3,324 research outputs found
Commuting symmetry operators of the Dirac equation, Killing-Yano and Schouten-Nijenhuis brackets
In this paper we derive the most general first-order symmetry operator
commuting with the Dirac operator in all dimensions and signatures. Such an
operator splits into Clifford even and Clifford odd parts which are given in
terms of odd Killing-Yano and even closed conformal Killing-Yano inhomogeneous
forms respectively. We study commutators of these symmetry operators and give
necessary and sufficient conditions under which they remain of the first-order.
In this specific setting we can introduce a Killing-Yano bracket, a bilinear
operation acting on odd Killing-Yano and even closed conformal Killing-Yano
forms, and demonstrate that it is closely related to the Schouten-Nijenhuis
bracket. An important non-trivial example of vanishing Killing-Yano brackets is
given by Dirac symmetry operators generated from the principal conformal
Killing-Yano tensor [hep-th/0612029]. We show that among these operators one
can find a complete subset of mutually commuting operators. These operators
underlie separability of the Dirac equation in Kerr-NUT-(A)dS spacetimes in all
dimensions [arXiv:0711.0078].Comment: 37 pages, no figure
Nonlinear stability of pulse solutions for the discrete FitzHugh-Nagumo equation with infinite-range interactions
We establish the existence and nonlinear stability of travelling pulse
solutions for the discrete FitzHugh-Nagumo equation with infinite-range
interactions close to the continuum limit. For the verification of the spectral
properties, we need to study a functional differential equation of mixed type
(MFDE) with unbounded shifts. We avoid the use of exponential dichotomies and
phase spaces, by building on a technique developed by Bates, Chen and Chmaj for
the discrete Nagumo equation. This allows us to transfer several crucial
Fredholm properties from the PDE setting to our discrete setting
A cryogenic amplifier for fast real-time detection of single-electron tunneling
We employ a cryogenic High Electron Mobility Transistor (HEMT) amplifier to
increase the bandwidth of a charge detection setup with a quantum point contact
(QPC) charge sensor. The HEMT is operating at 1K and the circuit has a
bandwidth of 1 MHz. The noise contribution of the HEMT at high frequencies is
only a few times higher than that of the QPC shot noise. We use this setup to
monitor single-electron tunneling to and from an adjacent quantum dot and we
measure fluctuations in the dot occupation as short as 400 nanoseconds, 20
times faster than in previous work.Comment: 4 pages, 3 figure
Incremental Distance Transforms (IDT)
A new generic scheme for incremental implementations of distance transforms (DT) is presented: Incremental Distance Transforms (IDT). This scheme is applied on the cityblock, Chamfer, and three recent exact Euclidean DT (E2DT). A benchmark shows that for all five DT, the incremental implementation results in a significant speedup: 3.4×−10×. However, significant differences (i.e., up to 12.5×) among the DT remain present. The FEED transform, one of the recent E2DT, even showed to be faster than both city-block and Chamfer DT. So, through a very efficient incremental processing scheme for DT, a relief is found for E2DT’s computational burden
ON NON-RIEMANNIAN PARALLEL TRANSPORT IN REGGE CALCULUS
We discuss the possibility of incorporating non-Riemannian parallel transport
into Regge calculus. It is shown that every Regge lattice is locally equivalent
to a space of constant curvature. Therefore well known-concepts of differential
geometry imply the definition of an arbitrary linear affine connection on a
Regge lattice.Comment: 12 pages, Plain-TEX, two figures (available from the author
Is the Quantum Hall Effect influenced by the gravitational field?
Most of the experiments on the quantum Hall effect (QHE) were made at
approximately the same height above sea level. A future international
comparison will determine whether the gravitational field
influences the QHE. In the realm of (1 + 2)-dimensional phenomenological
macroscopic electrodynamics, the Ohm-Hall law is metric independent
(`topological'). This suggests that it does not couple to . We
corroborate this result by a microscopic calculation of the Hall conductance in
the presence of a post-Newtonian gravitational field.Comment: 4 page
Josephson squelch filter for quantum nanocircuits
We fabricated and tested a squelch circuit consisting of a copper powder
filter with an embedded Josephson junction connected to ground. For small
signals (squelch-ON), the small junction inductance attenuates strongly from DC
to at least 1 GHz, while for higher frequencies dissipation in the copper
powder increases the attenuation exponentially with frequency. For large
signals (squelch-OFF) the circuit behaves as a regular metal powder filter. The
measured ON/OFF ratio is larger than 50dB up to 50 MHz. This squelch can be
applied in low temperature measurement and control circuitry for quantum
nanostructures such as superconducting qubits and quantum dots.Comment: Corrected and completed references 6,7,8. Updated some minor details
in figure
Multipole moments in Kaluza-Klein theories
This paper contains discussion of the problem of motion of extended i.e. non
point test bodies in multidimensional space. Extended bodies are described in
terms of so called multipole moments. Using approximated form of equations of
motion for extended bodies deviation from geodesic motion is derived. Results
are applied to special form of space-time.Comment: 11 pages, AMS-TeX, few misprints corrected, to appear in Classical
and Quantum Gravit
- …