Due to sphaleron processes in the high-temperature symmetric phase of the standard model the cosmological baryon asymmetry is related to neutrino properties. For hierarchical neutrino masses, with B-L broken at the unification scale ΛGUT~1016 GeV, the observed baryon asymmetry nB/s~10-10 can be naturally explained by the decay of heavy Majorana neutrinos. We illustrate this mechanism with two models of neutrino masses, consistent with the solar and atmospheric neutrino anomalies, which are based on the two symmetry groups SU(5)×U(1)F and SU(3)c×SU(3)L×SU(3)R×U(1)F. We also review related cosmological bounds on Majorana neutrino masses and the use of Boltzmann equations.

Neutrino masses and the baryon asymmetry

Phase transitions and relaxor properties of doped quantum paraelectrics

Critical behavior, scaling, and nonlinear properties of the susceptibility ${\ensuremath{\chi}}^{*}={\ensuremath{\chi}}^{\ensuremath{'}}\ensuremath{-}i{\ensuremath{\chi}}^{\ensuremath{''}}$ in $^{18}\mathrm{O}$ isotope exchanged $\mathrm{Sr}\mathrm{Ti}{\mathrm{O}}_{3}$ are revisited in a crystal that was perfectly single domained by an external electric field in the quantum paraelectric regime above ${T}_{c}\ensuremath{\approx}24\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. Corrections due to random-field induced nanoregions turn out to be important, if not decisive, for a reliable description. We find quantum critical exponents $\ensuremath{\gamma}=1.9\ifmmode\pm\else\textpm\fi{}0.1$, $\ensuremath{\delta}=2.7\ifmmode\pm\else\textpm\fi{}0.1$, and $\ensuremath{\Delta}=3.1\ifmmode\pm\else\textpm\fi{}0.1$, and a divergency of the nonlinearity coefficient $B$ with an exponent $3\ensuremath{\gamma}\ensuremath{-}2\ensuremath{\Delta}\ensuremath{\approx}\ensuremath{-}0.4$. Below ${T}_{c}$ critical and scaling analysis is inhibited by large contributions of domain walls to the susceptibility.

Nonlinear and scaling properties of the dielectric response of Sr Ti 18 O 3 in the quantum paraelectric regime

P. Szklarz,1 M. Galązka,2 P. Zielinski,2,3 and G. Bator1,* 1Faculty of Chemistry, University of Wroclaw, Joliot-Curie 14, 50-383 Wroclaw, Poland 2The H. Niewodniczanski Institute of Nuclear Physics PAS, Radzikowskiego 152, PL-31-342 Krakow, Poland 3Cracow University of Technology, Institute of Physics, ul. Podchorązych 1, 30-084 Krakow, Poland Received 23 February 2006; revised manuscript received 19 July 2006; published 13 November 2006

Phase transitions in the ferroelectric crystals [ C H 3 N H 3 ] 5 Bi 2 Cl 11 and [ C H 3 N H 3 ] 5 Bi 2 Br 11 studied by the nonlinear dielectric effect

We analyze the interaction of an electromagnetic spike (one cycle) with a thin layer of ferroelectric medium with two equilibrium states. The model is the set of Maxwell equations coupled to the undamped Landau-Khalatnikov equation, where we do not assume slowly varying envelopes. From linear-scattering theory, we show that low-amplitude pulses can be completely reflected by the medium. Large-amplitude pulses can switch the ferroelectric. Using numerical simulations and analysis, we study this switching for long and short pulses, estimate the switching times, and provide useful information for experiments.

Electromagnetically induced switching of ferroelectric thin films

Assuming the static scaling hypothesis, a proof is given for the existence of invariants (Q) associated with the extrema of the thermodynamic functions: nonzero-field susceptibility, nonzero-field specific heat, nonzero-wave-vector correlation function. In the framework of the Landau theory, the value of the invariant Q related to the susceptibility is found to be Q=2. Experimental measurements of the maxima of the nonzero-electric-field susceptibility for a ferroelectric triglycine sulfate TGS crystal give a value 1.87\ifmmode\pm\else\textpm\fi{}0.05 for the invariant Q. This result provides new evidence of a deviation from Landau theory in the thermodynamic behavior of the TGS crystal.

