311 research outputs found
Maximal rank for ΩPn
International Mathematical Forum, Vol. 6, 2011, no. 8, 389 - 398Full Tex
Fundamental length in quantum theories with PT-symmetric Hamiltonians II: The case of quantum graphs
Manifestly non-Hermitian quantum graphs with real spectra are introduced and
shown tractable as a new class of phenomenological models with several
appealing descriptive properties. For illustrative purposes, just equilateral
star-graphs are considered here in detail, with non-Hermiticities introduced by
interactions attached to the vertices. The facilitated feasibility of the
analysis of their spectra is achieved via their systematic approximative
Runge-Kutta-inspired reduction to star-shaped discrete lattices. The resulting
bound-state spectra are found real in a discretization-independent interval of
couplings. This conclusion is reinterpreted as the existence of a hidden
Hermiticity of our models, i.e., as the standard and manifest Hermiticity of
the underlying Hamiltonian in one of less usual, {\em ad hoc} representations
of the Hilbert space of states in which the inner product is local
(at ) or increasingly nonlocal (at ). Explicit examples of
these (of course, Hamiltonian-dependent) hermitizing inner products are offered
in closed form. In this way each initial quantum graph is assigned a menu of
optional, non-equivalent standard probabilistic interpretations exhibiting a
controlled, tunable nonlocality.Comment: 33 pp., 6 figure
PT-symmetric deformations of Calogero models
We demonstrate that Coxeter groups allow for complex PT-symmetric deformations across the boundaries of all Weyl chambers. We compute the explicit deformations for the A2 and G2-Coxeter group and apply these constructions to CalogeroâMoserâSutherland models invariant under the extended Coxeter groups. The eigenspectra for the deformed models are real and contain the spectra of the undeformed case as subsystems
q-breathers in Discrete Nonlinear Schroedinger lattices
-breathers are exact time-periodic solutions of extended nonlinear systems
continued from the normal modes of the corresponding linearized system. They
are localized in the space of normal modes. The existence of these solutions in
a weakly anharmonic atomic chain explained essential features of the
Fermi-Pasta-Ulam (FPU) paradox. We study -breathers in one- two- and
three-dimensional discrete nonlinear Sch\"{o}dinger (DNLS) lattices --
theoretical playgrounds for light propagation in nonlinear optical waveguide
networks, and the dynamics of cold atoms in optical lattices. We prove the
existence of these solutions for weak nonlinearity. We find that the
localization of -breathers is controlled by a single parameter which depends
on the norm density, nonlinearity strength and seed wave vector. At a critical
value of that parameter -breathers delocalize via resonances, signaling a
breakdown of the normal mode picture and a transition into strong mode-mode
interaction regime. In particular this breakdown takes place at one of the
edges of the normal mode spectrum, and in a singular way also in the center of
that spectrum. A stability analysis of -breathers supplements these
findings. For three-dimensional lattices, we find -breather vortices, which
violate time reversal symmetry and generate a vortex ring flow of energy in
normal mode space.Comment: 19 pages, 9 figure
Multivector Field Formulation of Hamiltonian Field Theories: Equations and Symmetries
We state the intrinsic form of the Hamiltonian equations of first-order
Classical Field theories in three equivalent geometrical ways: using
multivector fields, jet fields and connections. Thus, these equations are given
in a form similar to that in which the Hamiltonian equations of mechanics are
usually given. Then, using multivector fields, we study several aspects of
these equations, such as the existence and non-uniqueness of solutions, and the
integrability problem. In particular, these problems are analyzed for the case
of Hamiltonian systems defined in a submanifold of the multimomentum bundle.
Furthermore, the existence of first integrals of these Hamiltonian equations is
considered, and the relation between {\sl Cartan-Noether symmetries} and {\sl
general symmetries} of the system is discussed. Noether's theorem is also
stated in this context, both the ``classical'' version and its generalization
to include higher-order Cartan-Noether symmetries. Finally, the equivalence
between the Lagrangian and Hamiltonian formalisms is also discussed.Comment: Some minor mistakes are corrected. Bibliography is updated. To be
published in J. Phys. A: Mathematical and Genera
Detectable Viral Load in Late Pregnancy among Women in the Rwanda Option B+ PMTCT Program: Enrollment Results from the Kabeho Study.
