2,271 research outputs found
An Exactly Solvable Model for the Integrability-Chaos Transition in Rough Quantum Billiards
A central question of dynamics, largely open in the quantum case, is to what
extent it erases a system's memory of its initial properties. Here we present a
simple statistically solvable quantum model describing this memory loss across
an integrability-chaos transition under a perturbation obeying no selection
rules. From the perspective of quantum localization-delocalization on the
lattice of quantum numbers, we are dealing with a situation where every lattice
site is coupled to every other site with the same strength, on average. The
model also rigorously justifies a similar set of relationships recently
proposed in the context of two short-range-interacting ultracold atoms in a
harmonic waveguide. Application of our model to an ensemble of uncorrelated
impurities on a rectangular lattice gives good agreement with ab initio
numerics.Comment: 29 pages, 5 figure
Heterotic Models from Vector Bundles on Toric Calabi-Yau Manifolds
We systematically approach the construction of heterotic E_8 X E_8 Calabi-Yau
models, based on compact Calabi-Yau three-folds arising from toric geometry and
vector bundles on these manifolds. We focus on a simple class of 101 such
three-folds with smooth ambient spaces, on which we perform an exhaustive scan
and find all positive monad bundles with SU(N), N=3,4,5 structure groups,
subject to the heterotic anomaly cancellation constraint. We find that
anomaly-free positive monads exist on only 11 of these toric three-folds with a
total number of bundles of about 2000. Only 21 of these models, all of them on
three-folds realizable as hypersurfaces in products of projective spaces, allow
for three families of quarks and leptons. We also perform a preliminary scan
over the much larger class of semi-positive monads which leads to about 44000
bundles with 280 of them satisfying the three-family constraint. These 280
models provide a starting point for heterotic model building based on toric
three-folds.Comment: 41 pages, 5 figures. A table modified and a table adde
Algebraic charge liquids
High temperature superconductivity emerges in the cuprate compounds upon
changing the electron density of an insulator in which the electron spins are
antiferromagnetically ordered. A key characteristic of the superconductor is
that electrons can be extracted from them at zero energy only if their momenta
take one of four specific values (the `nodal points'). A central enigma has
been the evolution of the zero energy electrons in the metallic state between
the antiferromagnet and the superconductor, and recent experiments yield
apparently contradictory results. The oscillation of the resistance in this
metal as a function of magnetic field indicate that the zero energy electrons
carry momenta which lie on elliptical `Fermi pockets', while ejection of
electrons by high intensity light indicates that the zero energy electrons have
momenta only along arc-like regions. We present a theory of new states of
matter, which we call `algebraic charge liquids', which arise naturally between
the antiferromagnet and the superconductor, and reconcile these observations.
Our theory also explains a puzzling dependence of the density of
superconducting electrons on the total electron density, and makes a number of
unique predictions for future experiments.Comment: 6+8 pages, 2 figures; (v2) Rewritten for broader accessibility; (v3)
corrected numerical error in Eq. (5
Goodness-of-Fit Tests for Symmetric Stable Distributions -- Empirical Characteristic Function Approach
We consider goodness-of-fit tests of symmetric stable distributions based on
weighted integrals of the squared distance between the empirical characteristic
function of the standardized data and the characteristic function of the
standard symmetric stable distribution with the characteristic exponent
estimated from the data. We treat as an unknown parameter,
but for theoretical simplicity we also consider the case that is
fixed. For estimation of parameters and the standardization of data we use
maximum likelihood estimator (MLE) and an equivariant integrated squared error
estimator (EISE) which minimizes the weighted integral. We derive the
asymptotic covariance function of the characteristic function process with
parameters estimated by MLE and EISE. For the case of MLE, the eigenvalues of
the covariance function are numerically evaluated and asymptotic distribution
of the test statistic is obtained using complex integration. Simulation studies
show that the asymptotic distribution of the test statistics is very accurate.
