Electromagnetic radiation in a semi-compact space

In this note, we investigate the electromagnetic radiation emitted from a revolving point charge in a compact space. If the point charge is circulating with an angular frequency ${\omega }_0$ on the $(x,y)$-plane at $z=0$ with boundary conditions, $x～x+2\pi R$ and $y～y+2\pi R$, it emits radiation into the z-direction of $z\in [?\infty ,+\infty ]$. We find that the radiation shows discontinuities as a function of ${\omega }_{0}R$ at which a new propagating mode with a different Fourier component appears. For a small radius limit ${\omega }_{0}R?1$, all the Fourier modes except the zero mode on $(x,y)$-plane are killed, but an effect of squeezing the electric field totally enhances the radiation. In the large volume limit ${\omega }_{0}R\to \infty$, the energy flux of the radiation reduces to the expected Larmor formula.     

On the non-integrability of a generalized Darboux Halphen system

In this paper we study a generalized Darboux Halphen system given by ${\dot{x}}_1=x_2{x}_3-x_1(x_2+x_3)+{\tau }^2({\alpha }_1,{\alpha }_2,{\alpha }_3,x_1,x_2,x_3)\text{,}$${\dot{x}}_2=x_3{x}_1-x_2(x_3+x_1)+{\tau }^2({\alpha }_1,{\alpha }_2,{\alpha }_3,x_1,x_2,x_3)\text{,}$${\dot{x}}_3=x_1{x}_2-x_3(x_1+x_2)+{\tau }^2({\alpha }_1,{\alpha }_2,{\alpha }_3,x_1,x_2,x_3)\text{,}$ where $x_1$, $x_2$, $x_3$ are real variables, ${\alpha }_1,{\alpha }_2,{\alpha }_3$ are real constants and ${\tau }^2({\alpha }_1,{\alpha }_2,{\alpha }_3,x_1,x_2,x_3)={\alpha }_1^2(x_1-x_2)(x_3-x_1)+{\alpha }_2^2(x_2-x_3)(x_1-x_2)+{\alpha }_3^2(x_3-x_1)(x_2-x_3)\text{.}$ We prove that, for any $({\alpha }_1,{\alpha }_2,{\alpha }_3)\in {\mathbb{R}}^3\setminus \left\{(0,0,0)\right\}$, this system does not admit any non-constant global first integral that can be described by a formal power series. Furthermore, restricting the values of $({\alpha }_1,{\alpha }_2,{\alpha }_3)$ to a full Lebesgue measure set, we prove that this system does not admit any non-constant rational or Darbouxian global first integral. This is a first step toward proving that this system is chaotic.     

ESR in a gapped Anderson model

We applied the numerical renormalization group method to study the electron spin resonance (ESR) of a single-impurity Anderson model with a gap $\Delta$ in the conduction electron density of states, centered at the Fermi level. We analyzed the relaxation rate $1/T_1$ of a magnetic probe located at a position $\overrightarrow{R}$ around the Anderson impurity. It presents different behaviors for the symmetric and the asymmetric case. For the symmetric case and any $\Delta >0$, $1/T_1$ goes to a constant for $T?{\Gamma }_{\text{k}}$ (Kondo resonance). $1/T_1$ decreases monotonically to zero only for $\Delta =0$. For the asymmetric case, there is a $\Delta$ under which $1/T_1$ decreases monotonically to zero as $T\to 0$, and above which $1/T_1$ saturates, as occurs in the symmetric case for $\Delta >0$. This behavior indicates a quantum phase transition from the quenched to the unquenched magnetic moment in the ground state of the Anderson ion.     

