1,293 research outputs found
A topological realization of the congruence subgroup Kernel A
A number of years ago, Kumar Murty pointed out to me that the computation of
the fundamental group of a Hilbert modular surface ([7],IV,6), and the
computation of the congruence subgroup kernel of SL(2) ([6]) were surprisingly
similar. We puzzled over this, in particular over the role of elementary
matrices in both computations. We formulated a very general result on the
fundamental group of a Satake compactification of a locally symmetric space.
This lead to our joint paper [1] with Lizhen Ji and Les Saper on these
fundamental groups. Although the results in it were intriguingly similar to the
corresponding calculations of the congruence subgroup kernel of the underlying
algebraic group in [5], we were not able to demonstrate a direct connection
(cf. [1], 7). The purpose of this note is to explain such a connection. A
covering space is constructed from inverse limits of reductive Borel-Serre
compactifications. The congruence subgroup kernel then appears as the group of
deck transformations of this covering. The key to this is the computation of
the fundamental group in [1]
The Thirty Meter Telescope International Observatory facilitating transformative astrophysical science
The next major advancement in astronomy and cosmology will be driven by deep
observations using very sensitive telescopes with high spatial and spectral
resolution capabilities. An international consortium of astronomers, including
Indian astronomers are building the Thirty Meter Telescope to achieve
breakthroughs in different areas of astronomy starting from studies of the
solar system to that of the early universe. This article provides a brief
overview of the telescope, science objectives and details of the first light
instruments.Comment: 10 page
The Landau electron problem on a cylinder
We consider the quantum mechanics of an electron confined to move on an
infinite cylinder in the presence of a uniform radial magnetic field. This
problem is in certain ways very similar to the corresponding problem on the
infinite plane. Unlike the plane however, the group of symmetries of the
magnetic field, namely, rotations about the axis and the axial translations, is
{\em not} realized by the quantum electron but only a subgroup comprising
rotations and discrete translations along the axial direction, is. The basic
step size of discrete translations is such that the flux through the `unit
cylinder cell' is quantized in units of the flux quantum. The result is derived
in two different ways: using the condition of projective realization of
symmetry groups and using the more familiar approach of determining the
symmetries of a given Hamiltonian.Comment: 26 pages, revtex file, no figures. In version 2, introduction is
expanded to explain our approach and references are updated. Results and
conclusions are unchange
Gaussian approximation and single-spin measurement in OSCAR MRFM with spin noise
A promising technique for measuring single electron spins is magnetic
resonance force microscopy (MRFM), in which a microcantilever with a permanent
magnetic tip is resonantly driven by a single oscillating spin. If the quality
factor of the cantilever is high enough, this signal will be amplified over
time to the point that it can be detected by optical or other techniques. An
important requirement, however, is that this measurement process occur on a
time scale short compared to any noise which disturbs the orientation of the
measured spin. We describe a model of spin noise for the MRFM system, and show
how this noise is transformed to become time-dependent in going to the usual
rotating frame. We simplify the description of the cantilever-spin system by
approximating the cantilever wavefunction as a Gaussian wavepacket, and show
that the resulting approximation closely matches the full quantum behavior. We
then examine the problem of detecting the signal for a cantilever with thermal
noise and spin with spin noise, deriving a condition for this to be a useful
measurement.Comment: 12 pages, 8 figures in EPS format, RevTeX 4.
