Capillary pressure of van der Waals liquid nanodrops

The dependence of the surface tension on a nanodrop radius is important for the new-phase formation process. It is demonstrated that the famous Tolman formula is not unique and the size-dependence of the surface tension can distinct for different systems. The analysis is based on a relationship between the surface tension and disjoining pressure in nanodrops. It is shown that the van der Waals interactions do not affect the new-phase formation thermodynamics since the effect of the disjoining pressure and size-dependent component of the surface tension cancel each other.Comment: The paper is dedicated to the 80th anniversary of A.I. Rusano

Exact Solutions for Matter-Enhanced Neutrino Oscillations

The analogy between supersymmetric quantum mechanics and matter-enhanced neutrino oscillations is exploited to obtain exact solutions for a class of electron density profiles. This integrability condition is analogous to the shape-invariance in supersymmetric quantum mechanics. This method seems to be the most direct way to obtain the exact survival probabilities for a number of density profiles of interest, such as linear and exponential density profiles. The resulting neutrino amplitudes can also be utilized as comparison amplitudes for the uniform semiclassical treatment of neutrino propagation in arbitrary electron density profiles.Comment: Submitted to Physical Review D. Latex file, 8 pages. This paper is also available at http://nucth.physics.wisc.edu/preprints

Nonlinear level crossing models

We examine the effect of nonlinearity at a level crossing on the probability for nonadiabatic transitions $P$. By using the Dykhne-Davis-Pechukas formula, we derive simple analytic estimates for $P$ for two types of nonlinear crossings. In the first type, the nonlinearity in the detuning appears as a {\it perturbative} correction to the dominant linear time dependence. Then appreciable deviations from the Landau-Zener probability $P_{LZ}$ are found to appear for large couplings only, when $P$ is very small; this explains why the Landau-Zener model is often seen to provide more accurate results than expected. In the second type of nonlinearity, called {\it essential} nonlinearity, the detuning is proportional to an odd power of time. Then the nonadiabatic probability $P$ is qualitatively and quantitatively different from $P_{LZ}$ because on the one hand, it vanishes in an oscillatory manner as the coupling increases, and on the other, it is much larger than $P_{LZ}$. We suggest an experimental situation when this deviation can be observed.Comment: 9 pages final postscript file, two-column revtex style, 5 figure

The Oscillation Probability of GeV Solar Neutrinos of All Active Species

In this paper, I address the oscillation probability of O(GeV) neutrinos of all active flavours produced inside the Sun and detected at the Earth. Flavours other than electron-type neutrinos may be produced, for example, by the annihilation of WIMPs which may be trapped inside the Sun. In the GeV energy regime, matter effects are important both for the ``1-3'' system and the ``1-2'' system, and for different neutrino mass hierarchies. A numerical scan of the multidimensional three-flavour parameter space is performed, ``inspired'' by the current experimental situation. One important result is that, in the three-flavour oscillation case, P{alpha,beta} is different from P{beta,alpha} for a significant portion of the parameter space, even if there is no CP-violating phase in the MNS matrix. Furthermore, P{mu,mu} has a significantly different behaviour from P{tau,tau}, which may affect expectations for the number of events detected at large neutrino telescopes.Comment: 38 pages, 10 figure

Dislocation loops in overheated free-standing smectic films

Static and dynamic phenomena in overheated free-standing smectic-A films are studied using a generalization of de Gennes' theory for a confined presmectic liquid. A static application is to determine the profile of the film meniscus and the meniscus contact angle, the results being compared with those of a recent study employing de Gennes' original theory. The dynamical generalization of the theory is based on on a time-dependent Ginzburg-Landau approach. This is used to compare two modes for layer-thinning transitions in overheated films, namely "uniform thinning" vs. nucleation of dislocation loops. Properties such as the line tension and velocity of a moving dislocation line are evaluated self-consistently by the theory.Comment: 16 pages, 8 figure

