374 research outputs found
Semi-invariants of symmetric quivers of tame type
A symmetric quiver is a finite quiver without oriented cycles
equipped with a contravariant involution on . The involution allows us to define a nondegenerate bilinear form on
a representation $V$ of $Q$. We shall say that $V$ is orthogonal if is
symmetric and symplectic if is skew-symmetric. Moreover, we define an
action of products of classical groups on the space of orthogonal
representations and on the space of symplectic representations. So we prove
that if is a symmetric quiver of tame type then the rings of
semi-invariants for this action are spanned by the semi-invariants of
determinantal type and, when matrix defining is skew-symmetric, by
the Pfaffians . To prove it, moreover, we describe the symplectic and
orthogonal generic decomposition of a symmetric dimension vector
Cooling a nanomechanical resonator with quantum back-action
Quantum mechanics demands that the act of measurement must affect the
measured object. When a linear amplifier is used to continuously monitor the
position of an object, the Heisenberg uncertainty relationship requires that
the object be driven by force impulses, called back-action. Here we measure the
back-action of a superconducting single-electron transistor (SSET) on a
radiofrequency nanomechanical resonator. The conductance of the SSET, which is
capacitively coupled to the resonator, provides a sensitive probe of the
latter's position;back-action effects manifest themselves as an effective
thermal bath, the properties of which depend sensitively on SSET bias
conditions. Surprisingly, when the SSET is biased near a transport resonance,
we observe cooling of the nanomechanical mode from 550mK to 300mK-- an effect
that is analogous to laser cooling in atomic physics. Our measurements have
implications for nanomechanical readout of quantum information devices and the
limits of ultrasensitive force microscopy (such as single-nuclear-spin magnetic
resonance force microscopy). Furthermore, we anticipate the use of these
backaction effects to prepare ultracold and quantum states of mechanical
structures, which would not be accessible with existing technology.Comment: 28 pages, 7 figures; accepted for publication in Natur
Resonant Cooper-Pair Tunneling: Counting Statistics and Frequency-Dependent Current Noise
We discuss the counting statistics and current noise associated with the
double Josephson quasiparticle resonance point in a superconducting single
electron transistor. The counting statistics are in general phase-dependent,
despite the fact that the average current has no dependence on phase. Focusing
on parameter regimes where the counting statistics have no phase-dependence, we
use a general relation first derived by MacDonald in 1948 to obtain the full
frequency-dependent shot noise directly from the counting statistics, without
any further approximations. We comment on problems posed by the
phase-dependence of the counting statistics for the finite-frequency noise.Comment: 13 pages, 2 figures; to appear in the proceedings of the NATO ASI
"New Directions in Mesoscopic Physics", Erice, 200
Current measurement by real-time counting of single electrons
The fact that electrical current is carried by individual charges has been
known for over 100 years, yet this discreteness has not been directly observed
so far. Almost all current measurements involve measuring the voltage drop
across a resistor, using Ohm's law, in which the discrete nature of charge does
not come into play. However, by sending a direct current through a
microelectronic circuit with a chain of islands connected by small tunnel
junctions, the individual electrons can be observed one by one. The quantum
mechanical tunnelling of single charges in this one-dimensional array is time
correlated, and consequently the detected signal has the average frequency
f=I/e, where I is the current and e is the electron charge. Here we report a
direct observation of these time-correlated single-electron tunnelling
oscillations, and show electron counting in the range 5 fA-1 pA. This
represents a fundamentally new way to measure extremely small currents, without
offset or drift. Moreover, our current measurement, which is based on electron
counting, is self-calibrated, as the measured frequency is related to the
current only by a natural constant.Comment: 9 pages, 4 figures; v2: minor revisions, 2 refs added, words added to
title, typos correcte
Two-neutron transfer reaction mechanisms in C(He,He)C using a realistic three-body He model
The reaction mechanisms of the two-neutron transfer reaction
C(He,He) have been studied at 30 MeV at the TRIUMF ISAC-II
facility using the SHARC charged-particle detector array. Optical potential
parameters have been extracted from the analysis of the elastic scattering
angular distribution. The new potential has been applied to the study of the
transfer angular distribution to the 2 8.32 MeV state in C, using
a realistic 3-body He model and advanced shell model calculations for the
carbon structure, allowing to calculate the relative contributions of the
simultaneous and sequential two-neutron transfer. The reaction model provides a
good description of the 30 MeV data set and shows that the simultaneous process
is the dominant transfer mechanism. Sensitivity tests of optical potential
parameters show that the final results can be considerably affected by the
choice of optical potentials. A reanalysis of data measured previously at 18
MeV however, is not as well described by the same reaction model, suggesting
that one needs to include higher order effects in the reaction mechanism.Comment: 9 pages, 9 figure
Transmutations and spectral parameter power series in eigenvalue problems
We give an overview of recent developments in Sturm-Liouville theory
concerning operators of transmutation (transformation) and spectral parameter
power series (SPPS). The possibility to write down the dispersion
(characteristic) equations corresponding to a variety of spectral problems
related to Sturm-Liouville equations in an analytic form is an attractive
feature of the SPPS method. It is based on a computation of certain systems of
recursive integrals. Considered as families of functions these systems are
complete in the -space and result to be the images of the nonnegative
integer powers of the independent variable under the action of a corresponding
transmutation operator. This recently revealed property of the Delsarte
transmutations opens the way to apply the transmutation operator even when its
integral kernel is unknown and gives the possibility to obtain further
interesting properties concerning the Darboux transformed Schr\"{o}dinger
operators.
