168 research outputs found
Eigenvalue Integro-Differential Equations for Orthogonal Polynomials on the Real Line
The one-dimensional harmonic oscillator wave functions are solutions to a
Sturm-Liouville problem posed on the whole real line. This problem generates
the Hermite polynomials. However, no other set of orthogonal polynomials can be
obtained from a Sturm-Liouville problem on the whole real line. In this paper
we show how to characterize an arbitrary set of polynomials orthogonal on
in terms of a system of integro-differential equations of
Hartree-Fock type. This system replaces and generalizes the linear differential
equation associated with a Sturm-Liouville problem. We demonstrate our results
for the special case of Hahn-Meixner polynomials.Comment: 28 pages, Latex, U. Texas at Austin/ Washington University preprin
Scaling and Universality of the Complexity of Analog Computation
We apply a probabilistic approach to study the computational complexity of
analog computers which solve linear programming problems. We analyze
numerically various ensembles of linear programming problems and obtain, for
each of these ensembles, the probability distribution functions of certain
quantities which measure the computational complexity, known as the convergence
rate, the barrier and the computation time. We find that in the limit of very
large problems these probability distributions are universal scaling functions.
In other words, the probability distribution function for each of these three
quantities becomes, in the limit of large problem size, a function of a single
scaling variable, which is a certain composition of the quantity in question
and the size of the system. Moreover, various ensembles studied seem to lead
essentially to the same scaling functions, which depend only on the variance of
the ensemble. These results extend analytical and numerical results obtained
recently for the Gaussian ensemble, and support the conjecture that these
scaling functions are universal.Comment: 22 pages, latex, 12 eps fig
Integrated Models of Care for Individuals with Opioid Use Disorder: How Do We Prevent HIV and HCV?
Purpose of Review To describe models of integrated and co-located care for opioid use disorder (OUD), hepatitis C (HCV), and HIV. Recent Findings The design and scale-up of multidisciplinary care models that engage, retain, and treat individuals with HIV, HCV, and OUD are critical to preventing continued spread of HIV and HCV. We identified 17 models within primary care (N = 3), HIV specialty care (N = 5), opioid treatment programs (N = 6), transitional clinics (N = 2), and community-based harm reduction programs (N = 1), as well as two emerging models. Summary Key components of such models are the provision of (1) medication-assisted treatment for OUD, (2) HIV and HCV treatment, (3) HIV pre-exposure prophylaxis, and (4) behavioral health services. Research is needed to understand differences in effectiveness between co-located and fully integrated care, combat the deleterious racial and ethnic legacies of the âWar on Drugs,â and inform the delivery of psychiatric care. Increased access to harm reduction services is crucial
Beyond the second order magnetic anisotropy tensor: Higher-order components due to oriented magnetite exsolutions in pyroxenes, and implications for paleomagnetic and structural interpretations
Exsolved iron oxides in silicate minerals can be nearly ideal paleomagnetic recorders, due to their single-domain-like behaviour and the protection from chemical alteration by their surrounding silicate host. Because their geometry is crystallographically controlled by the host silicate, these exsolutions possess a shape preferred orientation that is ultimately controlled by the mineral fabric of the silicates. This leads to potentially significant anisotropic acquisition of remanence, which necessitates correction to make accurate interpretations in paleodirectional and paleointensity studies. Here, we investigate the magnetic shape anisotropy carried by magnetite exsolutions in pyroxene single crystals, and in pyroxene-bearing rocks based on torque measurements and rotational hysteresis data. Image analysis is used to characterize the orientation distribution of oxides, from which the observed anisotropy can be modelled. Both the high-field torque signal and corresponding models contain components of higher order, which cannot be accurately described by second order tensors usually employed to describe magnetic fabrics. Conversely, low-field anisotropy data do not show this complexity and can be adequately described with second-order tensors. Hence, magnetic anisotropy of silicate-hosted exsolutions is field-dependent and this should be taken into account when interpreting isolated ferromagnetic fabrics, and in anisotropy corrections
Stable Fermion Bag Solitons in the Massive Gross-Neveu Model: Inverse Scattering Analysis
Formation of fermion bag solitons is an important paradigm in the theory of
