Marginal Fermi Liquid with a Two-Dimensional Patched Fermi Surface

We consider a model composed of Landau quasiparticle states with patched Fermi surfaces (FS) sandwiched by states with flat FS to simulate the ``cold'' spot regions in cuprates. We calculate the one particle irreducible function and the self-energy up to two-loop order. Using renormalization group arguments we show that in the forward scattering channel the renormalized coupling constant is never infrared stable due to the flat FS sectors. Furthemore we show that the self-energy scales with energy as ${\rm Re} \Sigma \sim \omega \ln \omega$ as $\omega \to 0$, and thus the Fermi liquid state within each FS patch is turned into a marginal Fermi liquid.Comment: 5 pages, 3 ps figure

Low-energy effective representation of the Gutzwiller-projected BCS Hamiltonian close to half filling

We investigate analytically a connection between the t-J model and the strongly correlated Bardeen-Cooper-Schrieffer (BCS) Hamiltonian, with the effect of strong electron correlations accounted by the Gutzwiller projection. We show that in the immediate vicinity of half filling the projected 2D BCS Hamiltonian with strong pairing develops an antiferromagnetically (AF) ordered ground state. This result explicitly demonstrates that antiferromagnetism in this model appears as a natural consequence of the strong Coulomb repulsion in a low doped regime. At moderate doping the ground state of the Gutzwiller-projected BCS Hamiltonian becomes qualitatively similar to Anderson's resonating valence bond state which is known to fit nicely the properties of the t-J model in this regime. These two properties taken together indicate that the projected BCS Hamiltonian captures the essential low-energy physics of the t-J model in the whole underdoped region

Extrasolar Planets in Mean-Motion Resonance: Apses Alignment and Asymmetric Stationary Solutions

In recent years several pairs of extrasolar planets have been discovered in the vicinity of mean-motion commensurabilities. In some cases, such as the Gliese 876 system, the planets seem to be trapped in a stationary solution, the system exhibiting a simultaneous libration of the resonant angle theta_1 = 2 lambda_2 - lambda_1 - varpi_1 and of the relative position of the pericenters. In this paper we analyze the existence and location of these stable solutions, for the 2/1 and 3/1 resonances, as function of the masses and orbital elements of both planets. This is undertaken via an analytical model for the resonant Hamiltonian function. The results are compared with those of numerical simulations of the exact equations. In the 2/1 commensurability, we show the existence of three principal families of stationary solutions: (i) aligned orbits, in which theta_1 and varpi_1 - varpi_2 both librate around zero, (ii) anti-aligned orbits, in which theta_1=0 and the difference in pericenter is 180 degrees, and (iii) asymmetric stationary solutions, where both the resonant angle and varpi_1 - varpi_2 are constants with values different of 0 or 180 degrees. Each family exists in a different domain of values of the mass ratio and eccentricities of both planets. Similar results are also found in the 3/1 resonance. We discuss the application of these results to the extrasolar planetary systems and develop a chart of possible planetary orbits with apsidal corotation. We estimate, also, the maximum planetary masses in order that the stationary solutions are dynamically stable.Comment: 25 pages, 10 figures. Submitted to Ap

On planetary mass determination in the case of super-Earths orbiting active stars. The case of the CoRoT-7 system

This investigation uses the excellent HARPS radial velocity measurements of CoRoT-7 to re-determine the planet masses and to explore techniques able to determine mass and elements of planets discovered around active stars when the relative variation of the radial velocity due to the star activity cannot be considered as just noise and can exceed the variation due to the planets. The main technique used here is a self-consistent version of the high-pass filter used by Queloz et al. (2009) in the first mass determination of CoRoT-7b and CoRoT-7c. The results are compared to those given by two alternative techniques: (1) The approach proposed by Hatzes et al. (2010) using only those nights in which 2 or 3 observations were done; (2) A pure Fourier analysis. In all cases, the eccentricities are taken equal to zero as indicated by the study of the tidal evolution of the system; the periods are also kept fixed at the values given by Queloz et al. Only the observations done in the time interval BJD 2,454,847 - 873 are used because they include many nights with multiple observations; otherwise it is not possible to separate the effects of the rotation fourth harmonic (5.91d = Prot/4) from the alias of the orbital period of CoRoT-7b (0.853585 d). The results of the various approaches are combined to give for the planet masses the values 8.0 \pm 1.2 MEarth for CoRoT-7b and 13.6 \pm 1.4 MEarth for CoRoT 7c. An estimation of the variation of the radial velocity of the star due to its activity is also given.The results obtained with 3 different approaches agree to give masses larger than those in previous determinations. From the existing internal structure models they indicate that CoRoT-7b is a much denser super-Earth. The bulk density is 11 \pm 3.5 g.cm-3 . CoRoT-7b may be rocky with a large iron core.Comment: 12 pages, 11 figure

