The lollipop graph is determined by its spectrum

An even (resp. odd) lollipop is the coalescence of a cycle of even (resp. odd) length and a path with pendant vertex as distinguished vertex. It is known that the odd lollipop is determined by its spectrum and the question is asked by W. Haemers, X. Liu and Y. Zhang for the even lollipop. We revisit the proof for odd lollipop, generalize it for even lollipop and therefore answer the question. Our proof is essentially based on a method of counting closed walks

A combinatorial proof of the Rogers-Ramanujan and Schur identities

We give a combinatorial proof of the first Rogers-Ramanujan identity by using two symmetries of a new generalization of Dyson's rank. These symmetries are established by direct bijections.Comment: 12 pages, 5 figures; incorporated referee suggestions, simplified definition of (k,m)-rank, to appear in JCT(A

Heat Capacity of the Pressure-induced Superconductivity in Itinerant Ferromagnet UGe2_2

Recently co-existence of the ferromagnetism and superconductivity was reported in the high-pressure region (1.0-1.6 GPa) in UGe$_2$. We performed the heat capacity measurement on UGe$_2$ under high pressure. At 1.13 GPa, we found a peak corresponding to the superconducting transition. The superconducting temperature $T_{SC}$ and ${\it\Delta} C/(\gamma T_{SC})$ are 0.6 K and 0.25, respectively. The superconducting transition was also confirmed by the appearance of the Meissner effect in the {\it ac} susceptibility. From these results, we confirm a bulk nature of the superconductivity in UGe$_2$. The value of $C/T$ ($\sim$ 95 mJ/moleK$^2$) just above $T_{SC}$ at 1.15 GPa is as much as 3 times larger than that at ambient pressure, which indicates a large mass enhancement of quasiparticles under high pressure.Comment: submitted to the International Conference on Strongly Correlated Electron Systems 200

From bare interactions, low--energy constants and unitary gas to nuclear density functionals without free parameters: application to neutron matter

We further progress along the line of Ref. [Phys. Rev. {\bf A 94}, 043614 (2016)] where a functional for Fermi systems with anomalously large $s$-wave scattering length $a_s$ was proposed that has no free parameters. The functional is designed to correctly reproduce the unitary limit in Fermi gases together with the leading-order contributions in the s- and p-wave channels at low density. The functional is shown to be predictive up to densities $\sim0.01$ fm$^{-3}$ that is much higher densities compared to the Lee-Yang functional, valid for $\rho < 10^{-6}$ fm$^{-3}$. The form of the functional retained in this work is further motivated. It is shown that the new functional corresponds to an expansion of the energy in $(a_s k_F)$ and $(r_e k_F)$ to all orders, where $r_e$ is the effective range and $k_F$ is the Fermi momentum. One conclusion from the present work is that, except in the extremely low--density regime, nuclear systems can be treated perturbatively in $-(a_s k_F)^{-1}$ with respect to the unitary limit. Starting from the functional, we introduce density--dependent scales and show that scales associated to the bare interaction are strongly renormalized by medium effects. As a consequence, some of the scales at play around saturation are dominated by the unitary gas properties and not directly to low-energy constants. For instance, we show that the scale in the s-wave channel around saturation is proportional to the so-called Bertsch parameter $\xi_0$ and becomes independent of $a_s$. We also point out that these scales are of the same order of magnitude than those empirically obtained in the Skyrme energy density functional. We finally propose a slight modification of the functional such that it becomes accurate up to the saturation density $\rho\simeq 0.16$ fm$^{-3}$

Comentarios, preguntas sobre colonización y extractivismo

Fil: Boulet, Patrick. Universidad Nacional de Cuyo. Facultad de Ciencias Políticas y Sociale