The Hahn Quantum System

Using a formulation of quantum mechanics based on the theory of orthogonal polynomials, we introduce a four-parameter system associated with the Hahn and continuous Hahn polynomials. The continuum energy scattering states are written in terms of the continuous Hahn polynomial whose asymptotics give the scattering amplitude and phase shift. On the other hand, the finite number of discrete bound states are associated with the Hahn polynomial.Comment: 18 pages, 7 figure

Fluctuation limits of strongly degenerate branching systems

Functional limit theorems for scaled fluctuations of occupation time processes of a sequence of critical branching particle systems in $\R^d$ with anisotropic space motions and strongly degenerated splitting abilities are proved in the cases of critical and intermediate dimensions. The results show that the limit processes are constant measure-valued Wienner processes with degenerated temporal and simple spatial structures.Comment: 15 page

Boron nanobelts grown under intensive ion bombardment

High-quality α-tetragonal crystalline boronnanobelts with [001] growth axis were synthesized using a novel method combining e-beam evaporation and plasma ion bombardment techniques. Intensive ion bombardment of the growingboronnanobelts at a high substrate temperature (∼1200°C) was found to be effective in increasing the atomic density, reducing the crystal disorder, and improving the yield of the nanobelts.This work was supported by the Australian Research Council ARC

Doping dependance of the spin resonance peak in bilayer high-TcT_c superconductors

Motivated by a recent experiment on the bilayer Y$_{1-x}$Ca$_{x}$Ba$_2$Cu$_3$O$_y$ superconductor and based on a bilayer $t-J$ model, we calculate the spin susceptibility at different doping densities in the even and odd channels in a bilayer system. It is found that the intensity of the resonance peak in the even channel is much weaker than that in the odd one, with the resonance position being at a higher frequency. While this difference decreases as the doping increases, and both the position and amplitude of the resonance peaks in the two channels are very similar in the deeply overdoped sample. Moreover, the resonance frequency in the odd channel is found to be linear with the critical temperature $T_c$, while the resonance frequency increases as doping decreases in the even channel and tends to saturate at the underdoped sample. We elaborate the results based on the Fermi surface topology and the d-wave superconductivity.Comment: 6 pages, 5 figure

Microscopic Analysis of Order Parameters in Nuclear Quantum Phase Transitions

Microscopic signatures of nuclear ground-state shape phase transitions in Nd isotopes are studied using excitation spectra and collective wave functions obtained by diagonalization of a five-dimensional Hamiltonian for quadrupole vibrational and rotational degrees of freedom, with parameters determined by constrained self-consistent relativistic mean-field calculations for triaxial shapes. As a function of the physical control parameter -- the number of nucleons, energy gaps between the ground state and the excited vibrational states with zero angular momentum, isomer shifts, and monopole transition strengths, exhibit sharp discontinuities at neutron number N=90, characteristic of a first-order quantum phase transition.Comment: 5 pages, 4 figures, accepted for publication as a Rapid Communication in Physical Review

SLOCC determinant invariants of order 2^{n/2} for even n qubits

In this paper, we study SLOCC determinant invariants of order 2^{n/2} for any even n qubits which satisfy the SLOCC determinant equations. The determinant invariants can be constructed by a simple method and the set of all these determinant invariants is complete with respect to permutations of qubits. SLOCC entanglement classification can be achieved via the vanishing or not of the determinant invariants. We exemplify the method for several even number of qubits, with an emphasis on six qubits.Comment: J. Phys. A: Math. Theor. 45 (2012) 07530