273 research outputs found
Noncompact SL(2,R) spin chain
We consider the integrable spin chain model - the noncompact SL(2,R) spin
magnet. The spin operators are realized as the generators of the unitary
principal series representation of the SL(2,R) group. In an explicit form, we
construct R-matrix, the Baxter Q-operator and the transition kernel to the
representation of the Separated Variables (SoV). The expressions for the energy
and quasimomentum of the eigenstates in terms of the Baxter Q-operator are
derived. The analytic properties of the eigenvalues of the Baxter operator as a
function of the spectral parameter are established. Applying the diagrammatic
approach, we calculate Sklyanin's integration measure in the separated
variables and obtain the solution to the spectral problem for the model in
terms of the eigenvalues of the Q-operator. We show that the transition kernel
to the SoV representation is factorized into a product of certain operators
each depending on a single separated variable.Comment: 29 pages, 12 figure
Coulomb Blockade in low mobility nanometer size Si:MOSFETs
We investigate coherent transport in Si:MOSFETs with nominal gate lengths 50
to 100nm and various widths at very low temperature. Independent of the
geometry, localized states appear when G=e^{2}/h and transport is dominated by
resonant tunnelling through a single quantum dot formed by an impurity
potential. We find that the typical size of the relevant impurity quantum dot
is comparable to the channel length and that the periodicity of the observed
Coulomb blockade oscillations is roughly inversely proportional to the channel
length. The spectrum of resonances and the nonlinear I-V curves allow to
measure the charging energy and the mean level energy spacing for electrons in
the localized state. Furthermore, we find that in the dielectric regime, the
variance var(lng) of the logarithmic conductance lng is proportional to its
average value consistent with one-electron scaling models.Comment: 4 pages, 4 figure
An Extreme Solar Event of 20 January 2005: Properties of the Flare and the Origin of Energetic Particles
The extreme solar and SEP event of 20 January 2005 is analyzed from two
perspectives. Firstly, we study features of the main phase of the flare, when
the strongest emissions from microwaves up to 200 MeV gamma-rays were observed.
Secondly, we relate our results to a long-standing controversy on the origin of
SEPs arriving at Earth, i.e., acceleration in flares, or shocks ahead of CMEs.
All emissions from microwaves up to 2.22 MeV line gamma-rays during the main
flare phase originated within a compact structure located just above sunspot
umbrae. A huge radio burst with a frequency maximum at 30 GHz was observed,
indicating the presence of a large number of energetic electrons in strong
magnetic fields. Thus, protons and electrons responsible for flare emissions
during its main phase were accelerated within the magnetic field of the active
region. The leading, impulsive parts of the GLE, and highest-energy gamma-rays
identified with pi^0-decay emission, are similar and correspond in time. The
origin of the pi^0-decay gamma-rays is argued to be the same as that of lower
energy emissions. We estimate the sky-plane speed of the CME to be 2000-2600
km/s, i.e., high, but of the same order as preceding non-GLE-related CMEs from
the same active region. Hence, the flare itself rather than the CME appears to
determine the extreme nature of this event. We conclude that the acceleration,
at least, to sub-relativistic energies, of electrons and protons, responsible
for both the flare emissions and the leading spike of SEP/GLE by 07 UT, are
likely to have occurred simultaneously within the flare region. We do not rule
out a probable contribution from particles accelerated in the CME-driven shock
for the leading GLE spike, which seemed to dominate later on.Comment: 34 pages, 14 Postscript figures. Solar Physics, accepted. A typo
corrected. The original publication is available at
http://www.springerlink.co
Chemostratigraphy of Neoproterozoic carbonates: implications for 'blind dating'
The delta C-13(carb) and Sr-87/Sr-86 secular variations in Neoproteozoic seawater have been used for the purpose of 'isotope stratigraphy' but there are a number of problems that can preclude its routine use. In particular, it cannot be used with confidence for 'blind dating'. The compilation of isotopic data on carbonate rocks reveals a high level of inconsistency between various carbon isotope age curves constructed for Neoproteozoic seawater, caused by a relatively high frequency of both global and local delta C-13(carb) fluctuations combined with few reliable age determinations. Further complication is caused by the unresolved problem as to whether two or four glaciations, and associated negative delta C-13(carb) excursions, can be reliably documented. Carbon isotope stratigraphy cannot be used alone for geological correlation and 'blind dating'. Strontium isotope stratigraphy is a more reliable and precise tool for stratigraphic correlations and indirect age determinations. Combining strontium and carbon isotope stratigraphy, several discrete ages within the 590-544 Myr interval, and two age-groups at 660-610 and 740-690 Myr can be resolved
