Quantum Spectra of Triangular Billiards on the Sphere

We study the quantal energy spectrum of triangular billiards on a spherical surface. Group theory yields analytical results for tiling billiards while the generic case is treated numerically. We find that the statistical properties of the spectra do not follow the standard random matrix results and their peculiar behaviour can be related to the corresponding classical phase space structure.Comment: 18 pages, 5 eps figure

Phase Space Evolution and Discontinuous Schr\"odinger Waves

The problem of Schr\"odinger propagation of a discontinuous wavefunction -diffraction in time- is studied under a new light. It is shown that the evolution map in phase space induces a set of affine transformations on discontinuous wavepackets, generating expansions similar to those of wavelet analysis. Such transformations are identified as the cause for the infinitesimal details in diffraction patterns. A simple case of an evolution map, such as SL(2) in a two-dimensional phase space, is shown to produce an infinite set of space-time trajectories of constant probability. The trajectories emerge from a breaking point of the initial wave.Comment: Presented at the conference QTS7, Prague 2011. 12 pages, 7 figure

Fractals and Scars on a Compact Octagon

A finite universe naturally supports chaotic classical motion. An ordered fractal emerges from the chaotic dynamics which we characterize in full for a compact 2-dimensional octagon. In the classical to quantum transition, the underlying fractal can persist in the form of scars, ridges of enhanced amplitude in the semiclassical wave function. Although the scarring is weak on the octagon, we suggest possible subtle implications of fractals and scars in a finite universe.Comment: 6 pages, 3 figs, LaTeX fil

Decimation and Harmonic Inversion of Periodic Orbit Signals

We present and compare three generically applicable signal processing methods for periodic orbit quantization via harmonic inversion of semiclassical recurrence functions. In a first step of each method, a band-limited decimated periodic orbit signal is obtained by analytical frequency windowing of the periodic orbit sum. In a second step, the frequencies and amplitudes of the decimated signal are determined by either Decimated Linear Predictor, Decimated Pade Approximant, or Decimated Signal Diagonalization. These techniques, which would have been numerically unstable without the windowing, provide numerically more accurate semiclassical spectra than does the filter-diagonalization method.Comment: 22 pages, 3 figures, submitted to J. Phys.

An effect of age on implicit memory that is not due to explicit contamination: implications for single and multiple-systems theories

Recognition memory is typically weaker in healthy older relative to young adults, while performance on implicit tests (e.g., repetition priming) is often comparable between groups. Such observations are commonly taken as evidence for independent explicit and implicit memory systems. On a picture version of the continuous identification with recognition (CID-R) task, we found a reliable age-related reduction in recognition memory, while the age effect on priming did not reach statistical significance (Experiment 1). This pattern was consistent with the predictions of a formal single-system model. Experiment 2 replicated these observations using separate priming (continuous identification; CID) and recognition phases, while a combined data analysis revealed a significant effect of age on priming. In Experiment 3, we provide evidence that priming in this task is unaffected by explicit processing, and we conclude that the age difference in priming is unlikely to have been driven by differences in explicit processing between groups of young and older adults (“explicit contamination”). The results support the view that explicit and implicit expressions of memory are driven by a single underlying memory system

Age effects on explicit and implicit memory

It is well-documented that explicit memory (e.g., recognition) declines with age. In contrast, many argue that implicit memory (e.g., priming) is preserved in healthy aging. For example, priming on tasks such as perceptual identification is often not statistically different in groups of young and older adults. Such observations are commonly taken as evidence for distinct explicit and implicit learning/memory systems. In this article we discuss several lines of evidence that challenge this view. We describe how patterns of differential age-related decline may arise from differences in the ways in which the two forms of memory are commonly measured, and review recent research suggesting that under improved measurement methods, implicit memory is not age-invariant. Formal computational models are of considerable utility in revealing the nature of underlying systems. We report the results of applying single and multiple-systems models to data on age effects in implicit and explicit memory. Model comparison clearly favors the single-system view. Implications for the memory systems debate are discussed

Point perturbations of circle billiards

The spectral statistics of the circular billiard with a point-scatterer is investigated. In the semiclassical limit, the spectrum is demonstrated to be composed of two uncorrelated level sequences. The first corresponds to states for which the scatterer is located in the classically forbidden region and its energy levels are not affected by the scatterer in the semiclassical limit while the second sequence contains the levels which are affected by the point-scatterer. The nearest neighbor spacing distribution which results from the superposition of these sequences is calculated analytically within some approximation and good agreement with the distribution that was computed numerically is found.Comment: 9 pages, 2 figure

Does study duration have opposite effects on recognition and repetition priming?

We investigated whether manipulating the duration for which an item is studied has opposite effects on recognition memory and repetition priming, as has been reported by Voss and Gonsalves (2010). Robust evidence of this would support the idea that distinct explicit and implicit memory systems drive recognition and priming, and would constitute evidence against a single-system model (Berry, Shanks, Speekenbrink, & Henson, 2012). Across seven experiments using study durations ranging from 40 ms to 2250 ms, and two different priming tasks (a classification task in Experiments 1a, 2a, 3a, and 4, and a continuous identification with recognition (CID-R) task in Experiments 1b, 2b, and 3b), we found that although a longer study duration improved subsequent recognition in each experiment, there was either no detectable effect on priming (Experiments 1a, 2a, and 4) or a similar effect to that on recognition, albeit smaller in magnitude (Experiments 1b, 2b, 3a, and 3b). Our findings (1) question whether study duration has opposite effects on recognition and priming, and (2) are robustly consistent with a single-system model of recognition and priming

Thermalization of a Brownian particle via coupling to low-dimensional chaos

It is shown that a paradigm of classical statistical mechanics --- the thermalization of a Brownian particle --- has a low-dimensional, deterministic analogue: when a heavy, slow system is coupled to fast deterministic chaos, the resultant forces drive the slow degrees of freedom toward a state of statistical equilibrium with the fast degrees. This illustrates how concepts useful in statistical mechanics may apply in situations where low-dimensional chaos exists.Comment: Revtex, 11 pages, no figures