967 research outputs found
Semiclassical treatment of logarithmic perturbation theory
The explicit semiclassical treatment of logarithmic perturbation theory for
the nonrelativistic bound states problem is developed. Based upon
-expansions and suitable quantization conditions a new procedure for
deriving perturbation expansions for the one-dimensional anharmonic oscillator
is offered. Avoiding disadvantages of the standard approach, new handy
recursion formulae with the same simple form both for ground and exited states
have been obtained. As an example, the perturbation expansions for the energy
eigenvalues of the harmonic oscillator perturbed by are
considered.Comment: 6 pages, LATEX 2.09 using IOP style
Spin operator matrix elements in the quantum Ising chain: fermion approach
Using some modification of the standard fermion technique we derive
factorized formula for spin operator matrix elements (form-factors) between
general eigenstates of the Hamiltonian of quantum Ising chain in a transverse
field of finite length. The derivation is based on the approach recently used
to derive factorized formula for Z_N-spin operator matrix elements between
ground eigenstates of the Hamiltonian of the Z_N-symmetric superintegrable
chiral Potts quantum chain. The obtained factorized formulas for the matrix
elements of Ising chain coincide with the corresponding expressions obtained by
the Separation of Variables Method.Comment: 19 page
Are Preoperative Kattan and Stephenson Nomograms Predicting Biochemical Recurrence after Radical Prostatectomy Applicable in the Chinese Population?
Purpose. Kattan and Stephenson nomograms are based on the outcomes of patients with prostate cancer recruited in the USA, but their applicability to Chinese patients is yet to be validated. We aim at studying the predictive accuracy of these nomograms in the Chinese population. Patients and Methods. A total of 408 patients who underwent laparoscopic or open radical resection of prostate from 1995 to 2009 were recruited. The preoperative clinical parameters of these patients were collected, and they were followed up regularly with PSA monitored. Biochemical recurrence was defined as two or more consecutive PSA levels >0.4âng/mL after radical resection of prostate or secondary cancer treatment. Results. The overall observed 5-year and 10-year biochemical recurrence-free survival rates were 68.3% and 59.8%, which was similar to the predicted values by the Kattan and Stephenson nomograms, respectively. The results of our study achieved a good concordance with both nomograms (Kattan: 5-years, 0.64; Stephenson: 5-years, 0.62, 10-years, 0.71). Conclusions. The incidence of prostate cancer in Hong Kong is increasing together with the patientsâ awareness of this disease. Despite the fact that Kattan nomograms were derived from the western population, it has been validated in our study to be useful in Chinese patients as well
Nuclear matter incompressibility coefficient in relativistic and nonrelativistic microscopic models
We systematically analyze the recent claim that nonrelativistic and
relativistic mean field (RMF) based random phase approximation (RPA)
calculations for the centroid energy E_0 of the isoscalar giant monopole
resonance yield for the nuclear matter incompressibility coefficient, K_{nm},
values which differ by about 20%. For an appropriate comparison with the RMF
based RPA calculations, we obtain the parameters for the Skyrme force used in
the nonrelativistic model by adopting the same procedure as employed in the
determination of the NL3 parameter set of an effective Lagrangian used in the
RMF model. Our investigation suggest that the discrepancy between the values of
K_{nm} predicted by the relativistic and nonrelativistic models is
significantly less than 20%.Comment: Revtex file (13 pages), appearing in PRC-Rapid Com
The vertex formulation of the Bazhanov-Baxter Model
In this paper we formulate an integrable model on the simple cubic lattice.
The -- valued spin variables of the model belong to edges of the lattice.
The Boltzmann weights of the model obey the vertex type Tetrahedron Equation.
In the thermodynamic limit our model is equivalent to the Bazhanov -- Baxter
Model. In the case when we reproduce the Korepanov's and Hietarinta's
solutions of the Tetrahedron equation as some special cases.Comment: 20 pages, LaTeX fil
In memoriam two distinguished participants of the Bregenz Symmetries in Science Symposia: Marcos Moshinsky and Yurii Fedorovich Smirnov
Some particular facets of the numerous works by Marcos Moshinsky and Yurii
Fedorovich Smirnov are presented in these notes. The accent is put on some of
the common interests of Yurii and Marcos in physics, theoretical chemistry, and
mathematical physics. These notes also contain some more personal memories of
Yurii Smirnov.Comment: Submitted for publication in Journal of Physics: Conference Serie
The tau_2-model and the chiral Potts model revisited: completeness of Bethe equations from Sklyanin's SOV method
The most general cyclic representations of the quantum integrable tau_2-model
are analyzed. The complete characterization of the tau_2-spectrum (eigenvalues
and eigenstates) is achieved in the framework of Sklyanin's Separation of
Variables (SOV) method by extending and adapting the ideas first introduced in
[1, 2]: i) The determination of the tau_2-spectrum is reduced to the
classification of the solutions of a given functional equation in a class of
polynomials. ii) The determination of the tau_2-eigenstates is reduced to the
classification of the solutions of an associated Baxter equation. These last
solutions are proven to be polynomials for a quite general class of
tau_2-self-adjoint representations and the completeness of the associated Bethe
ansatz type equations is derived. Finally, the following results are derived
for the inhomogeneous chiral Potts model: i) Simplicity of the spectrum, for
general representations. ii) Complete characterization of the chiral Potts
spectrum (eigenvalues and eigenstates) and completeness of Bethe ansatz type
equations, for the self-adjoint representations of tau_2-model on the chiral
Potts algebraic curves.Comment: 40 pages. Minor modifications in the text and some notation
Three-Dimensional Vertex Model in Statistical Mechanics, from Baxter-Bazhanov Model
We find that the Boltzmann weight of the three-dimensional Baxter-Bazhanov
model is dependent on four spin variables which are the linear combinations of
the spins on the corner sites of the cube and the Wu-Kadanoff duality between
the cube and vertex type tetrahedron equations is obtained explicitly for the
Baxter-Bazhanov model. Then a three-dimensional vertex model is obtained by
considering the symmetry property of the weight function, which is
corresponding to the three-dimensional Baxter-Bazhanov model. The vertex type
weight function is parametrized as the dihedral angles between the rapidity
planes connected with the cube. And we write down the symmetry relations of the
weight functions under the actions of the symmetry group of the cube. The
six angles with a constrained condition, appeared in the tetrahedron equation,
can be regarded as the six spectrums connected with the six spaces in which the
vertex type tetrahedron equation is defined.Comment: 29 pages, latex, 8 pasted figures (Page:22-29
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