Electroweak phase transition in the reduced minimal 3-3-1 model

The electroweak phase transition is considered in framework of the reduced minimal 3-3-1 model (RM331). Structure of phase transition in this model is divided into two periods. The first period is the phase transition SU(3) ---> SU(2) at TeV scale and the second one is SU(2)--> U(1), which is the like-Standard Model electroweak phase transition. When mass of the neutral Higgs boson (h_1) is taken to be equal to the LHC value: m_{h_1}=125 GeV, then these phase transitions are the first order phase transitions, the mass of Z_2 is about 4.8 TeV; and we find the region of parameter space with the first order phase transition at v_{\rho_0}=246 GeV scale, leading to an effective potential, where mass of the charged Higgs boson is in range of 4.154 TeV < m_{h_{++}} < 5.946 TeV. Therefore, with this approach, new bosons are the triggers of the first order electroweak phase transition with significant implications for the viability of electroweak baryogenesis scenarios.Comment: 21 pages, 3 figure

Electroweak phase transition in the economical 3-3-1 model

We consider the EWPT in the economical 3-3-1 (E331) model. Our analysis shows that the EWPT in the model is a sequence of two first-order phase transitions, $SU(3) \rightarrow SU(2)$ at the TeV scale and $SU(2) \rightarrow U(1)$ at the $100$ GeV scale. The EWPT $SU(3) \rightarrow SU(2)$ is triggered by the new bosons and the exotic quarks; its strength is about $1 - 13$ if the mass ranges of these new particles are $10^2 \,\mathrm{GeV} - 10^3 \,\mathrm{GeV}$. The EWPT $SU(2) \rightarrow U(1)$ is strengthened by only the new bosons; its strength is about $1 - 1.15$ if the mass parts of $H^0_1$, $H^\pm_2$ and $Y^\pm$ are in the ranges $10 \,\mathrm{GeV} - 10^2 \,\mathrm{GeV}$. The contributions of $H^0_1$ and $H^{\pm}_2$ to the strengths of both EWPTs may make them sufficiently strong to provide large deviations from thermal equilibrium and B violation necessary for baryogenesis.Comment: 17 pages, 9 figure

On the definition and the properties of the principal eigenvalue of some nonlocal operators

In this article we study some spectral properties of the linear operator $\mathcal{L}\_{\Omega}+a$ defined on the space $C(\bar\Omega)$ by :$$\mathcal{L}\_{\Omega}[\varphi] +a\varphi:=\int\_{\Omega}K(x,y)\varphi(y)\,dy+a(x)\varphi(x)$$ where $\Omega\subset \mathbb{R}^N$ is a domain, possibly unbounded, $a$ is a continuous bounded function and $K$ is a continuous, non negative kernel satisfying an integrability condition. We focus our analysis on the properties of the generalised principal eigenvalue $\lambda\_p(\mathcal{L}\_{\Omega}+a)$ defined by \lambda\_p(\mathcal{L}\_{\Omega}+a):= \sup\{\lambda \in \mathbb{R} \,|\, \exists \varphi \in C(\bar \Omega), \varphi\textgreater{}0, \textit{such that}\, \mathcal{L}\_{\Omega}[\varphi] +a\varphi +\lambda\varphi \le 0 \, \text{in}\;\Omega\}. We establish some new properties of this generalised principal eigenvalue $\lambda\_p$. Namely, we prove the equivalence of different definitions of the principal eigenvalue. We also study the behaviour of $\lambda\_p(\mathcal{L}\_{\Omega}+a)$ with respect to some scaling of $K$. For kernels $K$ of the type, $K(x,y)=J(x-y)$ with $J$ a compactly supported probability density, we also establish some asymptotic properties of $\lambda\_{p} \left(\mathcal{L}\_{\sigma,m,\Omega} -\frac{1}{\sigma^m}+a\right)$ where $\mathcal{L}\_{\sigma,m,\Omega}$ is defined by $\displaystyle{\mathcal{L}\_{\sigma,m,\Omega}[\varphi]:=\frac{1}{\sigma^{2+N}}\int\_{\Omega}J\left(\frac{x-y}{\sigma}\right)\varphi(y)\, dy}$. In particular, we prove that $$\lim\_{\sigma\to 0}\lambda\_p\left(\mathcal{L}\_{\sigma,2,\Omega}-\frac{1}{\sigma^{2}}+a\right)=\lambda\_1\left(\frac{D\_2(J)}{2N}\Delta +a\right),$$where $D\_2(J):=\int\_{\mathbb{R}^N}J(z)|z|^2\,dz$ and $\lambda\_1$ denotes the Dirichlet principal eigenvalue of the elliptic operator. In addition, we obtain some convergence results for the corresponding eigenfunction $\varphi\_{p,\sigma}$

Evolution of structure of SiO2 nanoparticles upon cooling from the melt

Evolution of structure of spherical SiO2 nanoparticles upon cooling from the melt has been investigated via molecular-dynamics (MD) simulations under non-periodic boundary conditions (NPBC). We use the pair interatomic potentials which have weak Coulomb interaction and Morse type short-range interaction. The change in structure of SiO2 nanoparticles upon cooling process has been studied through the partial radial distribution functions (PRDFs), coordination number and bond-angle distributions at different temperatures. The core and surface structures of nanoparticles have been studied in details. Our results show significant temperature dependence of structure of nanoparticles. Moreover, temperature dependence of concentration of structural defects in nanoparticles upon cooling from the melt toward glassy state has been found and discussed.Comment: 12 pages, 6 figure