We introduce the systems of recursive integrals and the SPPS approach,
explain some of its applications to spectral problems with numerical
illustrations, give the definition and basic properties of transmutation
operators, introduce a parametrized family of transmutation operators, study
their mapping properties and construct the transmutation operators for Darboux
transformed Schr\"{o}dinger operators.Comment: 30 pages, 4 figures. arXiv admin note: text overlap with
arXiv:1111.444
Improved Limit on Direct α Decay of the Hoyle State
The current evaluation of the triple-α reaction rate assumes that the α decay of the 7.65 MeV, 0+ state in 12C, commonly known as the Hoyle state, proceeds sequentially via the ground state of 8Be. This assumption is challenged by the recent identification of two direct α-decay branches with a combined branching ratio of 17(5)%. If correct, this would imply a corresponding reduction in the triple-α reaction rate with important astrophysical consequences. We have used the 11B(3He,d) reaction to populate the Hoyle state and measured the decay to three α particles in complete kinematics. We find no evidence for direct α-decay branches, and hence our data do not support a revision of the triple-α reaction rate. We obtain an upper limit of 5×10-3 on the direct α decay of the Hoyle state at 95% C.L., which is 1 order of magnitude better than a previous upper limit
Influences of Excluded Volume of Molecules on Signaling Processes on Biomembrane
We investigate the influences of the excluded volume of molecules on
biochemical reaction processes on 2-dimensional surfaces using a model of
signal transduction processes on biomembranes. We perform simulations of the
2-dimensional cell-based model, which describes the reactions and diffusion of
the receptors, signaling proteins, target proteins, and crowders on the cell
membrane. The signaling proteins are activated by receptors, and these
activated signaling proteins activate target proteins that bind autonomously
from the cytoplasm to the membrane, and unbind from the membrane if activated.
If the target proteins bind frequently, the volume fraction of molecules on the
membrane becomes so large that the excluded volume of the molecules for the
reaction and diffusion dynamics cannot be negligible. We find that such
excluded volume effects of the molecules induce non-trivial variations of the
signal flow, defined as the activation frequency of target proteins, as
follows. With an increase in the binding rate of target proteins, the signal
flow varies by i) monotonically increasing; ii) increasing then decreasing in a
bell-shaped curve; or iii) increasing, decreasing, then increasing in an
S-shaped curve. We further demonstrate that the excluded volume of molecules
influences the hierarchical molecular distributions throughout the reaction
processes. In particular, when the system exhibits a large signal flow, the
signaling proteins tend to surround the receptors to form receptor-signaling
protein clusters, and the target proteins tend to become distributed around
such clusters. To explain these phenomena, we analyze the stochastic model of
the local motions of molecules around the receptor.Comment: 31 pages, 10 figure
Matrix Models for the Black Hole Information Paradox
We study various matrix models with a charge-charge interaction as toy models
of the gauge dual of the AdS black hole. These models show a continuous
spectrum and power-law decay of correlators at late time and infinite N,
implying information loss in this limit. At finite N, the spectrum is discrete
and correlators have recurrences, so there is no information loss. We study
these models by a variety of techniques, such as Feynman graph expansion, loop
equations, and sum over Young tableaux, and we obtain explicitly the leading
1/N^2 corrections for the spectrum and correlators. These techniques are
suggestive of possible dual bulk descriptions. At fixed order in 1/N^2 the
spectrum remains continuous and no recurrence occurs, so information loss
persists. However, the interchange of the long-time and large-N limits is
subtle and requires further study.Comment: 35 pages, 11 eps figures; v.2 minor typos fixe
Rotating Higher Spin Partition Functions and Extended BMS Symmetries
We evaluate one-loop partition functions of higher-spin fields in thermal
flat space with angular potentials; this computation is performed in arbitrary
space-time dimension, and the result is a simple combination of Poincar\'e
characters. We then focus on dimension three, showing that suitable products of
one-loop partition functions coincide with vacuum characters of higher-spin
asymptotic symmetry algebras at null infinity. These are extensions of the
bms_3 algebra that emerges in pure gravity, and we propose a way to build their
unitary representations and to compute the associated characters. We also
extend our investigations to supergravity and to a class of gauge theories
involving higher-spin fermionic fields.Comment: 58 pages; clarifications and references added; version to be
published in JHE
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