Microscopic theory for quantum mirages in quantum corrals

Scanning tunneling microscopy permits to image the Kondo resonance of a single magnetic atom adsorbed on a metallic surface. When the magnetic impurity is placed at the focus of an elliptical quantum corral, a Kondo resonance has been recently observed both on top of the impurity and on top of the focus where no magnetic impurity is present. This projection of the Kondo resonance to a remote point on the surface is referred to as quantum mirage. We present a quantum mechanical theory for the quantum mirage inside an ideal quantum corral and predict that the mirage will occur in corrals with shapes other than elliptical

Polarized interacting exciton gas in quantum wells and bulk semiconductors

We develop a theory to calculate exciton binding energies of both two- and three-dimensional spin polarized exciton gases within a mean field approach. Our method allows the analysis of recent experiments showing the importance of the polarization and intensity of the excitation light on the exciton luminescence of GaAs quantum wells. We study the breaking of the spin degeneracy observed at high exciton density $(5 \ \ 10^{10} cm ^2)$. Energy level splitting betwen spin +1 and spin -1 is shown to be due to many-body inter-excitonic exchange while the spin relaxation time is controlled by intra-exciton exchange.Comment: Revtex, 4 figures sent by fax upon request by e-mai

Early Arrival and Climatically-Linked Geographic Expansion of New World Monkeys from Tiny African Ancestors.

New World Monkeys (NWM) (platyrrhines) are one of the most diverse groups of primates, occupying today a wide range of ecosystems in the American tropics and exhibiting large variations in ecology, morphology, and behavior. Although the relationships among the almost 200 living species are relatively well understood, we lack robust estimates of the timing of origin, ancestral morphology, and geographic range evolution of the clade. Herein, we integrate paleontological and molecular evidence to assess the evolutionary dynamics of extinct and extant platyrrhines. We develop novel analytical frameworks to infer the evolution of body mass, changes in latitudinal ranges through time, and species diversification rates using a phylogenetic tree of living and fossil taxa. Our results show that platyrrhines originated 5-10 million years earlier than previously assumed, dating back to the Middle Eocene. The estimated ancestral platyrrhine was small-weighing 0.4 kg-and matched the size of their presumed African ancestors. As the three platyrrhine families diverged, we recover a rapid change in body mass range. During the Miocene Climatic Optimum, fossil diversity peaked and platyrrhines reached their widest latitudinal range, expanding as far South as Patagonia, favored by warm and humid climate and the lower elevation of the Andes. Finally, global cooling and aridification after the middle Miocene triggered a geographic contraction of NWM and increased their extinction rates. These results unveil the full evolutionary trajectory of an iconic and ecologically important radiation of monkeys and showcase the necessity of integrating fossil and molecular data for reliably estimating evolutionary rates and trends

Mean first-passage time for random walks on undirected networks

In this paper, by using two different techniques we derive an explicit formula for the mean first-passage time (MFPT) between any pair of nodes on a general undirected network, which is expressed in terms of eigenvalues and eigenvectors of an associated matrix similar to the transition matrix. We then apply the formula to derive a lower bound for the MFPT to arrive at a given node with the starting point chosen from the stationary distribution over the set of nodes. We show that for a correlated scale-free network of size $N$ with a degree distribution $P(d)\sim d^{-\gamma}$, the scaling of the lower bound is $N^{1-1/\gamma}$. Also, we provide a simple derivation for an eigentime identity. Our work leads to a comprehensive understanding of recent results about random walks on complex networks, especially on scale-free networks.Comment: 7 pages, no figures; definitive version published in European Physical Journal

Efficiency of transportation on weighted extended Koch networks

In this paper, we propose a family of weighted extended Koch networks based on a class of extended Koch networks. They originate from a r-complete graph, and each node in each r-complete graph of current generation produces mr-complete graphs whose weighted edges are scaled by factor h in subsequent evolutionary step. We study the structural properties of these networks and random walks on them. In more detail, we calculate exactly the average weighted shortest path length (AWSP), average receiving time (ART) and average sending time (AST). Besides, the technique of resistor network is employed to uncover the relationship between ART and AST on networks with unit weight. In the infinite network order limit, the average weighted shortest path lengths stay bounded with growing network order (0 < h < 1). The closed form expression of ART shows that it exhibits a sub-linear dependence (0 < h < 1) or linear dependence (h = 1) on network order. On the contrary, the AST behaves super-linearly with the network order. Collectively, all the obtained results show that the efficiency of message transportation on weighted extended Koch networks has close relation to the network parameters h, m and r. All these findings could shed light on the structure and random walks of general weighted networks