Reconstructing the thermal Green functions at real times from those at imaginary times

By exploiting the analyticity and boundary value properties of the thermal Green functions that result from the KMS condition in both time and energy complex variables, we treat the general (non-perturbative) problem of recovering the thermal functions at real times from the corresponding functions at imaginary times, introduced as primary objects in the Matsubara formalism. The key property on which we rely is the fact that the Fourier transforms of the retarded and advanced functions in the energy variable have to be the `unique Carlsonian analytic interpolations' of the Fourier coefficients of the imaginary-time correlator, the latter being taken at the discrete Matsubara imaginary energies, respectively in the upper and lower half-planes. Starting from the Fourier coefficients regarded as `data set', we then develop a method based on the Pollaczek polynomials for constructing explicitly their analytic interpolations.Comment: 23 pages, 2 figure

Coralline algae in a naturally acidified ecosystem persist by maintaining control of skeletal mineralogy and size

To understand the effects of ocean acidification (OA) on marine calcifiers, the trade-offs among different sublethal responses within individual species and the emergent effects of these trade-offs must be determined in an ecosystem setting. Crustose coralline algae (CCA) provide a model to test the ecological consequences of such sublethal effects as they are important in ecosystem functioning, service provision, carbon cycling and use dissolved inorganic carbon to calcify and photosynthesize. Settlement tiles were placed in ambient pH, low pH and extremely low pH conditions for 14 months at a natural CO2 vent. The size, magnesium (Mg) content and molecular-scale skeletal disorder of CCA patches were assessed at 3.5, 6.5 and 14 months from tile deployment. Despite reductions in their abundance in low pH, the largest CCA from ambient and low pH zones were of similar sizes and had similar Mg content and skeletal disorder. This suggests that the most resilient CCA in low pH did not trade-off skeletal structure to maintain growth. CCA that settled in the extremely low pH, however, were significantly smaller and exhibited altered skeletal mineralogy (high Mg calcite to gypsum (hydrated calcium sulfate)), although at present it is unclear if these mineralogical changes offered any fitness benefits in extreme low pH. This field assessment of biological effects of OA provides endpoint information needed to generate an ecosystem relevant understanding of calcifying system persistence

An equivariant isomorphism theorem for mod p\mathfrak p reductions of arboreal Galois representations

Let $\phi$ be a quadratic, monic polynomial with coefficients in $\mathcal O_{F,D}[t]$, where $\mathcal O_{F,D}$ is a localization of a number ring $\mathcal O_F$. In this paper, we first prove that if $\phi$ is non-square and non-isotrivial, then there exists an absolute, effective constant $N_\phi$ with the following property: for all primes $\mathfrak p\subseteq\mathcal O_{F,D}$ such that the reduced polynomial $\phi_\mathfrak p\in (\mathcal O_{F,D}/\mathfrak p)[t][x]$ is non-square and non-isotrivial, the squarefree Zsigmondy set of $\phi_{\mathfrak p}$ is bounded by $N_\phi$. Using this result, we prove that if $\phi$ is non-isotrivial and geometrically stable then outside a finite, effective set of primes of $\mathcal O_{F,D}$ the geometric part of the arboreal representation of $\phi_{\mathfrak p}$ is isomorphic to that of $\phi$. As an application of our results we prove R. Jones' conjecture on the arboreal Galois representation attached to the polynomial $x^2+t$

Strongly correlated gases of Rydberg-dressed atoms: quantum and classical dynamics

We discuss techniques to generate long-range interactions in a gas of groundstate alkali atoms, by weakly admixing excited Rydberg states with laser light. This provides a tool to engineer strongly correlated phases with reduced decoherence from inelastic collisions and spontaneous emission. As an illustration, we discuss the quantum phases of dressed atoms with dipole-dipole interactions confined in a harmonic potential, as relevant to experiments. We show that residual spontaneous emission from the Rydberg state acts as a heating mechanism, leading to a quantum-classical crossover.Comment: 4 pages, 4 figure

Strongly correlated 2D quantum phases with cold polar molecules: controlling the shape of the interaction potential

We discuss techniques to tune and shape the long-range part of the interaction potentials in quantum gases of polar molecules by dressing rotational excitations with static and microwave fields. This provides a novel tool towards engineering strongly correlated quantum phases in combination with low dimensional trapping geometries. As an illustration, we discuss a 2D crystalline phase, and a superfluid-crystal quantum phase transition.Comment: 4 pages, 3 figure

What is a Gene? A Two Sided View

The need to account for all currently available experimental observations concerning the gene nature, has reshaped the concept of gene turning it from the essentially mechanistic unit, predominant during the '70s, into a quite abstract open and generalized entity, whose contour appears less defined as compared to the past. Here we propose the essence of the gene to be considered double faced. In this respect genotypic and phenotypic entities of a gene would coexist and mix reciprocally. This harmonizes present knowledge with current definitions and predisposes for remodelling of our thinking as a consequence of future discoveries. A two sided view of the gene also allows to combine the genetic and epigenetic aspects in a unique solution, being structural and functional at the same time and simultaneously able to include the different levels in an overlapping unicum

A superfluid-droplet crystal and a free-space supersolid in a dipole-blockaded gas

A novel supersolid phase is predicted for an ensemble of Rydberg atoms in the dipole-blockade regime, interacting via a repulsive dipolar potential "softened" at short distances. Using exact numerical techniques, we study the low temperature phase diagram of this system, and observe an intriguing phase consisting of a crystal of mesoscopic superfluid droplets. At low temperature, phase coherence throughout the whole system, and the ensuing bulk superfluidity, are established through tunnelling of identical particles between neighbouring droplets.Comment: 4 pages, 4 figure