Relating multihadron production in hadronic and nuclear collisions

The energy-dependence of charged particle mean multiplicity and pseudorapidity density at midrapidity measured in nucleus-nucleus and (anti)proton-proton collisions are studied in the entire available energy range. The study is performed using a model, which considers the multiparticle production process according to the dissipating energy of the participants and their types, namely a combination of the constituent quark picture together with Landau relativistic hydrodynamics. The model reveals interrelations between the variables under study measured in nucleus-nucleus and nucleon-nucleon collisions. Measurements in nuclear reactions are shown to be well reproduced by the measurements in (anti)proton-proton interactions common and the corresponding fits are presented. Different observations in other types of collisions are discussed in the framework of the proposed model. Predictions are made for measurements at the forthcoming LHC energies.Comment: Europ. Phys. J. C (to appear). Recently CMS reported (arXiv:1005.3299) on the midrapidity density value of 5.78 +/- 0.01(stat) +/- 0.23(syst) in pp collisons at 7 TeV, which agrees well with the value of 5.8 of our prediction

Comparative Dating Of Attine Ant And Lepiotaceous Cultivar Phylogenies Reveals Coevolutionary Synchrony And Discord

The mutualistic symbiosis between fungus-gardening ants and their cultivars has made fundamental contributions to our understanding of the coevolution of complex species interactions. Reciprocal specialization and vertical symbiont cotransmission are thought to promote a pattern of largely synchronous coevolutionary diversification in attines. Here we test this hypothesis by inferring the first time-calibrated multigene phylogeny of the lepiotaceous attine cultivars and comparing it with the recently published fossil-anchored phylogeny of the attine ants. While this comparison reveals some possible cases of synchronous origins of ant and fungal clades, there were a number of surprising asynchronies. For example, leaf-cutter cultivars appear to be significantly younger than the corresponding ant genera. Similarly, a clade of fungi interacting with primitive fungus-gardening ants-thought to be ancestral to the more derived leaf-cutter symbionts-appears instead to be a more recent acquisition from free-living stock. These macroevolutionary patterns are consistent with recent population-level studies suggesting occasional acquisition of novel cultivar types from environmental sources and horizontal transmission of cultivars between different ant species. Horizontal transmission events, even if rare, appear to form loose ecological connections between diffusely coevolving ant and fungus lineages that permit punctuated changes in the topology of the mutualistic ant-fungus interaction network.Integrative Biolog

Smooth bumps, a Borel theorem and partitions of smooth functions on p.c.f. fractals

We provide two methods for constructing smooth bump functions and for smoothly cutting off smooth functions on fractals, one using a probabilistic approach and sub-Gaussian estimates for the heat operator, and the other using the analytic theory for p.c.f. fractals and a fixed point argument. The heat semigroup (probabilistic) method is applicable to a more general class of metric measure spaces with Laplacian, including certain infinitely ramified fractals, however the cut off technique involves some loss in smoothness. From the analytic approach we establish a Borel theorem for p.c.f. fractals, showing that to any prescribed jet at a junction point there is a smooth function with that jet. As a consequence we prove that on p.c.f. fractals smooth functions may be cut off with no loss of smoothness, and thus can be smoothly decomposed subordinate to an open cover. The latter result provides a replacement for classical partition of unity arguments in the p.c.f. fractal setting.Comment: 26 pages. May differ slightly from published (refereed) versio

Locally accurate MPS approximations for ground states of one-dimensional gapped local Hamiltonians

A key feature of ground states of gapped local 1D Hamiltonians is their relatively low entanglement --- they are well approximated by matrix product states (MPS) with bond dimension scaling polynomially in the length $N$ of the chain, while general states require a bond dimension scaling exponentially. We show that the bond dimension of these MPS approximations can be improved to a constant, independent of the chain length, if we relax our notion of approximation to be more local: for all length-$k$ segments of the chain, the reduced density matrices of our approximations are $\epsilon$-close to those of the exact state. If the state is a ground state of a gapped local Hamiltonian, the bond dimension of the approximation scales like $(k/\epsilon)^{1+o(1)}$, and at the expense of worse but still $\text{poly}(k,1/\epsilon)$ scaling of the bond dimension, we give an alternate construction with the additional features that it can be generated by a constant-depth quantum circuit with nearest-neighbor gates, and that it applies generally for any state with exponentially decaying correlations. For a completely general state, we give an approximation with bond dimension $\exp(O(k/\epsilon))$, which is exponentially worse, but still independent of $N$. Then, we consider the prospect of designing an algorithm to find a local approximation for ground states of gapped local 1D Hamiltonians. When the Hamiltonian is translationally invariant, we show that the ability to find $O(1)$-accurate local approximations to the ground state in $T(N)$ time implies the ability to estimate the ground state energy to $O(1)$ precision in $O(T(N)\log(N))$ time.Comment: 24 pages, 3 figures. v2: Theorem 1 extended to include construction for general states; Lemma 7 & Theorem 2 slightly improved; figures added; lemmas rearranged for clarity; typos fixed. v3: Reformatted & additional references inserte