3,899 research outputs found
Applicability of self-consistent mean-field theory
Within the constrained Hartree-Fock (CHF) theory, an analytic condition is
derived to estimate whether a concept of the self-consistent mean field is
realized or not in level repulsive region. The derived condition states that an
iterative calculation of CHF equation does not converge when the quantum
fluctuations coming from two-body residual interaction and quadrupole
deformation become larger than a single-particle energy difference between two
avoided crossing orbits. By means of the numerical calculation, it is shown
that the analytic condition works well for a realistic case.Comment: 11 pages, 8 figure
Properties of the superconducting state in compressed Sulphur
The thermodynamic properties of the superconducting state in Sulphur under
the pressure at 160 GPa were determined. It has been shown that: (i) the
critical value of the Coulomb pseudopotential is equal to 0.127; (ii) the
critical temperature (T_{C} =17 K) should be calculated by using the modified
Allen-Dynes formula; (iii) the effective electron-electron interaction is
attractive in the range of frequencies from zero to the frequency slightly
lesser than the maximum phonon frequency (~ 0.85\Omega_{max}); (iv) the
dimensionless ratios 2\Delta (0)/k_{B}T_{C}, $\Delta C(T_{C})/C^{N}(T_{C}) and
T_{C}C^{N}(T_{C})/H^{2}_{C}(0) are equal to 3.7, 1.65 and 0.16 respectively;
(v) the ratio of the effective to bare electron mass reaches maximum of 1.77
for T=T_{C}.Comment: 3 pages, 5 figure
To what extent does the self-consistent mean-field exist?
A non-convergent difficulty near level-repulsive region is discussed within
the self-consistent mean-field theory. It is shown by numerical and analytic
studies that the mean-field is not realized in the many-fermion system when
quantum fluctuations coming from two-body residual interaction and quadrupole
deformation are larger than an energy difference between two avoided crossing
orbits. An analytic condition indicating a limitation of the mean-field concept
is derived for the first time
Statistical Mechanics of Dictionary Learning
Finding a basis matrix (dictionary) by which objective signals are
represented sparsely is of major relevance in various scientific and
technological fields. We consider a problem to learn a dictionary from a set of
training signals. We employ techniques of statistical mechanics of disordered
systems to evaluate the size of the training set necessary to typically succeed
in the dictionary learning. The results indicate that the necessary size is
much smaller than previously estimated, which theoretically supports and/or
encourages the use of dictionary learning in practical situations.Comment: 6 pages, 4 figure
Replica symmetry breaking in an adiabatic spin-glass model of adaptive evolution
We study evolutionary canalization using a spin-glass model with replica
theory, where spins and their interactions are dynamic variables whose
configurations correspond to phenotypes and genotypes, respectively. The spins
are updated under temperature T_S, and the genotypes evolve under temperature
T_J, according to the evolutionary fitness. It is found that adaptation occurs
at T_S < T_S^{RS}, and a replica symmetric phase emerges at T_S^{RSB} < T_S <
T_S^{RS}. The replica symmetric phase implies canalization, and replica
symmetry breaking at lower temperatures indicates loss of robustness.Comment: 5pages, 2 figure
Critical Scale-invariance in Healthy Human Heart Rate
We demonstrate the robust scale-invariance in the probability density
function (PDF) of detrended healthy human heart rate increments, which is
preserved not only in a quiescent condition, but also in a dynamic state where
the mean level of heart rate is dramatically changing. This scale-independent
and fractal structure is markedly different from the scale-dependent PDF
evolution observed in a turbulent-like, cascade heart rate model. These results
strongly support the view that healthy human heart rate is controlled to
converge continually to a critical state.Comment: 9 pages, 3 figures. Phys. Rev. Lett., to appear (2004
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