Analytical description of quasivacuum oscillations of solar neutrinos

We propose a simple prescription to calculate the solar neutrino survival probability P_{ee} in the quasivacuum oscillation (QVO) regime. Such prescription is obtained by matching perturbative and exact analytical results, which effectively take into account the density distribution in the Sun as provided by the standard solar model. The resulting analytical recipe for the calculation of P_{ee} is shown to reach its highest accuracy |\Delta P_{ee}| < 2.6 x 10^{-2} in the whole QVO range) when the familiar prescription of choosing the solar density scale parameter r_0 at the Mikheyev-Smirnov-Wolfenstein (MSW) resonance point is replaced by a new one, namely, when r_0 is chosen at the point of ``maximal violation of adiabaticity'' (MVA) along the neutrino trajectory in the Sun. The MVA prescription admits a smooth transition from the QVO regime to the MSW transition one. We discuss in detail the phase acquired by neutrinos in the Sun, and show that it might be of relevance for the studies of relatively short timescale variations of the fluxes of the solar \nu lines in the future real-time solar neutrino experiments. Finally, we elucidate the role of matter effects in the convective zone of the Sun.Comment: 25 pages (RevTeX) + 11 figures (postscript

On the Evolution of the Neutrino State inside the Sun

We reexamine the conventional physical description of the neutrino evolution inside the Sun. We point out that the traditional resonance condition has physical meaning only in the limit of small values of the neutrino mixing angle, theta<<1. For large values of theta, the resonance condition specifies neither the point of the maximal violation of adiabaticity in the nonadiabatic case, nor the point where the flavor conversion occurs at the maximal rate in the adiabatic case. The corresponding correct conditions, valid for all values of theta including theta>pi/4, are presented. An adiabaticity condition valid for all values of theta is also described. The results of accurate numerical computations of the level jumping probability in the Sun are presented. These calculations cover a wide range of Delta m^2, from the vacuum oscillation region to the region where the standard exponential approximation is good. A convenient empirical parametrization of these results in terms of elementary functions is given. The matter effects in the so-called "quasi-vacuum oscillation regime" are discussed. Finally, it is shown how the known analytical results for the exponential, 1/x, and linear matter distributions can be simply obtained from the formula for the hyperbolic tangent profile. An explicit formula for the jumping probability for the distribution N_e ~ (coth(x/l) +- 1) is obtained.Comment: 34 pages, 8 figure

Three-Neutrino Mixing and Combined Vacuum Oscillations and MSW Transitions of Solar Neutrinos

Assuming three flavour neutrino mixing takes place in vacuum, we investigate the possibility that the solar nu_e take part in MSW transitions in the Sun due to Delta m^2_{31} from 10^{-7} eV^2 to 10^{-4} eV^2, followed by long wave length vacuum oscillations on the way to the Earth, triggered by Delta m^2_{21} (or Delta m^2_{32}) from 10^{-12} eV^2 to 10^{-10} eV^2, Delta m^2_{31} and Delta m^2_{21} (Delta m^2_{32}) being the corresponding neutrino mass squared differences. The solar nu_e survival probability is shown to be described in this case by a simple analytic expression. Depending on whether the vacuum oscillations are due to Delta m^2_{21} or Delta m^2_{32} there are two very different types of interplay between the MSW transitions and the vacuum oscillations of the solar nu_e. Performing an analysis of the most recently published solar neutrino data we have found several qualitatively new solutions of the solar neutrino problem of the hybrid MSW transitions + vacuum oscillations type. The solutions differ in the way the pp, 7Be and 8B neutrino fluxes are affected by the transitions in the Sun and the oscillations in vacuum. The specific features of the new solutions are discussed.Comment: 37 pages Latex, 16 Postscript Figure

Unity of CP and T Violation in Neutrino Oscillations

In a previous work a simultaneous P- CP[P] and P- T[P] bi-probability plot was proposed as a useful tool for unified graphical description of CP and T violation in neutrino oscillation. The ``baseball diamond'' structure of the plot is understood as a consequence of the approximate CP-CP and the T-CP relations obeyed by the oscillation probabilities. In this paper, we make a step forward toward deeper understanding of the unified graphical representation by showing that these two relations are identical in its content, suggesting a truly unifying view of CP and T violation in neutrino oscillations. We suspect that the unity reflects the underlying CPT theorem. We also present calculation of corrections to the CP-CP and the T-CP relations to leading order in Delta m^2_{21} / Delta m^2_{31} and s^2_{13}.Comment: 20 references added, version to appear in "Focus Issue on Neutrino Physics" of New Journal of Physic