We also present a formula of the asymptotic covariance function of the
characteristic function process with parameters estimated by an efficient
estimator for general distributions
Compressibility of titanosilicate melts
The effect of composition on the relaxed adiabatic bulk modulus (K0) of a range of alkali- and alkaline earth-titanosilicate [X 2 n/n+ TiSiO5 (X=Li, Na, K, Rb, Cs, Ca, Sr, Ba)] melts has been investigated. The relaxed bulk moduli of these melts have been measured using ultrasonic interferometric methods at frequencies of 3, 5 and 7 MHz in the temperature range of 950 to 1600°C (0.02 Pa s < s < 5 Pa s). The bulk moduli of these melts decrease with increasing cation size from Li to Cs and Ca to Ba, and with increasing temperature. The bulk moduli of the Li-, Na-, Ca- and Ba-bearing metasilicate melts decrease with the addition of both TiO2 and SiO2 whereas those of the K-, Rb- and Cs-bearing melts increase. Linear fits to the bulk modulus versus volume fraction of TiO2 do not converge to a common compressibility of the TiO2 component, indicating that the structural role of TiO2 in these melts is dependent on the identity of the cation. This proposition is supported by a number of other property data for these and related melt compositions including heat capacity and density, as well as structural inferences from X-ray absorption spectroscopy (XANES). The compositional dependence of the compressibility of the TiO2 component in these melts explains the difficulty incurred in previous attempts to incorporate TiO2 in calculation schemes for melt compressibility. The empirical relationship KV-4/3 for isostructural materials has been used to evaluate the compressibility-related structural changes occurring in these melts. The alkali metasilicate and disilicate melts are isostructural, independent of the cation. The addition of Ti to the metasilicate composition (i.e. X2TiSiO5), however, results in a series of melts which are not isostructural. The alkaline-earth metasilicate and disilicate compositions are not isostructural, but the addition of Ti to the metasilicate compositions (i.e. XTiSiO5) would appear, on the basis of modulus-volume systematics, to result in the melts becoming isostructural with respect to compressibility
The MSSM Spectrum from (0,2)-Deformations of the Heterotic Standard Embedding
We construct supersymmetric compactifications of E_8 \times E_8 heterotic
string theory which realise exactly the massless spectrum of the Minimal
Supersymmetric Standard Model (MSSM) at low energies. The starting point is the
standard embedding on a Calabi-Yau threefold which has Hodge numbers
(h^11,h^21) = (1,4) and fundamental group Z_12, which gives an E_6 grand
unified theory with three net chiral generations. The gauge symmetry is then
broken to that of the standard model by a combination of discrete Wilson lines
and continuous deformation of the gauge bundle. On eight distinct branches of
the moduli space, we find stable bundles with appropriate cohomology groups to
give exactly the massless spectrum of the MSSM.Comment: 37 pages including appendice
Spacial and temporal dynamics of the volume fraction of the colloidal particles inside a drying sessile drop
Using lubrication theory, drying processes of sessile colloidal droplets on a
solid substrate are studied. A simple model is proposed to describe temporal
dynamics both the shape of the drop and the volume fraction of the colloidal
particles inside the drop. The concentration dependence of the viscosity is
taken into account. It is shown that the final shapes of the drops depend on
both the initial volume fraction of the colloidal particles and the capillary
number. The results of our simulations are in a reasonable agreement with the
published experimental data. The computations for the drops of aqueous solution
of human serum albumin (HSA) are presented.Comment: Submitted to EPJE, 7 pages, 8 figure
Towards a large-scale quantum simulator on diamond surface at room temperature
Strongly-correlated quantum many-body systems exhibits a variety of exotic
phases with long-range quantum correlations, such as spin liquids and
supersolids. Despite the rapid increase in computational power of modern
computers, the numerical simulation of these complex systems becomes
intractable even for a few dozens of particles. Feynman's idea of quantum
simulators offers an innovative way to bypass this computational barrier.
However, the proposed realizations of such devices either require very low
temperatures (ultracold gases in optical lattices, trapped ions,
superconducting devices) and considerable technological effort, or are
extremely hard to scale in practice (NMR, linear optics). In this work, we
propose a new architecture for a scalable quantum simulator that can operate at
room temperature. It consists of strongly-interacting nuclear spins attached to
the diamond surface by its direct chemical treatment, or by means of a
functionalized graphene sheet. The initialization, control and read-out of this
quantum simulator can be accomplished with nitrogen-vacancy centers implanted
in diamond. The system can be engineered to simulate a wide variety of
interesting strongly-correlated models with long-range dipole-dipole
interactions. Due to the superior coherence time of nuclear spins and
nitrogen-vacancy centers in diamond, our proposal offers new opportunities
towards large-scale quantum simulation at room temperatures
Optical Lattices: Theory
This chapter presents an overview of the properties of a Bose-Einstein
condensate (BEC) trapped in a periodic potential. This system has attracted a
wide interest in the last years, and a few excellent reviews of the field have
already appeared in the literature (see, for instance, [1-3] and references
therein). For this reason, and because of the huge amount of published results,
we do not pretend here to be comprehensive, but we will be content to provide a
flavor of the richness of this subject, together with some useful references.
On the other hand, there are good reasons for our effort. Probably, the most
significant is that BEC in periodic potentials is a truly interdisciplinary
problem, with obvious connections with electrons in crystal lattices, polarons
and photons in optical fibers. Moreover, the BEC experimentalists have reached
such a high level of accuracy to create in the lab, so to speak, paradigmatic
Hamiltonians, which were first introduced as idealized theoretical models to
study, among others, dynamical instabilities or quantum phase transitions.Comment: Chapter 13 in Part VIII: "Optical Lattices" of "Emergent Nonlinear
Phenomena in Bose-Einstein Condensates: Theory and Experiment," edited by P.
G. Kevrekidis, D. J. Frantzeskakis, and R. Carretero-Gonzalez (Springer
Series on Atomic, Optical, and Plasma Physics, 2007) - pages 247-26
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