271,981 research outputs found
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 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- superconductors
Motivated by a recent experiment on the bilayer
YCaBaCuO superconductor and based on a bilayer
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 , 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
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