Baxter Q-operator and Separation of Variables for the open SL(2,R) spin chain
We construct the Baxter Q-operator and the representation of the Separated
Variables (SoV) for the homogeneous open SL(2,R) spin chain. Applying the
diagrammatical approach, we calculate Sklyanin's integration measure in the
separated variables and obtain the solution to the spectral problem for the
model in terms of the eigenvalues of the Q-operator. We show that the
transition kernel to the SoV representation is factorized into the product of
certain operators each depending on a single separated variable. As a
consequence, it has a universal pyramid-like form that has been already
observed for various quantum integrable models such as periodic Toda chain,
closed SL(2,R) and SL(2,C) spin chains.Comment: 29 pages, 9 figures, Latex styl
Separation of variables for the quantum SL(2,R) spin chain
We construct representation of the Separated Variables (SoV) for the quantum
SL(2,R) Heisenberg closed spin chain and obtain the integral representation for
the eigenfunctions of the model. We calculate explicitly the Sklyanin measure
defining the scalar product in the SoV representation and demonstrate that the
language of Feynman diagrams is extremely useful in establishing various
properties of the model. The kernel of the unitary transformation to the SoV
representation is described by the same "pyramid diagram" as appeared before in
the SoV representation for the SL(2,C) spin magnet. We argue that this kernel
is given by the product of the Baxter Q-operators projected onto a special
reference state.Comment: 26 pages, Latex style, 9 figures. References corrected, minor
stylistic changes, version to be publishe
Quantized W-algebra of sl(2,1) and quantum parafermions of U_q(sl(2))
In this paper, we establish the connection between the quantized W-algebra of
and quantum parafermions of that a
shifted product of the two quantum parafermions of
generates the quantized W-algebra of
Classical and Quantum Integrable Systems in \wt{\gr{gl}}(2)^{+*} and Separation of Variables
Classical integrable Hamiltonian systems generated by elements of the Poisson
commuting ring of spectral invariants on rational coadjoint orbits of the loop
algebra \wt{\gr{gl}}^{+*}(2,{\bf R}) are integrated by separation of
variables in the Hamilton-Jacobi equation in hyperellipsoidal coordinates. The
canonically quantized systems are then shown to also be completely integrable
and separable within the same coordinates. Pairs of second class constraints
defining reduced phase spaces are implemented in the quantized systems by
choosing one constraint as an invariant, and interpreting the other as
determining a quotient (i.e., by treating one as a first class constraint and
the other as a gauge condition). Completely integrable, separable systems on
spheres and ellipsoids result, but those on ellipsoids require a further
modification of order \OO(\hbar^2) in the commuting invariants in order to
assure self-adjointness and to recover the Laplacian for the case of free
motion. For each case - in the ambient space , the sphere and the
ellipsoid - the Schr\"odinger equations are completely separated in
hyperellipsoidal coordinates, giving equations of generalized Lam\'e type.Comment: 28 page
Kaon Production and Kaon to Pion Ratio in Au+Au Collisions at \snn=130 GeV
Mid-rapidity transverse mass spectra and multiplicity densities of charged
and neutral kaons are reported for Au+Au collisions at \snn=130 GeV at RHIC.
The spectra are exponential in transverse mass, with an inverse slope of about
280 MeV in central collisions. The multiplicity densities for these particles
scale with the negative hadron pseudo-rapidity density. The charged kaon to
pion ratios are and
for the most central collisions. The ratio is lower than the same
ratio observed at the SPS while the is higher than the SPS result.
Both ratios are enhanced by about 50% relative to p+p and +p
collision data at similar energies.Comment: 6 pages, 3 figures, 1 tabl
Azimuthal anisotropy and correlations in p+p, d+Au and Au+Au collisions at 200 GeV
We present the first measurement of directed flow () at RHIC. is
found to be consistent with zero at pseudorapidities from -1.2 to 1.2,
then rises to the level of a couple of percent over the range . The latter observation is similar to data from NA49 if the SPS rapidities
are shifted by the difference in beam rapidity between RHIC and SPS.
Back-to-back jets emitted out-of-plane are found to be suppressed more if
compared to those emitted in-plane, which is consistent with {\it jet
quenching}. Using the scalar product method, we systematically compared
azimuthal correlations from p+p, d+Au and Au+Au collisions. Flow and non-flow
from these three different collision systems are discussed.Comment: Quark Matter 2004 proceeding, 4 pages, 3 figure
- …