Symmetries of differential-difference dynamical systems in a two-dimensional lattice

Classification of differential-difference equation of the form $\ddot{u}_{nm}=F_{nm}\big(t, \{u_{pq}\}|_{(p,q)\in \Gamma}\big)$ are considered according to their Lie point symmetry groups. The set $\Gamma$ represents the point $(n,m)$ and its six nearest neighbors in a two-dimensional triangular lattice. It is shown that the symmetry group can be at most 12-dimensional for abelian symmetry algebras and 13-dimensional for nonsolvable symmetry algebras.Comment: 24 pages, 1 figur

On the Klein-Gordon equation and hyperbolic pseudoanalytic function theory

Elliptic pseudoanalytic function theory was considered independently by Bers and Vekua decades ago. In this paper we develop a hyperbolic analogue of pseudoanalytic function theory using the algebra of hyperbolic numbers. We consider the Klein-Gordon equation with a potential. With the aid of one particular solution we factorize the Klein-Gordon operator in terms of two Vekua-type operators. We show that real parts of the solutions of one of these Vekua-type operators are solutions of the considered Klein-Gordon equation. Using hyperbolic pseudoanalytic function theory, we then obtain explicit construction of infinite systems of solutions of the Klein-Gordon equation with potential. Finally, we give some examples of application of the proposed procedure

Higher order effective low-energy theories

Three well-known perturbative approaches to deriving low-energy effective theories, the degenerate Brillouin-Wigner perturbation theory (projection method), the canonical transformation, and the resolvent methods are compared. We use the Hubbard model as an example to show how, to fourth order in hopping t, all methods lead to the same effective theory, namely the t-J model with ring exchange and various correlated hoppings. We emphasize subtle technical difficulties that make such a derivation less trivial to carry out for orders higher than second. We also show that in higher orders, different approaches can lead to seemingly different forms for the low-energy Hamiltonian. All of these forms are equivalent since they are connected by an additional unitary transformation whose generator is given explicitly. The importance of transforming the operators is emphasized and the equivalence of their transformed structure within the different approaches is also demonstrated.Comment: 14 pages, no figure

First order Mott transition at zero temperature in two dimensions: Variational plaquette study

The nature of the metal-insulator Mott transition at zero temperature has been discussed for a number of years. Whether it occurs through a quantum critical point or through a first order transition is expected to profoundly influence the nature of the finite temperature phase diagram. In this paper, we study the zero temperature Mott transition in the two-dimensional Hubbard model on the square lattice with the variational cluster approximation. This takes into account the influence of antiferromagnetic short-range correlations. By contrast to single-site dynamical mean-field theory, the transition turns out to be first order even at zero temperature.Comment: 6 pages, 5 figures, version 2 with additional results for 8 bath site

Temperatures recorded by cosmogenic noble gases since the last glacial maximum in the Maritime Alps

While proxy records have been used to reconstruct late Quaternary climate parameters throughout the European Alps, our knowledge of deglacial climate conditions in the Maritime Alps is limited. Here, we report temperatures recorded by a new and independent geochemical technique—cosmogenic noble gas paleothermometry—in the Maritime Alps since the last glacial maximum. We measured cosmogenic 3He in quartz from boulders in nested moraines in the Gesso Valley, Italy. Paired with cosmogenic 10Be measurements and 3He diffusion experiments on quartz from the same boulders, the cosmogenic 3He abundances record the temperatures these boulders experienced during their exposure. We calculate effective diffusion temperatures (EDTs) over the last ~22 ka ranging from 8°C to 25°C. These EDTs, which are functionally related to, but greater than, mean ambient temperatures, are consistent with temperatures inferred from other proxies in nearby Alpine regions and those predicted by a transient general circulation model. In detail, however, we also find different EDTs for boulders from the same moraines, thus limiting our ability to interpret these temperatures. We explore possible causes for these intra-moraine discrepancies, including variations in radiative heating, our treatment of complex helium diffusion, uncertainties in our grain size analyses, and unaccounted-for erosion or cosmogenic inheritance

Climate of the Past Open Access Using palaeo-climate comparisons to constrain future projections

www.clim-past.net/10/221/2014/ doi:10.5194/cp-10-221-2014 © Author(s) 2014. CC Attribution 3.0 License

MtDNA Analyses on Hair Samples Confirm Cougar, Puma concolor, Presence in Southern New Brunswick, Eastern Canada

For the last 40 years, the presence of Cougars (Puma concolor) in eastern Canada has been highly controversial. The purpose of this study was to collect physical evidence of Cougars using a passive detection method. Baited hair-traps combined with camera-traps were installed in New Brunswick and Nova Scotia, Canada. DNA analyses on two hair samples confirmed that the species was present in southern New Brunswick in 2003. A footprint photographed after an observation of a Cougar by reliable observers was examined by experts and was consistent with a Cougar footprint. Additional data are required to determine the status of Cougars in the northeastern part of its historical range

Characteristics of EGRET Blazars in the VLBA Imaging and Polarimetry Survey (VIPS)

We examine the radio properties of EGRET-detected blazars observed as part of the VLBA Imaging and Polarimetry Survey (VIPS). VIPS has a flux limit roughly an order of magnitude below the MOJAVE survey and most other samples that have been used to study the properties of EGRET blazars. At lower flux levels, radio flux density does not directly correlate with gamma-ray flux density. We do find that the EGRET-detected blazars tend to have higher brightness temperatures, greater core fractions, and possibly larger than average jet opening angles. A weak correlation is also found with jet length and with polarization. All of the well-established trends can be explained by systematically larger Doppler factors in the gamma-ray loud blazars, consistent with the measurements of higher apparent velocities found in monitoring programs carried out at radio frequencies above 10 GHz.Comment: 20 pages, 7 figures, accepted to Ap