2,862 research outputs found
Cayley--Klein Contractions of Quantum Orthogonal Groups in Cartesian Basis
Spaces of constant curvature and their motion groups are described most
naturally in Cartesian basis. All these motion groups also known as CK groups
are obtained from orthogonal group by contractions and analytical
continuations. On the other hand quantum deformation of orthogonal group is most easily performed in so-called symplectic basis. We reformulate its
standard quantum deformation to Cartesian basis and obtain all possible
contractions of quantum orthogonal group both for untouched and
transformed deformation parameter. It turned out, that similar to undeformed
case all CK contractions of are realized. An algorithm for obtaining
nonequivalent (as Hopf algebra) contracted quantum groups is suggested.
Contractions of are regarded as an examples.Comment: The statement of the basic theorem have correct. 30 pages, Latex.
Report given at X International Conference on Symmetry Methods in Physics,
August 13-19, 2003, Yerevan, Armenia. Submitted in Journal Physics of Atomic
Nucle
3-manifolds with(out) metrics of nonpositive curvature
In the context of Thurstons geometrisation program we address the question
which compact aspherical 3-manifolds admit Riemannian metrics of nonpositive
curvature. We show that non-geometric Haken manifolds generically, but not
always, admit such metrics. More precisely, we prove that a Haken manifold
with, possibly empty, boundary of zero Euler characteristic admits metrics of
nonpositive curvature if the boundary is non-empty or if at least one atoroidal
component occurs in its canonical topological decomposition. Our arguments are
based on Thurstons Hyperbolisation Theorem. We give examples of closed
graph-manifolds with linear gluing graph and arbitrarily many Seifert
components which do not admit metrics of nonpositive curvature.Comment: 16 page
On the possibility of applying the quasi-isothermal St\"ackel's model to our Galaxy
An earlier derived quasi-isothermal St\"ackel's model of mass distribution in
stellar systems and the corresponding formula for space density are applied to
our Galaxy. The model rotation curve is fitted to HI kinematical data. The
structural and scale parameters of the model are estimated and the
corresponding density contours for our Galaxy are presented.Comment: 7 pages, 3 figures. Accepted for publication in Baltic Astronomy (BA
Quark--anti-quark potential in N=4 SYM
We construct a closed system of equations describing the quark--anti-quark
potential at any coupling in planar N=4 supersymmetric Yang-Mills theory. It is
based on the Quantum Spectral Curve method supplemented with a novel type of
asymptotics. We present a high precision numerical solution reproducing the
classical and one-loop string predictions very accurately. We also analytically
compute the first 7 nontrivial orders of the weak coupling expansion.
Moreover, we study analytically the generalized quark--anti-quark potential
in the limit of large imaginary twist to all orders in perturbation theory. We
demonstrate how the QSC reduces in this case to a one-dimensional Schrodinger
equation. In the process we establish a link between the Q-functions and the
solution of the Bethe-Salpeter equation.Comment: 31 pages, 1 figure; v2: minor correcton
Flow induced ultrasound scattering: experimental studies
Sound scattering by a finite width beam on a single rigid body rotation
vortex flow is detected by a linear array of transducers (both smaller than a
flow cell), and analyzed using a revised scattering theory. Both the phase and
amplitude of the scattered signal are obtained on 64 elements of the detector
array and used for the analysis of velocity and vorticity fields. Due to
averaging on many pulses the signal-to-noise ratio of the phases difference in
the scattered sound signal can be amplified drastically, and the resolution of
the method in the detection of circulation, vortex radius, vorticity, and
vortex location becomes comparable with that obtained earlier by time-reversal
mirror (TRM) method (P. Roux, J. de Rosny, M. Tanter, and M. Fink, {\sl Phys.
Rev. Lett.} {\bf 79}, 3170 (1997)). The revised scattering theory includes two
crucial steps, which allow overcoming limitations of the existing theories.
First, the Huygens construction of a far field scattering signal is carried out
from a signal obtained at any intermediate plane. Second, a beam function that
describes a finite width beam is introduced, which allows using a theory
developed for an infinite width beam for the relation between a scattering
amplitude and the vorticity structure function. Structure functions of the
velocity and vorticity fields deduced from the sound scattering signal are
compared with those obtained from simultaneous particle image velocimetry (PIV)
measurements. Good quantitative agreement is found.Comment: 14 pages, 23 figures. accepted for publication in Phys. Fluids(June
issue
On the Fermionic Frequencies of Circular Strings
We revisit the semiclassical computation of the fluctuation spectrum around
different circular string solutions in AdS_5xS^5 and AdS_4xCP^3, starting from
the Green-Schwarz action. It has been known that the results for these
frequencies obtained from the algebraic curve and from the worldsheet
computations sometimes do not agree. In particular, different methods give
different results for the half-integer shifts in the mode numbers of the
frequencies. We find that these discrepancies can be removed if one carefully
takes into account the transition matrices in the spin bundle over the target
space.Comment: 13 pages, 1 figur
Numerical results for the exact spectrum of planar AdS4/CFT3
We compute the anomalous dimension for a short single-trace operator in
planar ABJM theory at intermediate coupling. This is done by solving
numerically the set of Thermodynamic Bethe Ansatz equations which are expected
to describe the exact spectrum of the theory. We implement a truncation method
which significantly reduces the number of integral equations to be solved and
improves numerical efficiency. Results are obtained for a range of 't Hooft
coupling lambda corresponding to , where h(lambda) is
the interpolating function of the AdS4/CFT3 Bethe equations.Comment: v3: corrected Acknowledgements section; v4: minor changes, published
version; v5: fixed typos in Eq. (3.9
A Radiation hard bandgap reference circuit in a standard 0.13um CMOS Technology
With ongoing CMOS evolution, the gate-oxide thickness steadily decreases, resulting in an increased radiation tolerance of MOS transistors. Combined with special layout techniques, this yields circuits with a high inherent robustness against X-rays and other ionizing radiation. In bandgap voltage references, the dominant radiation-susceptibility is then no longer associated with the MOS transistors, but is dominated by the diodes. This paper gives an analysis of radiation effects in both MOSdevices and diodes and presents a solution to realize a radiation-hard voltage reference circuit in a standard CMOS technology. A demonstrator circuit was implemented in a standard 0.13 m CMOS technology. Measurements show correct operation with supply voltages in the range from 1.4 V down to 0.85 V, a reference voltage of 405 mV 7.5 mV ( = 6mVchip-to-chip statistical spread), and a reference voltage shift of only 1.5 mV (around 0.8%) under irradiation up to 44 Mrad (Si)
Virtually Abelian Quantum Walks
We introduce quantum walks on Cayley graphs of non-Abelian groups. We focus
on the easiest case of virtually Abelian groups, and introduce a technique to
reduce the quantum walk to an equivalent one on an Abelian group with coin
system having larger dimension. We apply the technique in the case of two
quantum walks on virtually Abelian groups with planar Cayley graphs, finding
the exact solution.Comment: 10 pages, 3 figure
The Isoperimetric Profile of a Noncompact Riemannian Manifold for Small Volumes
In the main theorem of this paper we treat the problem of existence of
minimizers of the isoperimetric problem under the assumption of small volumes.
Applications of the main theorem to asymptotic expansions of the isoperimetric
problem are given.Comment: 33 pages, improved version after the referee comments, (Submitted
- …