Persistent luminescence and synchrotron radiation study of the Ca2MgSi2O7:Eu2+,R3+ materials

The tetragonal ${\mathrm{Ca}}_2{\mathrm{MgSi}}_2{\mathrm{O}}_7$:${\mathrm{Eu}}^{2+},{\mathrm{R}}^{3+}$ persistent luminescence materials were prepared by a solid state reaction. The UV excited and persistent luminescence was observed in the green region centred at 535 nm. Both luminescence phenomena are due to the same ${\mathrm{Eu}}^{2+}$ ion occupying the single ${\mathrm{Ca}}^{2+}$ site in the host lattice. The ${\mathrm{R}}^{3+}$ codoping usually reduced the persistent luminescence of ${\mathrm{Ca}}_2{\mathrm{MgSi}}_2{\mathrm{O}}_7$:${\mathrm{Eu}}^{2+}$, which differs from the ${\mathrm{M}}_2{\mathrm{MgSi}}_2{\mathrm{O}}_7$:${\mathrm{Eu}}^{2+}$ $(\mathrm{M}=\mathrm{Sr},\mathrm{Ba})$ and ${\mathrm{MAl}}_2{\mathrm{O}}_4$:${\mathrm{Eu}}^{2+}$ $(\mathrm{M}=\mathrm{Ca},\mathrm{Sr})$ materials. Only the ${\mathrm{Tb}}^{3+}$ ion enhanced slightly the persistent luminescence. With the aid of synchrotron radiation, the band gap energy of ${\mathrm{Ca}}_2{\mathrm{MgSi}}_2{\mathrm{O}}_7$:${\mathrm{Eu}}^{2+}$ was found to be about 7 eV that is very similar to those of the ${\mathrm{M}}_2{\mathrm{MgSi}}_2{\mathrm{O}}_7$:${\mathrm{Eu}}^{2+}$ $(\mathrm{M}=\mathrm{Sr},\mathrm{Ba})$ materials. Thermoluminescence results suggested that the ${\mathrm{R}}^{3+}$ ions might act as electron traps, but only the TL peaks created by ${\mathrm{Tm}}^{3+}$ and ${\mathrm{Sm}}^{3+}$ can be found in the temperature range accessible. Lattice defects (e.g. oxygen vacancies) are also important, since the same main thermoluminescence peak was observed at about $100{}^{\circ }\mathrm{C}$ with and without ${\mathrm{R}}^{3+}$ codoping.     

A fresh look into m¯c,b(m¯c,b) and precise fD(s),B(s) from heavy–light QCD spectral sum rules

Using recent values of the QCD (non-)perturbative parameters given in Table 1 and an estimate of the N3LO QCD perturbative contributions based on the geometric growth of the PT series, we re-use QCD spectral sum rules (QSSR) known to N2LO PT series and including all dimension-six NP condensate contributions in the full QCD theory, for improving the existing estimates of ${\overline{m}}_{c,b}$ and $f_{D_{(s)},B_{(s)}}$ from the open charm and beauty systems. We especially study the effects of the subtraction point on “different QSSR data” and use (for the first time) the Renormalization Group Invariant (RGI) scale-independent quark masses in the analysis. The estimates [rigourous model-independent upper bounds within the SVZ framework] reported in Table 8: $f_D/f_{\pi }=1.56(5)$ $[?1.68(1)]$, $f_B/f_{\pi }=1.58(5)$ $[?1.80(3)]$ and $f_{D_s}/f_K=1.58(4)$ $[?1.63(1)]$, $f_{B_s}/f_K=1.50(3)$ $[?1.61(3.5)]$, which improve previous QSSR estimates, are in perfect agreement (in values and precisions) with some of the experimental data on $f_{D,D_s}$ and on recent lattice simulations within dynamical quarks. These remarkable agreements confirm both the success of the QSSR semi-approximate approach based on the OPE in terms of the quark and gluon condensates and of the Minimal Duality Ansatz (MDA) for parametrizing the hadronic spectral function which we have tested from the complete data of the $J/\psi$ and ? systems. The values of the running quark masses ${\overline{m}}_c(m_c)=1286(66)\text{MeV}$ and ${\overline{m}}_b(m_b)=4236(69)\text{MeV}$ from $M_{D,B}$ are in good agreement though less accurate than the ones from recent $J/\psi$ and ? sum rules.     

Numerically anticanonical divisors on Kato surfaces

The compact curves of an intermediate Kato surface $S$ form a basis of $H^2(S,\mathbb{Q})$. We present a way to compute the associated rational coefficients of the first Chern class $c_1\left(S\right)$. We get in particular a simple geometric obstruction for $c_1\left(S\right)$ to be an integral class, or equivalently index $\left(S\right)=1$. In the final part we discuss relations with some recent work of Dloussky (2011) and Oeljeklaus and Toma (2009).