735 research outputs found
Comparing periodic-orbit theory to perturbation theory in the asymmetric infinite square well
An infinite square well with a discontinuous step is one of the simplest
systems to exhibit non-Newtonian ray-splitting periodic orbits in the
semiclassical limit. This system is analyzed using both time-independent
perturbation theory (PT) and periodic-orbit theory and the approximate formulas
for the energy eigenvalues derived from these two approaches are compared. The
periodic orbits of the system can be divided into classes according to how many
times they reflect from the potential step. Different classes of orbits
contribute to different orders of PT. The dominant term in the second-order PT
correction is due to non-Newtonian orbits that reflect from the step exactly
once. In the limit in which PT converges the periodic-orbit theory results
agree with those of PT, but outside of this limit the periodic-orbit theory
gives much more accurate results for energies above the potential step.Comment: 22 pages, 2 figures, 2 tables, submitted to Physical Review
Do rats learn conditional independence?
If acquired associations are to accurately represent real relevance relations, there is motivation for the hypothesis that learning will, in some circumstances, be more appropriately modelled, not as direct dependence, but as conditional independence. In a serial compound conditioning experiment, two groups of rats were presented with a conditioned stimulus (CS1) that imperfectly (50%) predicted food, and was itself imperfectly predicted by a CS2. Groups differed in the proportion of CS2 presentations that were ultimately followed by food (25% versus 75%). Thus, the information presented regarding the relevance of CS2 to food was ambiguous between direct dependence and conditional independence (given CS1). If rats learnt that food was conditionally independent of CS2, given CS1, subjects of both groups should thereafter respond similarly to CS2 alone. Contrary to the conditionality hypothesis, subjects attended to the direct food predictability of CS2, suggesting that rats treat even distal stimuli in a CS sequence as immediately relevant to food, not conditional on an intermediate stimulus. These results urge caution in representing indirect associations as conditional associations, accentuate the theoretical weight of the Markov condition in graphical models, and challenge theories to articulate the conditions under which animals are expected to learn conditional associations, if ever.All funding for the project was internal, from Indiana University
Ontology-Based Event Modeling for Semantic Understanding of Chinese News Story
Describing and extracting event semantic information is essential to build an event knowledge base and applications in event and semantic level. However, most existing work deals with documents so they fail to provide sufficient semantic information about events in news articles. In this paper, considering What, Who, When, Where, Why and How, the 5W1H elements of a piece of news, we propose a News Ontology Event Model (NOEM) which can describe 5W1H semantic elements of an event. The model defines concepts of entities (time, person, location, organization etc.), events and relationships to capture temporal, spatial, information, experiential, structural and causal aspect of events. A comparison to existing event models and an empirical case study show that NOEM can effectively model the semantic elements of news events and their relationship; and has a strong ability to represent knowledge facts and easily adapt to new domains.Computer Science, Artificial IntelligenceComputer Science, Theory & MethodsEICPCI-S(ISTP)
Dynamics of quantum systems
A relation between the eigenvalues of an effective Hamilton operator and the
poles of the matrix is derived which holds for isolated as well as for
overlapping resonance states. The system may be a many-particle quantum system
with two-body forces between the constituents or it may be a quantum billiard
without any two-body forces. Avoided crossings of discrete states as well as of
resonance states are traced back to the existence of branch points in the
complex plane. Under certain conditions, these branch points appear as double
poles of the matrix. They influence the dynamics of open as well as of
closed quantum systems. The dynamics of the two-level system is studied in
detail analytically as well as numerically.Comment: 21 pages 7 figure
Classical Scattering for a driven inverted Gaussian potential in terms of the chaotic invariant set
We study the classical electron scattering from a driven inverted Gaussian
potential, an open system, in terms of its chaotic invariant set. This chaotic
invariant set is described by a ternary horseshoe construction on an
appropriate Poincare surface of section. We find the development parameters
that describe the hyperbolic component of the chaotic invariant set. In
addition, we show that the hierarchical structure of the fractal set of
singularities of the scattering functions is the same as the structure of the
chaotic invariant set. Finally, we construct a symbolic encoding of the
hierarchical structure of the set of singularities of the scattering functions
and use concepts from the thermodynamical formalism to obtain one of the
measures of chaos of the fractal set of singularities, the topological entropy.Comment: accepted in Phy. Rev.
Interaction and Localization of One-electron Orbitals in an Organic Molecule: Fictitious Parameter Analysis for Multi-physics Simulations
We present a new methodology to analyze complicated multi-physics simulations
by introducing a fictitious parameter. Using the method, we study quantum
mechanical aspects of an organic molecule in water. The simulation is
variationally constructed from the ab initio molecular orbital method and the
classical statistical mechanics with the fictitious parameter representing the
coupling strength between solute and solvent. We obtain a number of
one-electron orbital energies of the solute molecule derived from the
Hartree-Fock approximation, and eigenvalue-statistical analysis developed in
the study of nonintegrable systems is applied to them. Based on the results, we
analyze localization properties of the electronic wavefunctions under the
influence of the solvent.Comment: 4 pages, 5 figures, the revised version will appear in J. Phys. Soc.
Jpn. Vol.76 (No.1
Changes in Floquet state structure at avoided crossings: delocalization and harmonic generation
Avoided crossings are common in the quasienergy spectra of strongly driven
nonlinear quantum wells. In this paper we examine the sinusoidally driven
particle in a square potential well to show that avoided crossings can alter
the structure of Floquet states in this system. Two types of avoided crossings
are identified: on type leads only to temporary changes (as a function of
driving field strength) in Floquet state structure while the second type can
lead to permanent delocalization of the Floquet states. Radiation spectra from
these latter states show significant increase in high harmonic generation as
the system passes through the avoided crossing.Comment: 8 pages with 10 figures submitted to Physical Review
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