Asymptotic iteration method for eigenvalue problems

An asymptotic interation method for solving second-order homogeneous linear differential equations of the form y'' = lambda(x) y' + s(x) y is introduced, where lambda(x) \neq 0 and s(x) are C-infinity functions. Applications to Schroedinger type problems, including some with highly singular potentials, are presented.Comment: 14 page

Limits on entanglement in rotationally-invariant scattering of spin systems

This paper investigates the dynamical generation of entanglement in scattering systems, in particular two spin systems that interact via rotationally-invariant scattering. The spin degrees of freedom of the in-states are assumed to be in unentangled, pure states, as defined by the entropy of entanglement. Because of the restriction of rotationally-symmetric interactions, perfectly-entangling S-matrices, i.e. those that lead to a maximally entangled out-state, only exist for a certain class of separable in-states. Using Clebsch-Gordan coefficients for the rotation group, the scattering phases that determine the S-matrix are determined for the case of spin systems with $\sigma = 1/2$, 1, and 3/2.Comment: 6 pages, no figures; v.2: sections added, edited for clarity, conclusions and calculation unchanged, typos corrected; v.3: new abstrct, revised first two sections, added reference

Perturbation expansions for a class of singular potentials

Harrell's modified perturbation theory [Ann. Phys. 105, 379-406 (1977)] is applied and extended to obtain non-power perturbation expansions for a class of singular Hamiltonians H = -D^2 + x^2 + A/x^2 + lambda/x^alpha, (A\geq 0, alpha > 2), known as generalized spiked harmonic oscillators. The perturbation expansions developed here are valid for small values of the coupling lambda > 0, and they extend the results which Harrell obtained for the spiked harmonic oscillator A = 0. Formulas for the the excited-states are also developed.Comment: 23 page

General energy bounds for systems of bosons with soft cores

We study a bound system of N identical bosons interacting by model pair potentials of the form V(r) = A sgn(p)r^p + B/r^2, A > 0, B >= 0. By using a variational trial function and the `equivalent 2-body method', we find explicit upper and lower bound formulas for the N-particle ground-state energy in arbitrary spatial dimensions d > 2 for the two cases p = 2 and p = -1. It is demonstrated that the upper bound can be systematically improved with the aid of a special large-N limit in collective field theory

The relationship between Hippocampal asymmetry and working memory processing in combat-related PTSD: a monozygotic twin study

BACKGROUND: PTSD is associated with reduction in hippocampal volume and abnormalities in hippocampal function. Hippocampal asymmetry has received less attention, but potentially could indicate lateralised differences in vulnerability to trauma. The P300 event-related potential component reflects the immediate processing of significant environmental stimuli and has generators in several brain regions including the hippocampus. P300 amplitude is generally reduced in people with PTSD. METHODS: Our study examined hippocampal volume asymmetry and the relationship between hippocampal asymmetry and P300 amplitude in male monozygotic twins discordant for Vietnam combat exposure. Lateralised hippocampal volume and P300 data were obtained from 70 male participants, of whom 12 had PTSD. We were able to compare (1) combat veterans with current PTSD; (2) their non-combat-exposed co-twins; (3) combat veterans without current PTSD and (4) their non-combat-exposed co-twins. RESULTS: There were no significant differences between groups in hippocampal asymmetry. There were no group differences in performance of an auditory oddball target detection task or in P300 amplitude. There was a significant positive correlation between P300 amplitude and the magnitude of hippocampal asymmetry in participants with PTSD. CONCLUSIONS: These findings suggest that greater hippocampal asymmetry in PTSD is associated with a need to allocate more attentional resources when processing significant environmental stimuli.Timothy Hall, Cherrie Galletly, C.R. Clark, Melinda Veltmeyer, Linda J. Metzger, Mark W. Gilbertson, Scott P. Orr, Roger K. Pitman and Alexander McFarlan

Proof of Rounding by Quenched Disorder of First Order Transitions in Low-Dimensional Quantum Systems

We prove that for quantum lattice systems in d<=2 dimensions the addition of quenched disorder rounds any first order phase transition in the corresponding conjugate order parameter, both at positive temperatures and at T=0. For systems with continuous symmetry the statement extends up to d<=4 dimensions. This establishes for quantum systems the existence of the Imry-Ma phenomenon which for classical systems was proven by Aizenman and Wehr. The extension of the proof to quantum systems is achieved by carrying out the analysis at the level of thermodynamic quantities rather than equilibrium states.Comment: This article presents the detailed derivation of results which were announced in Phys. Rev. Lett. 103 (2009) 197201 (arXiv:0907.2419). v3 incorporates many corrections and improvements resulting from referee comment

Variational analysis for a generalized spiked harmonic oscillator

A variational analysis is presented for the generalized spiked harmonic oscillator Hamiltonian operator H, where H = -(d/dx)^2 + Bx^2+ A/x^2 + lambda/x^alpha, and alpha and lambda are real positive parameters. The formalism makes use of a basis provided by exact solutions of Schroedinger's equation for the Gol'dman and Krivchenkov Hamiltonian (alpha = 2), and the corresponding matrix elements that were previously found. For all the discrete eigenvalues the method provides bounds which improve as the dimension of the basis set is increased. Extension to the N-dimensional case in arbitrary angular-momentum subspaces is also presented. By minimizing over the free parameter A, we are able to reduce substantially the number of basis functions needed for a given accuracy.Comment: 15 pages, 1 figur

Spiked oscillators: exact solution

A procedure to obtain the eigenenergies and eigenfunctions of a quantum spiked oscillator is presented. The originality of the method lies in an adequate use of asymptotic expansions of Wronskians of algebraic solutions of the Schroedinger equation. The procedure is applied to three familiar examples of spiked oscillators