hadron structure. We study this phenomenon non-perturbatively in the 1+1
dimensional Massive Gross-Neveu model, in the large limit. We find,
applying inverse scattering techniques, that the extremal static bag
configurations are reflectionless, as in the massless Gross-Neveu model. This
adds to existing results of variational calculations, which used reflectionless
bag profiles as trial configurations. Only reflectionless trial configurations
which support a single pair of charge-conjugate bound states of the associated
Dirac equation were used in those calculations, whereas the results in the
present paper hold for bag configurations which support an arbitrary number of
such pairs. We compute the masses of these multi-bound state solitons, and
prove that only bag configurations which bear a single pair of bound states are
stable. Each one of these configurations gives rise to an O(2N) antisymmetric
tensor multiplet of soliton states, as in the massless Gross-Neveu model.Comment: 10 pages, revtex, no figures; v2: typos corrected, references added;
v3: version accepted for publication in the PRD. referencess added. Some
minor clarifications added at the beginning of section
Effective Non-Hermitian Hamiltonians for Studying Resonance Statistics in Open Disordered Systems
We briefly discuss construction of energy-dependent effective non-hermitian
hamiltonians for studying resonances in open disordered systemsComment: Latex, 20 pages, 1 fig. Expanded version of a talk at the Workshop on
Pseudo-Hermitian Hamiltonians in Quantum Physics IX, June 21-24 2010,
Zhejiang University, Hangzhou, China. Accepted for publication in the
Internationa Journal of Theoretical Physics (Springer Verlag
Does the complex deformation of the Riemann equation exhibit shocks?
The Riemann equation , which describes a one-dimensional
accelerationless perfect fluid, possesses solutions that typically develop
shocks in a finite time. This equation is \cP\cT symmetric. A one-parameter
\cP\cT-invariant complex deformation of this equation,
( real), is solved exactly using the
method of characteristic strips, and it is shown that for real initial
conditions, shocks cannot develop unless is an odd integer.Comment: latex, 8 page
Dynamical Generation of Extended Objects in a Dimensional Chiral Field Theory: Non-Perturbative Dirac Operator Resolvent Analysis
We analyze the dimensional Nambu-Jona-Lasinio model non-perturbatively.
In addition to its simple ground state saddle points, the effective action of
this model has a rich collection of non-trivial saddle points in which the
composite fields \sigx=\lag\bar\psi\psi\rag and \pix=\lag\bar\psi
i\gam_5\psi\rag form static space dependent configurations because of
non-trivial dynamics. These configurations may be viewed as one dimensional
chiral bags that trap the original fermions (``quarks") into stable extended
entities (``hadrons"). We provide explicit expressions for the profiles of
these objects and calculate their masses. Our analysis of these saddle points
is based on an explicit representation we find for the diagonal resolvent of
the Dirac operator in a \{\sigx, \pix\} background which produces a
prescribed number of bound states. We analyse in detail the cases of a single
as well as two bound states. We find that bags that trap fermions are the
most stable ones, because they release all the fermion rest mass as binding
energy and become massless. Our explicit construction of the diagonal resolvent
is based on elementary Sturm-Liouville theory and simple dimensional analysis
and does not depend on the large approximation. These facts make it, in our
view, simpler and more direct than the calculations previously done by Shei,
using the inverse scattering method following Dashen, Hasslacher, and Neveu.
Our method of finding such non-trivial static configurations may be applied to
other dimensional field theories
On Kinks and Bound States in the Gross-Neveu Model
We investigate static space dependent \sigx=\lag\bar\psi\psi\rag saddle
point configurations in the two dimensional Gross-Neveu model in the large N
limit. We solve the saddle point condition for \sigx explicitly by employing
supersymmetric quantum mechanics and using simple properties of the diagonal
resolvent of one dimensional Schr\"odinger operators rather than inverse
scattering techniques. The resulting solutions in the sector of unbroken
supersymmetry are the Callan-Coleman-Gross-Zee kink configurations. We thus
provide a direct and clean construction of these kinks. In the sector of broken
supersymmetry we derive the DHN saddle point configurations. Our method of
finding such non-trivial static configurations may be applied also in other two
dimensional field theories.Comment: Revised version. A new section added with derivation of the DHN
static configurations in the sector of broken supersymmetry. Some references
added as well. 25 pp, latex, e-mail [email protected]
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