hong-Ou-Mandel like setup as a tool to probe it.
Collisions of two electrons with the same spin show a Pauli dip, analogous to
the one obtained in the integer quantum Hall case. Moreover, the collisions
between electrons of opposite spin also lead to a dip, known as
dip, which is a direct consequence of the constraints imposed
by time-reversal symmetry. In contrast to the integer quantum Hall case, the
visibility of these dips is reduced by the presence of the additional edge
channels, and crucially depends on the properties of the quantum point contact.
As a unique feature of this system, we show the possibility of three-electron
interference, which leads to a total suppression of the noise independently of
the point contact configuration. This is assured by the peculiar interplay
between Fermi statistics and topology. This work intends to extend the domain
of applicability of electron quantum optics.Comment: 12 pages, 7 figure
An interesting example for spectral invariants
In "Illinois J. of Math. {\bf 38} (1994) 653--678", the heat operator of a
Bismut superconnection for a family of generalized Dirac operators is defined
along the leaves of a foliation with Hausdorff groupoid. The Novikov-Shubin
invariants of the Dirac operators were assumed greater than three times the
codimension of the foliation. It was then showed that the associated heat
operator converges to the Chern character of the index bundle of the operator.
In "J. K-Theory {\bf 1} (2008) 305--356", we improved this result by reducing
the requirement on the Novikov-Shubin invariants to one half of the
codimension. In this paper, we construct examples which show that this is the
best possible result.Comment: Third author added. Some typos corrected and some material added.
Appeared in Journal of K Theory, Volume 13, in 2014, pages 305 to 31
Projected entangled-pair states can describe chiral topological states
We show that Projected Entangled-Pair States (PEPS) in two spatial dimensions
can describe chiral topological states by explicitly constructing a family of
such states with a non-trivial Chern number. They are ground states of two
different kinds of free-fermion Hamiltonians: (i) local and gapless; (ii)
gapped, but with hopping amplitudes that decay according to a power law. We
derive general conditions on topological free fermionic PEPS which show that
they cannot correspond to exact ground states of gapped, local parent
Hamiltonians, and provide numerical evidence demonstrating that they can
nevertheless approximate well the physical properties of topological insulators
with local Hamiltonians at arbitrary temperatures.Comment: v2: minor changes, references added. v3: accepted version,
Journal-Ref adde
An Icosahedron for Two: a Many-Sided Look at Making a Duet
The space around our bodies is not empty or neutral. In fact, the space around our bodies is loaded with meaning and important. When we move through it, whether it be in our daily lives or a choreographer making specific choices in order to convey a message, we activate new understandings in our lives. As a dancer and choreographer, I created a duet from improvisational climbs on an icosahedron. This article discusses choreographing from the form icosahedron and connects Laban\u27s theories of space harmony with the activation of meaning in my life
Polynomial regression under shape constraints
Calculating regression under shape constraints is a problem addressed by statisticians since long. This paper shows how to calculate a polynomial regression of any degree and of any number of variables under shape constraints, which include bounds, monotony, concavity constraints. Theoretical explanations are first introduced for monotony constraints and then applied to ad hoc examples to show the behavior of the proposed algorithm. Two real industrial cases are then detailed and worked out
On analysing sea level rise in the German Bight since 1844
In this paper, a methodology to analyse observed sea level rise (SLR) in the German Bight, the shallow south-eastern part of the North Sea, is presented. The paper focuses on the description of the methods used to generate and analyse mean sea level (MSL) time series. Parametric fitting approaches as well as non-parametric data adaptive filters, such as Singular System Analysis (SSA) are applied. For padding non-stationary sea level time series, an advanced approach named Monte-Carlo autoregressive padding (MCAP) is introduced. This approach allows the specification of uncertainties of the behaviour of smoothed time series near the boundaries. As an example, the paper includes the results from analysing the sea level records of the Cuxhaven tide gauge and the Heligoland tide gauge, both located in the south-eastern North Sea. For comparison, the results from analysing a worldwide sea level reconstruction are also presented. The results for the North Sea point to a weak negative acceleration of SLR since 1844 with a strong positive acceleration at the end of the 19th century, to a period of almost no SLR around the 1970s with subsequent positive acceleration and to high recent rates
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