Structure and decay of the pygmy dipole resonance in 26Ne

The low-lying spectra of $^{24,25,26}{\rm Ne}$ and the structure of the pygmy dipole resonance (PDR) in $^{26}{\rm Ne}$ have been theoretically studied by the antisymmetrized molecular dynamics (AMD) and its extended version called shifted-basis AMD. The calculated energy and strength of the PDR reasonably agree with the observation, and the analysis of the wave function shows that the PDR is dominated by neutron excitation coupled to the quadrupole excited core nucleus $^{25}{\rm Ne}$, which explains the observed unexpected decay of PDR to the excited states of $^{25}{\rm Ne}$. The large isoscalar component of PDR is also shown and the enhancement of the core excitation in neutron-rich Ne isotopes is conjectured

The intruder feature of 31Mg and the coexistence of many particle and many hole states

The low-lying level structure of $^{31}{\rm Mg}$ has been investigated by the antisymmetrized molecular dynamics (AMD) plus generator coordinate method (GCM) with the Gogny D1S force. It is shown that the N=20 magic number is broken and the ground state has the pure neutron $2p3h$ configuration. The coexistence of many particle and many hole states at very low excitation energy is discussed

Structure and decay pattern of linear-chain state in 14C

The linear-chain states of $^{14}$C are theoretically investigated by using the antisymmetrized molecular dynamics. The calculated excitation energies and the $\alpha$ decay widths of the linear-chain states were compared with the observed data reported by the recent experiments. The properties of the positive-parity linear-chain states reasonably agree with the observation, that convinces us of the linear-chain formation in the positive-parity states. On the other hand, in the negative-parity states, it is found that the linear-chain configuration is fragmented into many states and do not form a single rotational band. As a further evidence of the linear-chain formation, we focus on the $\alpha$ decay pattern. It is shown that the linear-chain states decay to the excited states of daughter nucleus $^{10}{\rm Be}$ as well as to the ground state, while other cluster states dominantly decay into the ground state. Hence, we regard that this characteristic decay pattern is a strong signature of the linear-chain formation

Regularity of the minimiser of one-dimensional interaction energies

We consider both the minimisation of a class of nonlocal interaction energies over non-negative measures with unit mass and a class of singular integral equations of the first kind of Fredholm type. Our setting covers applications to dislocation pile-ups, contact problems, fracture mechanics and random matrix theory. Our main result shows that both the minimisation problems and the related singular integral equations have the same unique solution, which provides new regularity results on the minimiser of the energy and new positivity results on the solutions to singular integral equations.Comment: 46 page

Anisotropic Electronic Structure of the Kondo Semiconductor CeFe2Al10 Studied by Optical Conductivity

We report temperature-dependent polarized optical conductivity [$\sigma(\omega)$] spectra of CeFe$_2$Al$_{10}$, which is a reference material for CeRu$_2$Al$_{10}$ and CeOs$_2$Al$_{10}$ with an anomalous magnetic transition at 28 K. The $\sigma(\omega)$ spectrum along the b-axis differs greatly from that in the $ac$-plane, indicating that this material has an anisotropic electronic structure. At low temperatures, in all axes, a shoulder structure due to the optical transition across the hybridization gap between the conduction band and the localized $4f$ states, namely $c$-$f$ hybridization, appears at 55 meV. However, the gap opening temperature and the temperature of appearance of the quasiparticle Drude weight are strongly anisotropic indicating the anisotropic Kondo temperature. The strong anisotropic nature in both electronic structure and Kondo temperature is considered to be relevant the anomalous magnetic phase transition in CeRu$_2$Al$_{10}$ and CeOs$_2$Al$_{10}$.Comment: 5 pages, 4 figure

Representation of quantum states as points in a probability simplex associated to a SIC-POVM

The quantum state of a $d$-dimensional system can be represented by the $d^2$ probabilities corresponding to a SIC-POVM, and then this distribution of probability can be represented by a vector of $\R^{d^2-1}$ in a simplex, we will call this set of vectors $\mathcal{Q}$. Other way of represent a $d$-dimensional system is by the corresponding Bloch vector also in $\R^{d^2-1}$, we will call this set of vectors $\mathcal{B}$. In this paper it is proved that with the adequate scaling $\mathcal{B}=\mathcal{Q}$. Also we indicate some features of the shape of $\mathcal{Q}$.Comment: 12 pages. Added journal referenc

Inversion doublets of reflection-asymmetric clustering in 28Si and their isoscalar monopole and dipole transitions

[Background] Various cluster states of astrophysical interest are expected to exist in the excited states of $^{28}{\rm Si}$. However, they have not been identified firmly, because of the experimental and theoretical difficulties. [Purpose] To establish the $^{24}$Mg+$\alpha$, $^{16}$O+$^{12}$C and $^{20}$Ne+2$\alpha$ cluster bands, we theoretically search for the negative-parity cluster bands that are paired with the positive-parity bands to constitute the inversion doublets. We also offer the isoscalar monopole and dipole transitions as a promising probe for the clustering. We numerically show that these transition strengths from the ground state to the cluster states are very enhanced. [Method] The antisymmetrized molecular dynamics with Gogny D1S effective interaction is employed to calculate the excited states of $^{28}{\rm Si}$. The isoscalar monopole and dipole transition strengths are directly evaluated from wave functions of the ground and excited states. [Results] Negative-parity bands having $^{24}$Mg+$\alpha$ and $^{16}$O+$^{12}$C cluster configurations are obtained in addition to the newly calculated $^{20}$Ne+2$\alpha$ cluster bands. All of them are paired with the corresponding positive-parity bands to constitute the inversion doublets with various cluster configurations. The calculation show that the band-head of the $^{24}$Mg+$\alpha$ and $^{20}$Ne+2$\alpha$ cluster bands are strongly excited by the isoscalar monopole and dipole transitions. [Conclusions] The present calculation suggests the existence of the inversion doublets with the $^{24}$Mg+$\alpha$, $^{16}$O+$^{12}$C and $^{20}$Ne+2$\alpha$ configurations.Because of the enhanced transition strengths, we offer the isoscalar monopole and dipole transitions as good probe for the $^{24}$Mg+$\alpha$ and $^{20}$Ne+2$\alpha$ cluster bands.Comment: 28 pages, 8 figure

Stochastic delocalization of finite populations

Heterogeneities in environmental conditions often induce corresponding heterogeneities in the distribution of species. In the extreme case of a localized patch of increased growth rates, reproducing populations can become strongly concentrated at the patch despite the entropic tendency for population to distribute evenly. Several deterministic mathematical models have been used to characterize the conditions under which localized states can form, and how they break down due to convective driving forces. Here, we study the delocalization of a finite population in the presence of number fluctuations. We find that any finite population delocalizes on sufficiently long time scales. Depending on parameters, however, populations may remain localized for a very long time. The typical waiting time to delocalization increases exponentially with both population size and distance to the critical wind speed of the deterministic approximation. We augment these simulation results by a mathematical analysis that treats the reproduction and migration of individuals as branching random walks subject to global constraints. For a particular constraint, different from a fixed population size constraint, this model yields a solvable first moment equation. We find that this solvable model approximates very well the fixed population size model for large populations, but starts to deviate as population sizes are small. The analytical approach allows us to map out a phase diagram of the order parameter as a function of the two driving parameters, inverse population size and wind speed. Our results may be used to extend the analysis of delocalization transitions to different settings, such as the viral quasi-species scenario