Scaling hypothesis and nonzero-field critical invariants

A method to determine the dominant powers of the order parameter in the free energy of real physical systems is proposed. A series of equations for the susceptibility scaling functions were obtained from the analytical two-term scaling free energy. The experimental scaling functions for triglycine selenate (TGSe) and triglycine sulfate (TGS) ferroelectrics inserted into these equations show marked deviations from linearity. Relations between these deviations and the nonzero-field critical invariant Q=\ensuremath{\chi}(${\mathrm{\ensuremath{\tau}}}_{\mathit{m}}$, E=0)/\ensuremath{\chi}(${\mathrm{\ensuremath{\tau}}}_{\mathit{m}}$,E) were found, where ${\mathrm{\ensuremath{\tau}}}_{\mathit{m}}$ is the reduced temperature (${\mathrm{\ensuremath{\tau}}}_{\mathit{m}}$=${\mathit{T}}_{\mathit{m}}$/${\mathit{T}}_{\mathit{c}}$-1) at which the susceptibility \ensuremath{\chi}(\ensuremath{\tau},E) is maximum for a given value of the electric field E. This nonlinearity proves the existence of a nonzero-field critical invariant describing the competition of the three scaling terms ${\mathit{P}}^{2}$,${\mathit{P}}^{4}$, and ${\mathit{P}}^{6}$ in the singular free energy for TGSe and TGS ferroelectrics. The higher-order terms ${\mathit{P}}^{8}$,${\mathit{P}}^{10}$,..., are shown to be absent or much less important than the ${\mathit{P}}^{2}$,${\mathit{P}}^{4}$, and ${\mathit{P}}^{6}$ powers of the polarization P.

Structure of the singular free energy for triglycine selenate and triglycine sulfate ferroelectrics.

A method of constructing a susceptibility scaling function and extracting critical exponents from experimental susceptibility data for physical systems with discontinuous phase transitions and/or unsymmetrical critical points induced by a nonzero field is proposed. The coordinates of these points do not appear in the derived form of the scaling function. The transformation of the field E conjugate to the order parameter to a new field h=E-${\mathit{E}}_{0}$(T) where ${\mathit{E}}_{0}$(T) represents the critical isochore and/or two-phase equilibrium line, is shown to reduce the scaling function for unsymmetrical systems to that for symmetrical ones. Transforming original isothermal experimental data for deuterated triglycine selenate with a deuterium content of x\ensuremath{\simeq}100%, the asymmetrical scaling function and values of the nonzero-field critical invariants \ensuremath{\delta}, a=\ensuremath{\Delta}/\ensuremath{\gamma}, and Q (equal to 1.5, 3, and 1.2, respectively) were obtained.

Scaling in ferroelectrics with critical points induced by an electric field.

A singular free energy consisting of three terms ${\mathit{P}}^{2}$, ${\mathrm{P}}^{4}$, and ${\mathit{P}}^{6}$ that contribute simultaneously to the susceptibility scaling function is proposed for the description of triglycine sulfate (TGS) and triglycine selenate (TGSe) ferroelectrics, where P is the polarization. It is shown that the combination ${\mathit{C}}_{2}$${\mathit{C}}_{6}$/${\mathit{C}}_{4}^{2}$ of the nonuniversal critical amplitudes ${\mathit{C}}_{2}$,${\mathit{C}}_{4}$, and ${\mathit{C}}_{6}$ of the singular free energy is a nonzero-field critical invariant. This invariant is measured experimentally for TGS and TGSe ferroelectrics. It is proved theoretically and demonstrated experimentally that this invariant is proportional to another invariant which represents the parabolic approximation of the equation for the susceptibility scaling function for a Landau critical point in the case of TGS and TGSe ferroelectrics.

B. Westwański

Papers

Scaling hypothesis and nonzero-field critical invariants

Structure of the singular free energy for triglycine selenate and triglycine sulfate ferroelectrics.

Scaling in ferroelectrics with critical points induced by an electric field.

Free-energy amplitudes and a critical invariant for uniaxial ferroelectrics.