Cosmic Microwave Background, Matter-Antimatter Asymmetry and Neutrino Masses

We study the implications of thermal leptogenesis for neutrino parameters. Assuming that decays of N_1, the lightest of the heavy Majorana neutrinos, initiate baryogenesis, we show that the final baryon asymmetry is determined by only four parameters: the CP asymmetry epsilon_1, the heavy neutrino mass M_1, the effective light neutrino mass \tilde{m}_1, and the quadratic mean \bar{m} of the light neutrino masses. Imposing the CMB measurement of the baryon asymmetry as constraint on the neutrino parameters, we show, in a model independent way, that quasi-degenerate neutrinos are incompatible with thermal leptogenesis. For maximal CP asymmetry epsilon_1, and neutrino masses in the range from (\Delta m^2_{sol})^{1/2} to (\Delta m^2_{atm})^{1/2}, the baryogenesis temperature is T_B = O(10^{10}) GeV.Comment: 28 pages, 14 figures included; v2: erratum added, M_1 lower bound in the strong wash-out regime (see Eq. (63)) relaxed by a factor 2/

Density-correlator signatures of the vulcanization transition

Certain density correlators, measurable via various experimental techniques, are studied in the context of the vulcanization transition. It is shown that these correlators contain essential information about both the vulcanization transition and the emergent amorphous solid state. Contact is made with various physical ingredients that have featured in experimental studies of amorphous colloidal and gel systems and in theoretical studies of the glassy state.Comment: 7 pages, 1 figur

Quantum Phase-Slip Junction Under Microwave Irradiation

We consider the dynamics of a quantum phase-slip junction (QPSJ) -- a dual Josephson junction -- connected to a microwave source with frequency $\omega_\textrm{mw}$. With respect to an ordinary Josephson junction, a QPSJ can sustain dual Shapiro steps, consisting of well-defined current plateaus at multiple integers of $e \omega_\textrm{mw} / \pi$ in the current-voltage (I-V) characteristic. The experimental observation of these plateaus has been elusive up to now. We argue that thermal as well as quantum fluctuations can smear the I-V characteristic considerably. In order to understand these effects, we study a current-biased QPSJ under microwave irradiation and connected to an inductive and resistive environment. We find that the effect of these fluctuations are governed by the resistance of the environment and by the ratio of the phase-slip energy and the inductive energy. Our results are of interest for experiments aimed at the observation of dual Shapiro steps in QPSJ devices for the definition of a new quantum current standard.Comment: 12 pages, 9 figures, comments and suggestions would be greatly appreciate

Universal quantum Hawking evaporation of integrable two-dimensional solitons

We show that any soliton solution of an arbitrary two-dimensional integrable equation has the potential to eventually evaporate and emit the exact analogue of Hawking radiation from black holes. From the AKNS matrix formulation of integrability, we show that it is possible to associate a real spacetime metric tensor which defines a curved surface, perceived by the classical and quantum fluctuations propagating on the soliton. By defining proper scalar invariants of the associated Riemannian geometry, and introducing the conformal anomaly, we are able to determine the Hawking temperatures and entropies of the fundamental solitons of the nonlinear Schroedinger, KdV and sine-Gordon equations. The mechanism advanced here is simple, completely universal and can be applied to all integrable equations in two dimensions, and is easily applicable to a large class of black holes of any dimensionality, opening up totally new windows on the quantum mechanics of solitons and their deep connections with black hole physics

Planar L-Drawings of Directed Graphs

We study planar drawings of directed graphs in the L-drawing standard. We provide necessary conditions for the existence of these drawings and show that testing for the existence of a planar L-drawing is an NP-complete problem. Motivated by this result, we focus on upward-planar L-drawings. We show that directed st-graphs admitting an upward- (resp. upward-rightward-) planar L-drawing are exactly those admitting a bitonic (resp. monotonically increasing) st-ordering. We give a linear-time algorithm that computes a bitonic (resp. monotonically increasing) st-ordering of a planar st-graph or reports that there exists none.Comment: Appears in the Proceedings of the 25th International Symposium on Graph Drawing and Network Visualization (GD 2017