Intrinsic pseudo-volume forms for logarithmic pairs

31 pagesInternational audienceWe study an adaptation to the logarithmic case of the Kobayashi-Eisenman pseudo-volume form, or rather an adaptation of its variant defined by Claire Voisin, for which she replaces holomorphic maps by holomorphic K-correspondences. We define an intrinsic logarithmic pseudo-volume form \Phi_{X,D} for every pair (X,D) consisting of a complex manifold X and a normal crossing Weil divisor, the positive part of which is reduced. We then prove that \Phi_{X,D} is generically non-degenerate when X is projective and K_X+D is ample. This result is analogous to the classical Kobayashi-Ochiai theorem. We also show the vanishing of \Phi_{X,D} for a large class of log-K-trivial pairs, which is an important step in the direction of the Kobayashi conjecture about infinitesimal measure hyperbolicity in the logarithmic case

Statistical mechanics of secondary structures formed by random RNA sequences

The formation of secondary structures by a random RNA sequence is studied as a model system for the sequence-structure problem omnipresent in biopolymers. Several toy energy models are introduced to allow detailed analytical and numerical studies. First, a two-replica calculation is performed. By mapping the two-replica problem to the denaturation of a single homogeneous RNA in 6-dimensional embedding space, we show that sequence disorder is perturbatively irrelevant, i.e., an RNA molecule with weak sequence disorder is in a molten phase where many secondary structures with comparable total energy coexist. A numerical study of various models at high temperature reproduces behaviors characteristic of the molten phase. On the other hand, a scaling argument based on the extremal statistics of rare regions can be constructed to show that the low temperature phase is unstable to sequence disorder. We performed a detailed numerical study of the low temperature phase using the droplet theory as a guide, and characterized the statistics of large-scale, low-energy excitations of the secondary structures from the ground state structure. We find the excitation energy to grow very slowly (i.e., logarithmically) with the length scale of the excitation, suggesting the existence of a marginal glass phase. The transition between the low temperature glass phase and the high temperature molten phase is also characterized numerically. It is revealed by a change in the coefficient of the logarithmic excitation energy, from being disorder dominated to entropy dominated.Comment: 24 pages, 16 figure

Superconducting States in pseudo-Landau Levels of Strained Graphene

We describe the formation of superconducting states in graphene in the presence of pseudo-Landau levels induced by strain, when time reversal symmetry is preserved. We show that superconductivity in strained graphene is quantum critical when the pseudo-Landau levels are completely filled, whereas at partial fillings superconductivity survives at weak coupling. In the weak coupling limit, the critical temperature scales \emph{linearly} with the coupling strength and shows a sequence of quantum critical points as a function of the filling factor that can be accessed experimentally. We argue that superconductivity can be induced by electron-phonon coupling and that the transition temperature can be controlled with the amount of strain and with the filling fraction of the Landau levels.Comment: 4.5 pages, 3 figues. To appear in PR

Ambient metric construction of Q-curvature in conformal and CR geometries

We give a geometric derivation of Branson's Q-curvature in terms of the ambient metric associated with conformal structures; it naturally follows from the ambient metric construction of conformally invariant operators and can be applied to a large class of invariant operators. This procedure can be also applied to CR geometry and gives a CR analog of the Q-curvature; it then turns out that the Q-curvature gives the coefficient of the logarithmic singularity of the Szego kernel of 3-dimensional CR manifolds.Comment: 14 pages, corrected typos and updated reference

Stripe-Like Inhomogeneities, Spectroscopies, Pairing, and Coherence in the High-Tc Cuprates

It is found that the carriers of the high-T_c cuprates are polaron-like "stripons" carrying charge and located in stripe-like inhomogeneities, "quasi-electrons" carrying charge and spin, and "svivons" carrying spin and lattice distortion. This is shown to result in the observed anomalous spectroscopic properties of the cuprates. The AF/stripe-like inhomogeneities result from the Bose condensation of the svivon field, and the speed of their dynamics is determined by the width of the double-svivon neutron-resonance peak. Pairing results from transitions between pair states of stripons and quasi-electrons through the exchange of svivons. The obtained pairing symmetry is of the d_{x^2-y^2} type; however, sign reversal through the charged stripes results in features not characteristic of this symmetry. The phase diagram is determined by a pairing and a coherence line, associated with a Mott transition, and the pseudogap state corresponds to incoherent pairing.Comment: 13 pages, 8 figures; version including recent references, to be published in J. Phys. Chem. Solid