Initial pseudo-steady state & asymptotic KPZ universality in semiconductor on polymer deposition

The Kardar-Parisi-Zhang (KPZ) class is a paradigmatic example of universality in nonequilibrium phenomena, but clear experimental evidences of asymptotic 2D-KPZ statistics are still very rare, and far less understanding stems from its short-time behavior. We tackle such issues by analyzing surface fluctuations of CdTe films deposited on polymeric substrates, based on a huge spatio-temporal surface sampling acquired through atomic force microscopy. A \textit{pseudo}-steady state (where average surface roughness and spatial correlations stay constant in time) is observed at initial times, persisting up to deposition of $\sim 10^{4}$ monolayers. This state results from a fine balance between roughening and smoothening, as supported by a phenomenological growth model. KPZ statistics arises at long times, thoroughly verified by universal exponents, spatial covariance and several distributions. Recent theoretical generalizations of the Family-Vicsek scaling and the emergence of log-normal distributions during interface growth are experimentally confirmed. These results confirm that high vacuum vapor deposition of CdTe constitutes a genuine 2D-KPZ system, and expand our knowledge about possible substrate-induced short-time behaviors.Comment: 13 pages, 8 figures, 2 table

Dynamics of Enceladus and Dione inside the 2:1 Mean-Motion Resonance under Tidal Dissipation

In a previous work (Callegari and Yokoyama 2007, Celest. Mech. Dyn. Astr. vol. 98), the main features of the motion of the pair Enceladus-Dione were analyzed in the frozen regime, i.e., without considering the tidal evolution. Here, the results of a great deal of numerical simulations of a pair of satellites similar to Enceladus and Dione crossing the 2:1 mean-motion resonance are shown. The resonance crossing is modeled with a linear tidal theory, considering a two-degrees-of-freedom model written in the framework of the general three-body planar problem. The main regimes of motion of the system during the passage through resonance are studied in detail. We discuss our results comparing them with classical scenarios of tidal evolution of the system. We show new scenarios of evolution of the Enceladus-Dione system through resonance not shown in previous approaches of the problem.Comment: 36 pages, 12 figures. Accepted in Celestial Mechanics and Dynamical Astronom

Planetary Migration and Extrasolar Planets in the 2/1 Mean-Motion Resonance

We analyze the possible relationship between the current orbital elements fits of known exoplanets in the 2/1 mean-motion resonance and the expected orbital configuration due to migration. It is found that, as long as the orbital decay was sufficiently slow to be approximated by an adiabatic process, all captured planets should be in apsidal corotations. In other words, they should show a simultaneous libration of both the resonant angle and the difference in longitudes of pericenter. We present a complete set of corotational solutions for the 2/1 commensurability, including previously known solutions and new results. Comparisons with observed exoplanets show that current orbital fits of three known planetary systems in this resonance are either consistent with apsidal corotations (GJ876 and HD82943) or correspond to bodies with uncertain orbits (HD160691). Finally, we discuss the applicability of these results as a test for the planetary migration hypothesis itself. If all future systems in this commensurability are found to be consistent with corotational solutions, then resonance capture of these bodies through planetary migration is a working hypothesis. Conversely, If any planetary pair is found in a different configuration, then either migration did not occur for those bodies, or it took a different form than currently believed.Comment: Submitted to MNRA