2,532 research outputs found
Hohenberg-Kohn theorem for the lowest-energy resonance of unbound systems
We show that under well-defined conditions the Hohenberg-Kohn theorem (HKT)
can be extended to the lowest-energy resonance of unbound systems. Using the
Gel'fand Levitan theorem, the extended version of the HKT can also be applied
to systems that support a finite number of bound states. The extended version
of the HKT provides an adequate framework to carry out DFT calculations of
negative electron affinities.Comment: 4 pages, 3 figure
Coherent states for polynomial su(1,1) algebra and a conditionally solvable system
In a previous paper [{\it J. Phys. A: Math. Theor.} {\bf 40} (2007) 11105],
we constructed a class of coherent states for a polynomially deformed
algebra. In this paper, we first prepare the discrete representations of the
nonlinearly deformed algebra. Then we extend the previous procedure
to construct a discrete class of coherent states for a polynomial su(1,1)
algebra which contains the Barut-Girardello set and the Perelomov set of the
SU(1,1) coherent states as special cases. We also construct coherent states for
the cubic algebra related to the conditionally solvable radial oscillator
problem.Comment: 2 figure
Methods for lineage tracing on the organism-wide level
Determining the lineage origin of cell types is a major goal in developmental biology. Furthermore, lineage tracing is a powerful approach for understanding the origin of developmental defects as well as the origin of diseases such as cancer. There is now a variety of complementary approaches for identifying lineage relationships, ranging from direct observation of cell divisions by light microscopy to genetic labeling of cells using inducible recombinases and fluorescent reporters. A recent development, and the main topic of this review article, is the use of high-throughput sequencing data for lineage analysis. This emerging approach holds the promise of increased multiplexing capacity, allowing lineage analysis of large cell numbers up to the organism-wide level combined with simultaneous transcription profiling by single cell RNA sequencing
More on coupling coefficients for the most degenerate representations of SO(n)
We present explicit closed-form expressions for the general group-theoretical
factor appearing in the alpha-topology of a high-temperature expansion of
SO(n)-symmetric lattice models. This object, which is closely related to
6j-symbols for the most degenerate representation of SO(n), is discussed in
detail.Comment: 9 pages including 1 table, uses IOP macros Update of Introduction and
Discussion, References adde
Klein tunneling in carbon nanostructures: a free particle dynamics in disguise
The absence of backscattering in metallic nanotubes as well as perfect Klein
tunneling in potential barriers in graphene are the prominent electronic
characteristics of carbon nanostructures. We show that the phenomena can be
explained by a peculiar supersymmetry generated by a first order Hamiltonian
and zero order supercharge operators. Like the supersymmetry associated with
second order reflectionless finite-gap systems, it relates here the low-energy
behavior of the charge carriers with the free particle dynamics.Comment: 4 pages, 1 fig., typos correcte
The Use of Cognitive Ability Measures As Explanatory Variables In Regression Analysis
Cognitive ability measures are often taken as explanatory variables in regression analysis, e.g., as a factor affecting a market outcome such as an individualâs wage, or a decision such as an individualâs education acquisition. Cognitive ability is a latent construct; its true value is unobserved. Nonetheless, researchers often assume that a test score, constructed via standard psychometric practice from individualsâ responses to test items, can be safely used in regression analysis. We examine problems that can arise, and suggest that an alternative approach, a âmixed effects structural equationsâ (MESE) model, may be more appropriate in many circumstances
Topological methods for searching barriers and reaction paths
We present a family of algorithms for the fast determination of reaction
paths and barriers in phase space and the computation of the corresponding
rates. The method requires the reaction times be large compared to the
microscopic time, irrespective of the origin - energetic, entropic, cooperative
- of the timescale separation. It lends itself to temperature cycling as in
simulated annealing and to activation-relaxation routines. The dynamics is
ultimately based on supersymmetry methods used years ago to derive Morse
theory. Thus, the formalism automatically incorporates all relevant topological
information.Comment: 4 pages, 4 figures, RevTex
Supersymmetry of the Nonstationary Schr\"odinger equation and Time-Dependent Exactly Solvable Quantum Models
New exactly solvable quantum models are obtained with the help of the
supersymmetric extencion of the nonstationary Schr/"odinger equation.Comment: Talk at the 8th International Conference "Symmetry Methods in
Physics". Dubna, Russia, 28 July - 2 August, 199
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