There are limited viral load (VL) data available from programs implementing Option B+, lifelong antiretroviral treatment (ART) to all HIV-positive pregnant and postpartum women, in resource-limited settings. Extent of viral suppression from a prevention of mother-to-child transmission of HIV program in Rwanda was assessed among women enrolled in the Kigali Antiretroviral and Breastfeeding Assessment for the Elimination of HIV (Kabeho) Study. ARV drug resistance testing was conducted on women with VL\u3e2000 copies/ml. In April 2013-January 2014, 608 pregnant or early postpartum HIV-positive women were enrolled in 14 facilities. Factors associated with detectable enrollment VL (\u3e20 copies/ml) were examined using generalized estimating equations. The most common antiretroviral regimen (56.7%, 344/607) was tenofovir/lamivudine/efavirenz. Median ART duration was 13.5 months (IQR 3.0-48.8); 76.1% of women were on ART at first antenatal visit. Half of women (315/603) had undetectable RNA-PCR VL and 84.6% (510) had36 months compared to those on ART 4-36 months (72/191, 37.7% versus 56/187, 29.9%), though the difference was not significant. The odds of having detectable enrollment VL decreased significantly as duration on ART at enrollment increased (AOR = 0.99, 95% CI: 0.9857, 0.9998, p = 0.043). There was a higher likelihood of detectable VL for women with lower gravidity (AOR = 0.90, 95% CI: 0.84, 0.97, p = 0.0039), no education (AOR = 2.25, (95% CI: 1.37, 3.70, p = 0.0004), nondisclosure to partner (AOR = 1.97, 95% CI: 1.21, 3.21, p = 0.0063) and side effects (AOR = 2.63, 95% CI: 1.72, 4.03, p36 months with genotyping available. Most women were receiving ART at first antenatal visit, with relatively high viral suppression rates. Shorter ART duration was associated with higher VL, with a concerning increasing trend for higher viremia and drug resistance among women on ART for \u3e3 years
An exactly solvable quantum-lattice model with a tunable degree of nonlocality
An array of N subsequent Laguerre polynomials is interpreted as an
eigenvector of a non-Hermitian tridiagonal Hamiltonian with real spectrum
or, better said, of an exactly solvable N-site-lattice cryptohermitian
Hamiltonian whose spectrum is known as equal to the set of zeros of the N-th
Laguerre polynomial. The two key problems (viz., the one of the ambiguity and
the one of the closed-form construction of all of the eligible inner products
which make Hermitian in the respective {\em ad hoc} Hilbert spaces) are
discussed. Then, for illustration, the first four simplest, parametric
definitions of inner products with and are explicitly
displayed. In mathematical terms these alternative inner products may be
perceived as alternative Hermitian conjugations of the initial N-plet of
Laguerre polynomials. In physical terms the parameter may be interpreted as
a measure of the "smearing of the lattice coordinates" in the model.Comment: 35 p
Molecular dynamics of a short range ordered smectic phase nanoconfined into porous silicon
4-n-octyl-4-cyanobiphenyl (8CB) has been recently shown to display an unusual
sequence of phases when confined into porous silicon (PSi). The gradual
increase of oriented short-range smectic (SRS) correlations in place of a phase
transition has been interpreted as a consequence of the anisotropic quenched
disorder induced by confinement in PSi. Combining two quasielastic neutron
scattering experiments with complementary energy resolutions, we present the
first investigation of the individual molecular dynamics of this system. A
large reduction of the molecular dynamics is observed in the confined liquid
phase, as a direct consequence of the dynamical boundary conditions imposed by
the confinement. Temperature fixed window scans (FWS) reveal a continuous
'glass-like' reduction of the molecular dynamics of the confined liquid and SRS
phases on cooling down to 250 K, where a solid-like behavior is finally reached
by a two steps crystallization process
- âŠ