Majorana and the quasi-stationary states in Nuclear Physics

A complete theoretical model describing artificial disintegration of nuclei by bombardment with alpha-particles, developed by Majorana as early as in 1930, is discussed in detail alongside the basic experimental evidences that motivated it. By following the quantum dynamics of a state resulting from the superposition of a discrete state with a continuum one, whose interaction is described by a given potential term, Majorana obtained (among the other predictions) the explicit expression for the integrated cross section of the nuclear process, which is the direct measurable quantity of interest in the experiments. Though this is the first application of the concept of quasi-stationary states to a Nuclear Physics problem, it seems also that the unpublished Majorana's work anticipates by several years the related seminal paper by Fano on Atomic Physics.Comment: latex, amsart, 13 page

Random wave functions and percolation

Recently it was conjectured that nodal domains of random wave functions are adequately described by critical percolation theory. In this paper we strengthen this conjecture in two respects. First, we show that, though wave function correlations decay slowly, a careful use of Harris' criterion confirms that these correlations are unessential and nodal domains of random wave functions belong to the same universality class as non critical percolation. Second, we argue that level domains of random wave functions are described by the non-critical percolation model.Comment: 13 page

Semi-Phenomenological Analysis of Dynamics of Nonlinear Excitations in One-Dimensional Electron-Phonon System

The structure of moving nonlinear excitations in one-dimensional electron-phonon systems is studied semi-phenomenologically by using an effective action in which the width of the nonlinear excitation is treated as a dynamical variable. The effective action can be derived from Su, Schrieffer and Heeger's model or its continuum version proposed by Takayama, Lin-Liu and Maki with an assumption that the nonlinear excitation moves uniformly without any deformation except the change of its width. The form of the action is essentially the same as that discussed by Bishop and coworkers in studying the dynamics of the soliton in polyacetylene, though some details are different. For the moving excitation with a velocity $v$, the width is determined by minimizing the effective action. A requirement that there must be a minimum in the action as a function of its width provides a maximum velocity. The velocity dependence of the width and energy can be determined. The motions of a soliton in p olyacetylene and an acoustic polaron in polydiacetylene are studied within this formulation. The obtained results are in good agreement with those of numerical simulations.Comment: 19 pages, LaTeX, 7 Postscript figures, to be published in J. Phys. Soc. Jpn. vol.65 (1996) No.

Fermion zero modes on vortices in chiral superconductors

The energy levels of the fermions bound to the vortex core are considered for the general case of chiral superconductors. There are two classes of chiral superconductivity: in the superconducting state of class I the axisymmetric singly quantized vortex has the same energy spectrum of bound states as in s-wave superconductor: E=(n+1/2)\omega_0 with integral n. In the class II the corresponding spectrum is E=n\omega_0 and thus contains the state with exactly zero energy. The effect of a single impurity on the spectrum of bound state is also considered. For the class I the spectrum acquires the double period \Delta E=2\omega_0 and consists of two equidistant sets of levels in accordance with A.I. Larkin and Yu.N. Ovchinnikov, Phys. Rev. B57 (1998) 5457. The spectrum is not influenced by a single impurity if the same approximation is applied for vortices in the class II superconducting states.Comment: 4 pages, no figures, corrected version accepted in JETP Letter

The influence of chiral surface states on the London penetration depth in Sr2_2RuO4_4

The London penetration depth for the unconventional superconductor Sr$_2$RuO$_4$ is analyzed assuming an order parameter which breaks time reversal symmetry and parity simultaneously. Such a superconducting state possesses chiral quasiparticle states with subgap energies at the surface. We show that these subgap states can give a significant contribution to the low-temperature behavior of the London penetration depth yielding a $T^2$ power-law even though bulk quasiparticle spectrum is gapped. The presence of several electron bands gives rise to interband transition among the subgap surface states and influences the properties of the surface impedance. Furthermore, the surface states lead also to a non-linear Meissner effect.Comment: 4 pages, 1 figure, the definition of the Nambu field operator introduced, and some typos correcte

Pigeons Choose to Gamble in a Categorical Discrimination Task

In slot-machine play, near wins are stimuli that visually approximate winning stimuli but deliver no reinforcers. In two experiments, a categorical discrimination task was embedded in a concurrent chain to investigate how near wins affect preference for probabilistic versus certain food. Pecking in variable-interval initial links produced access to a fixed-ratio (FR) 1-FR 1-FR 1 chain. When all links were red, the chain was a “win” that produced access to food. A “clear loss” chain involved three green stimuli, and in a “near win,” key colors during successive FR 1 links were red, red, and green. In Experiment 1, the magnitude and probability of reinforcement were varied across conditions with and without near wins. Response allocation was sensitive to changes in reinforcer magnitude and probability. Generalized matching analyses revealed a consistent bias for probabilistic over certain outcomes, but only when they included near wins. Response rates on near-win trials were also intermediate to that of clear losses and wins. Near-win probability was varied across conditions of Experiment 2 and probability of near wins was positively associated with bias for probabilistic outcomes. The results from both experiments suggest that near wins encourage individuals to choose to gamble by functioning as conditioned reinforcers

Generalized Stacking Fault Energy Surfaces and Dislocation Properties of Silicon: A First-Principles Theoretical Study

The generalized stacking fault (GSF) energy surfaces have received considerable attention due to their close relation to the mechanical properties of solids. We present a detailed study of the GSF energy surfaces of silicon within the framework of density functional theory. We have calculated the GSF energy surfaces for the shuffle and glide set of the (111) plane, and that of the (100) plane of silicon, paying particular attention to the effects of the relaxation of atomic coordinates. Based on the calculated GSF energy surfaces and the Peierls-Nabarro model, we obtain estimates for the dislocation profiles, core energies, Peierls energies, and the corresponding stresses for various planar dislocations of silicon.Comment: 9 figures (not included; send requests to [email protected]

Dynamical Masses of Low Mass Stars in the Taurus and Ophiuchus Star Forming Regions

We report new dynamical masses for 5 pre-main sequence (PMS) stars in the L1495 region of the Taurus star-forming region (SFR) and 6 in the L1688 region of the Ophiuchus SFR. Since these regions have VLBA parallaxes these are absolute measurements of the stars' masses and are independent of their effective temperatures and luminosities. Seven of the stars have masses $<0.6$ solar masses, thus providing data in a mass range with little data, and of these, 6 are measured to precision $< 5 \%$. We find 8 stars with masses in the range 0.09 to 1.1 solar mass that agree well with the current generation of PMS evolutionary models. The ages of the stars we measured in the Taurus SFR are in the range 1-3 MY, and $<1$ MY for those in L1688. We also measured the dynamical masses of 14 stars in the ALMA archival data for Akeson~\&~Jensen's Cycle 0 project on binaries in the Taurus SFR. We find that the masses of 7 of the targets are so large that they cannot be reconciled with reported values of their luminosity and effective temperature. We suggest that these targets are themselves binaries or triples.Comment: 20 page