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

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

Dynamics of quantum systems

A relation between the eigenvalues of an effective Hamilton operator and the poles of the $S$ 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 $S$ 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

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

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.

Foil deposition alpha collector probe for TFTR`s D-T phase

A new foil deposition alpha collector sample probe has been developed for TFTR`s D-T phase. D-T fusion produced alpha particles escaping from the plasma are implanted in nickel foils located in a series of collimating ports on the detector. The nickel foils are removed from the tokamak after exposure to one or more plasma discharges and analyzed for helium content. This detector is intended to provide improved alpha particle energy resolution and pitch angle coverage over existing lost alpha detectors, and to provide an absolutely calibrated cross-check with these detectors. The ability to resolve between separate energy components of alpha particle loss is estimated to be {approx} 20%. A full 360{degree} of pitch angle coverage is provided for by 8 channels having an acceptance range of {approx} 53{degree} per channel. These detectors will be useful in characterizing classical and anomalous alpha losses and any collective alpha instabilities that may be excited during the D-T campaign of TFTR

Methods for the measuring surface tritium inside TFTR using beta decay

Three potential methods for evaluating the surface tritium content of the TFTR vacuum vessel are described, each based on a different technique for measuring the in situ beta emission from tritium. These methods should be able to provide both a local and a global assessment of the tritium content within the top {approximately}1{mu}m of the inner wall surface