78 research outputs found
Universal Correlations of Coulomb Blockade Conductance Peaks and the Rotation Scaling in Quantum Dots
We show that the parametric correlations of the conductance peak amplitudes
of a chaotic or weakly disordered quantum dot in the Coulomb blockade regime
become universal upon an appropriate scaling of the parameter. We compute the
universal forms of this correlator for both cases of conserved and broken time
reversal symmetry. For a symmetric dot the correlator is independent of the
details in each lead such as the number of channels and their correlation. We
derive a new scaling, which we call the rotation scaling, that can be computed
directly from the dot's eigenfunction rotation rate or alternatively from the
conductance peak heights, and therefore does not require knowledge of the
spectrum of the dot. The relation of the rotation scaling to the level velocity
scaling is discussed. The exact analytic form of the conductance peak
correlator is derived at short distances. We also calculate the universal
distributions of the average level width velocity for various values of the
scaled parameter. The universality is illustrated in an Anderson model of a
disordered dot.Comment: 35 pages, RevTex, 6 Postscript figure
Weakly-Bound Three-Body Systems with No Bound Subsystems
We investigate the domain of coupling constants which achieve binding for a
3-body system, while none of the 2-body subsystems is bound. We derive some
general properties of the shape of the domain, and rigorous upper bounds on its
size, using a Hall--Post decomposition of the Hamiltonian. Numerical
illustrations are provided in the case of a Yukawa potential, using a simple
variational method.Comment: gzipped ps with 11 figures included. To appear in Phys. Rev.
Tall tales from de Sitter space II: Field theory dualities
We consider the evolution of massive scalar fields in (asymptotically) de
Sitter spacetimes of arbitrary dimension. Through the proposed dS/CFT
correspondence, our analysis points to the existence of new nonlocal dualities
for the Euclidean conformal field theory. A massless conformally coupled scalar
field provides an example where the analysis is easily explicitly extended to
'tall' background spacetimes.Comment: 31 pages, 2 figure
Monotonicity of quantum ground state energies: Bosonic atoms and stars
The N-dependence of the non-relativistic bosonic ground state energy is
studied for quantum N-body systems with either Coulomb or Newton interactions.
The Coulomb systems are "bosonic atoms," with their nucleus fixed, and the
Newton systems are "bosonic stars". In either case there exists some third
order polynomial in N such that the ratio of the ground state energy to the
respective polynomial grows monotonically in N. Some applications of these new
monotonicity results are discussed
De Sitter Gravity and Liouville Theory
We show that the spectrum of conical defects in three-dimensional de Sitter
space is in one-to-one correspondence with the spectrum of vertex operators in
Liouville conformal field theory. The classical conformal dimensions of vertex
operators are equal to the masses of the classical point particles in dS_3 that
cause the conical defect. The quantum dimensions instead are shown to coincide
with the mass of the Kerr-dS_3 solution computed with the Brown-York stress
tensor. Therefore classical de Sitter gravity encodes the quantum properties of
Liouville theory. The equality of the gravitational and the Liouville stress
tensor provides a further check of this correspondence. The Seiberg bound for
vertex operators translates on the bulk side into an upper mass bound for
classical point particles. Bulk solutions with cosmological event horizons
correspond to microscopic Liouville states, whereas those without horizons
correspond to macroscopic (normalizable) states. We also comment on recent
criticism by Dyson, Lindesay and Susskind, and point out that the
contradictions found by these authors may be resolved if the dual CFT is not
able to capture the thermal nature of de Sitter space. Indeed we find that on
the CFT side, de Sitter entropy is merely Liouville momentum, and thus has no
statistical interpretation in this approach.Comment: 22 pages, LateX2e; added references for section 1 and section 2;
corrected typos; improved discussion in section
Primeval Corrections to the CMB Anisotropies
We show that deviations of the quantum state of the inflaton from the thermal
vacuum of inflation may leave an imprint in the CMB anisotropies. The quantum
dynamics of the inflaton in such a state produces corrections to the
inflationary fluctuations, which may be observable. Because these effects
originate from IR physics below the Planck scale, they will dominate over any
trans-Planckian imprints in any theory which obeys decoupling. Inflation sweeps
away these initial deviations and forces its quantum state closer to the
thermal vacuum. We view this as the quantum version of the cosmic no-hair
theorem. Such imprints in the CMB may be a useful, independent test of the
duration of inflation, or of significant features in the inflaton potential
about 60 e-folds before inflation ended, instead of an unlikely discovery of
the signatures of quantum gravity. The absence of any such substructure would
suggest that inflation lasted uninterrupted much longer than
e-folds.Comment: 17 pages, latex, no figures; v3: added references and comments, final
version to appear in Phys. Rev.
Hierarchical Spherical Model from a Geometric Point of View
A continuous version of the hierarchical spherical model at dimension d=4 is
investigated. Two limit distribution of the block spin variable X^{\gamma},
normalized with exponents \gamma =d+2 and \gamma =d at and above the critical
temperature, are established. These results are proven by solving certain
evolution equations corresponding to the renormalization group (RG)
transformation of the O(N) hierarchical spin model of block size L^{d} in the
limit L to 1 and N to \infty . Starting far away from the stationary Gaussian
fixed point the trajectories of these dynamical system pass through two
different regimes with distinguishable crossover behavior. An interpretation of
this trajectories is given by the geometric theory of functions which describe
precisely the motion of the Lee--Yang zeroes. The large-- limit of RG
transformation with L^{d} fixed equal to 2, at the criticality, has recently
been investigated in both weak and strong (coupling) regimes by Watanabe
\cite{W}. Although our analysis deals only with N=\infty case, it complements
various aspects of that work.Comment: 27 pages, 6 figures, submitted to Journ. Stat. Phy
Initial Conditions for Inflation
Free scalar fields in de Sitter space have a one-parameter family of states
invariant under the de Sitter group, including the standard thermal vacuum. We
show that, except for the thermal vacuum, these states are unphysical when
gravitational interactions are included. We apply these observations to the
quantum state of the inflaton, and find that, at best, dramatic fine tuning is
required for states other than the thermal vacuum to lead to observable
features in the CMBR anisotropy.Comment: 31 pages, 4 figure
Quantitative analyses and modelling to support achievement of the 2020 goals for nine neglected tropical diseases
Quantitative analysis and mathematical models are useful tools in informing strategies to control or eliminate disease. Currently, there is an urgent need to develop these tools to inform policy to achieve the 2020 goals for neglected tropical diseases (NTDs). In this paper we give an overview of a collection of novel model-based analyses which aim to address key questions on the dynamics of transmission and control of nine NTDs: Chagas disease, visceral leishmaniasis, human African trypanosomiasis, leprosy, soil-transmitted helminths, schistosomiasis, lymphatic filariasis, onchocerciasis and trachoma. Several common themes resonate throughout these analyses, including: the importance of epidemiological setting on the success of interventions; targeting groups who are at highest risk of infection or re-infection; and reaching populations who are not accessing interventions and may act as a reservoir for infection,. The results also highlight the challenge of maintaining elimination 'as a public health problem' when true elimination is not reached. The models elucidate the factors that may be contributing most to persistence of disease and discuss the requirements for eventually achieving true elimination, if that is possible. Overall this collection presents new analyses to inform current control initiatives. These papers form a base from which further development of the models and more rigorous validation against a variety of datasets can help to give more detailed advice. At the moment, the models' predictions are being considered as the world prepares for a final push towards control or elimination of neglected tropical diseases by 2020
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