A structure in the early Universe at z 1.3 that exceeds the homogeneity scale of the R-W concordance cosmology
A Large Quasar Group (LQG) of particularly large size and high membership has been identified in the DR7QSO catalogue of the Sloan Digital Sky Survey. It has characteristic size (volume^1/3) ~ 500 Mpc (proper size, present epoch), longest dimension ~ 1240 Mpc, membership of 73 quasars, and mean redshift = 1.27. In terms of both size and membership it is the most extreme LQG found in the DR7QSO catalogue for the redshift range 1.0 = 1.28, which is itself one of the more extreme examples. Their boundaries approach to within ~ 2 deg (~ 140 Mpc projected). This new, huge LQG appears to be the largest structure currently known in the early universe. Its size suggests incompatibility with the Yadav et al. scale of homogeneity for the concordance cosmology, and thus challenges the assumption of the cosmological principle
Enhancement of steric repulsion with temperature in oriented lipid multilayers
We have studied the temperature dependence of the stacking periodicity, d, of oriented phospholipid multilayers using grazing angle neutron scattering techniques. d is found to increase substantially at higher temperatures, just before the bilayers peel off from the substrate. Although we do not observe thermal unbinding, our results are consistent with the notion that the unbinding transition is driven by steric repulsion arising from thermal fluctuations of the membranes, in contrast to those of a recent study by Vogel et al. [Phys. Rev. Lett. 84, 390 (2000)]
Search on a Hypercubic Lattice through a Quantum Random Walk: II. d=2
We investigate the spatial search problem on the two-dimensional square
lattice, using the Dirac evolution operator discretised according to the
staggered lattice fermion formalism. is the critical dimension for the
spatial search problem, where infrared divergence of the evolution operator
leads to logarithmic factors in the scaling behaviour. As a result, the
construction used in our accompanying article \cite{dgt2search} provides an
algorithm, which is not optimal. The scaling behaviour can
be improved to by cleverly controlling the massless Dirac
evolution operator by an ancilla qubit, as proposed by Tulsi \cite{tulsi}. We
reinterpret the ancilla control as introduction of an effective mass at the
marked vertex, and optimise the proportionality constants of the scaling
behaviour of the algorithm by numerically tuning the parameters.Comment: Revtex4, 5 pages (v2) Introduction and references expanded. Published
versio
Accidental deep field bias in CMB T and SNe z correlation
Evidence presented by Yershov, Orlov and Raikov apparently showed that the WMAP/Planck cosmic microwave background (CMB) pixel-temperatures (T) at supernovae (SNe) locations tend to increase with increasing redshift (z). They suggest this correlation could be caused by the Integrated Sachs-Wolfe effect and/or by some unrelated foreground emission. Here, we assess this correlation independently using Planck 2015 SMICA R2.01 data and, following Yershov et al., a sample of 2783 SNe from the Sternberg Astronomical Institute. Our analysis supports the prima facie existence of the correlation but attributes it to a composite selection bias (high CMB T × high SNe z) caused by the accidental alignment of seven deep survey fields with CMB hotspots. These seven fields contain 9.2 per cent of the SNe sample (256 SNe). Spearman’s rank-order correlation coefficient indicates the correlation present in the whole sample (ρs = 0.5, p-value =6.7 × 10−9) is insignificant for a sub-sample of the seven fields together (ρs = 0.2, p-value =0.2) and entirely absent for the remainder of the SNe (ρs = 0.1, p-value =0.6). We demonstrate the temperature and redshift biases of these seven deep fields, and estimate the likelihood of their falling on CMB hotspots by chance is at least ∼ 6.8 per cent (approximately 1 in 15). We show that a sample of 7880 SNe from the Open Supernova Catalogue exhibits the same effect and we conclude that the correlation is an accidental but not unlikely selection bias
Microscopic Model for High-spin vs. Low-spin ground state in () magnetic clusters
Conventional superexchange rules predict ferromagnetic exchange interaction
between Ni(II) and M (M=Mo(V), W(V), Nb(IV)). Recent experiments show that in
some systems this superexchange is antiferromagnetic. To understand this
feature, in this paper we develop a microscopic model for Ni(II)-M systems and
solve it exactly using a valence bond approach. We identify the direct exchange
coupling, the splitting of the magnetic orbitals and the inter-orbital electron
repulsions, on the M site as the parameters which control the ground state spin
of various clusters of the Ni(II)-M system. We present quantum phase diagrams
which delineate the high-spin and low-spin ground states in the parameter
space. We fit the spin gap to a spin Hamiltonian and extract the effective
exchange constant within the experimentally observed range, for reasonable
parameter values. We also find a region in the parameter space where an
intermediate spin state is the ground state. These results indicate that the
spin spectrum of the microscopic model cannot be reproduced by a simple
Heisenberg exchange Hamiltonian.Comment: 8 pages including 7 figure
Microscopic Model for Photoinduced Magnetism in the Molecular Complex Perchlorate
A theoretical model for understanding photomagnetism in the heptanuclear
complex perchlorate is developed. It is a
many-body model involving the active orbitals on the transition metal ions. The
model is exactly solved using a valence bond approach. The ground state
solution of the model is highly degenerate and is spanned by five S=0 states,
nine S=1 states, five S=2 states and one S=3 state. The orbital occupancies in
all these states correspond to six ions and one diamagnetic
ion. The optically excited charge-transfer (CT) state in each spin sector occur
at nearly the same excitation energy of 2.993 eV for the physically reasonable
parameter values. The degeneracy of the CT states is largest in the S=3 sector
and so is the transition dipole moment from the ground state to these excited
states. Thus laser irradiation with light of this energy results in most
intense absorption in the S=3 sector. The life-time of the S=3 excited states
is also expected to be the largest as the number of states below that energy is
very sparse in this spin sector when compared to other spin sectors. These twin
features of our model explain the observed photomagnetism in the
complex.Comment: 8 pages, 6 figures and 1 tabl
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