Three Inequivalent Mass-Degenerate Majorana Neutrinos and a Model of Their Splitting for Neutrino Oscillations

The mass matrix of three Majorana neutrinos of equal mass is not necessarily proportional to the identity matrix, but expressible in terms of two angles and one phase. We discuss how such a mass matrix may be stable or unstable against radiative corrections. We then propose a model with additional explicit breaking of the threefold degeneracy to account for the atmospheric neutrino data, while the radiative breaking explains the solar neutrino data, using the large-angle Mikheyev-Smirnov-Wolfenstein solution. Our model requires a nonzero effective $\nu_e$ mass for neutrinoless double beta decay close to the present experimental upper limit of 0.2 eV.Comment: 10 pages, no figur

Universal scaling in BCS superconductivity in two dimensions in non-s waves

The solutions of a renormalized BCS model are studied in two space dimensions in $s$, $p$ and $d$ waves for finite-range separable potentials. The gap parameter, the critical temperature $T_c$, the coherence length $\xi$ and the jump in specific heat at $T_c$ as a function of zero-temperature condensation energy exhibit universal scalings. In the weak-coupling limit, the present model yields a small $\xi$ and large $T_c$ appropriate to those for high-$T_c$ cuprates. The specific heat, penetration depth and thermal conductivity as a function of temperature show universal scaling in $p$ and $d$ waves.Comment: 11 pages, LATEX, 4 postscript figures embedded using eps

Two phase transitions in (s+id)-wave Bardeen-Cooper-Schrieffer superconductivity

We establish universal behavior in temperature dependencies of some observables in $(s+id)$-wave BCS superconductivity in the presence of a weak $s$ wave. There also could appear a second second-order phase transition. As temperature is lowered past the usual critical temperature $T_c$, a less ordered superconducting phase is created in $d$ wave, which changes to a more ordered phase in $(s+id)$ wave at $T_{c1}$ ($< T_c$). The presence of two phase transitions manifest in two jumps in specific heat at $T_c$ and $T_{c1}$. The temperature dependencies of susceptibility, penetration depth, and thermal conductivity also confirm the new phase transition.Comment: 6 pages, 5 post-script figures

Reply to Comment on Extension of the Bethe-Weizsacker mass formula to light nuclei and some new shell closures

Some properties of the modified Bethe-Weizsacker mass formula (BWM) are discussed. As BWM has no shell effect included, the extra-stability or, magicity in nuclei clearly stands out when experimental mass data are compared with BWM predictions. If the shell effect quenches, the BWM predictions come closer to the experimental data.Comment: 2 pages, no figur

Free expansion of fermionic dark solitons in a boson-fermion mixture

We use a time-dependent dynamical mean-field-hydrodynamic model to study the formation of fermionic dark solitons in a trapped degenerate fermi gas mixed with a Bose-Einstein condensate in a harmonic as well as a periodic optical-lattice potential. The dark soliton with a "notch" in the probability density with a zero at the minimum is simulated numerically as a nonlinear continuation of the first vibrational excitation of the linear mean-field-hydrodynamic equations, as suggested recently for pure bosons. We study the free expansion of these dark solitons as well as the consequent increase in the size of their central notch and discuss the possibility of experimental observation of the notch after free expansion.Comment: 14 pages, 6 figure

Quantum scattering in one dimension

A self-contained discussion of nonrelativistic quantum scattering is presented in the case of central potentials in one space dimension, which will facilitate the understanding of the more complex scattering theory in two and three dimensions. The present discussion illustrates in a simple way the concept of partial-wave decomposition, phase shift, optical theorem and effective-range expansion.Comment: 8 page

Self-trapping of a binary Bose-Einstein condensate induced by interspecies interaction

The problem of self-trapping of a Bose-Einstein condensate (BEC) and a binary BEC in an optical lattice (OL) and double well (DW) is studied using the mean-field Gross-Pitaevskii equation. For both DW and OL, permanent self-trapping occurs in a window of the repulsive nonlinearity $g$ of the GP equation: $g_{c1}<g<g_{c2}$. In case of OL, the critical nonlinearities $g_{c1}$ and $g_{c2}$ correspond to a window of chemical potentials $\mu_{c1}<\mu<\mu_{c2}$ defining the band gap(s) of the periodic OL. The permanent self-trapped BEC in an OL usually represents a breathing oscillation of a stable stationary gap soliton. The permanent self-trapped BEC in a DW, on the other hand, is a dynamically stabilized state without any stationary counterpart. For a binary BEC with intraspecies nonlinearities outside this window of nonlinearity, a permanent self trapping can be induced by tuning the interspecies interaction such that the effective nonlinearities of the components fall in the above window