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