121 research outputs found
Singular Short Range Potentials in the J-Matrix Approach
We use the tools of the J-matrix method to evaluate the S-matrix and then
deduce the bound and resonance states energies for singular screened Coulomb
potentials, both analytic and piecewise differentiable. The J-matrix approach
allows us to absorb the 1/r singularity of the potential in the reference
Hamiltonian, which is then handled analytically. The calculation is performed
using an infinite square integrable basis that supports a tridiagonal matrix
representation for the reference Hamiltonian. The remaining part of the
potential, which is bound and regular everywhere, is treated by an efficient
numerical scheme in a suitable basis using Gauss quadrature approximation. To
exhibit the power of our approach we have considered the most delicate region
close to the bound-unbound transition and compared our results favorably with
available numerical data.Comment: 14 pages, 5 tables, 2 figure
Renormalization--Group Solutions for Yukawa Potential
The self--similar renormalization group is used to obtain expressions for the
spectrum of the Hamiltonian with the Yukawa potential. The critical screening
parameter above which there are no bound states is also obtained by this
method. The approach presented illustrates that one can achieve good accuracy
without involving extensive numerical calculations, but invoking instead the
renormalization--group techniques.Comment: 1 file, 12 pages, RevTe
About disposition of energy levels
The unique properties of central potential of the form were studied using the recently developed critical parameter
technique. The particular cases of and yield,
respectively, the exponential and Yukawa potentials widely used in the atomic,
molecular and nuclear physics. We found different behavior of the energy levels
of this potential for three different ranges of the value of . For
it was found that the energy of bound states with the same
principal quantum number decreases with increasing angular momentum .
The Gaussian and Woods-Saxon potentials also show this behavior. On the
contrary, for increasing gives a higher energy,
resembling the Hulthen potential. However, a potential with
possesses mixed properties, which give rise to several interesting results. For
one, the order of energy levels with different quantum numbers is not preserved
when varying the parameter . This leads to a quantum degeneracy of the
states, and in fact, for a given value of we can find the values
for which two energy levels with different quantum numbers
coincide. Another interesting phenomena is the possibility, for some values of
in this range, for two new energy levels with different quantum
numbers to appear simultaneously when reaches their common critical
value.Comment: 10 pages, 3 table
Symmetric Hubbard Systems with Superconducting Magnetic Response
In purely repulsive, -symmetric Hubbard clusters a correlation effect
produces an effective two-body attraction and pairing; the key ingredient is
the availability of W=0 pairs, that is, two-body solutions of appropriate
symmetry. We study the tunneling of bound pairs in rings of 5-site units
connected by weak intercell links; each unit has the topology of a CuO
cluster and a repulsive interaction is included on every site. Further, we test
the superconducting nature of the response of this model to a threading
magnetic field. We present a detailed numerical study of the two-unit ring
filled with 6 particles and the three-unit ring with 8 particles; in both cases
a lower filling yields normal behavior. In previous studies on 1d Hubbard
chains, level crossings were reported (half-integer or fractional Aharonov-Bohm
effect) which however cannot be due to superconducting pairs. In contrast, the
nontrivial basis of clusters carrying W=0 pairs leads to genuine
Superconducting Flux Quantization (SFQ). The data are understood in terms of a
cell-perturbation theory scheme which is very accurate for weak links. This
low-energy approach leads to an effective hard core boson Hamiltonian which
naturally describes itinerant pairs and SFQ in mesoscopic rings. For the
numerical calculations, we take advantage of a recently proposed exact
diagonalization technique which can be generally applied to many-fermion
problems and drastically reduces the size of the matrices to be handled.Comment: 12 pages, 11 figure
W=0 pairing in Hubbard and related models of low-dimensional superconductors
Lattice Hamiltonians with on-site interaction have W=0 solutions, that
is, many-body {\em singlet} eigenstates without double occupation. In
particular, W=0 pairs give a clue to understand the pairing force in repulsive
Hubbard models. These eigenstates are found in systems with high enough
symmetry, like the square, hexagonal or triangular lattices. By a general
theorem, we propose a systematic way to construct all the W=0 pairs of a given
Hamiltonian. We also introduce a canonical transformation to calculate the
effective interaction between the particles of such pairs. In geometries
appropriate for the CuO planes of cuprate superconductors, armchair
Carbon nanotubes or Cobalt Oxides planes, the dressed pair becomes a bound
state in a physically relevant range of parameters. We also show that W=0 pairs
quantize the magnetic flux like superconducting pairs do. The pairing mechanism
breaks down in the presence of strong distortions. The W=0 pairs are also the
building blocks for the antiferromagnetic ground state of the half-filled
Hubbard model at weak coupling. Our analytical results for the
Hubbard square lattice, compared to available numerical data, demonstrate that
the method, besides providing intuitive grasp on pairing, also has quantitative
predictive power. We also consider including phonon effects in this scenario.
Preliminary calculations with small clusters indicate that vector phonons
hinder pairing while half-breathing modes are synergic with the W=0 pairing
mechanism both at weak coupling and in the polaronic regime.Comment: 42 pages, Topical Review to appear in Journal of Physics C: Condensed
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