Perturbation theory without wave function for multidimensional systems

A new method to obtain perturbation corrections to the eigenvalues of multidimensional quantummechanical models is developed. It consists of rearranging the Rayleigh-Schrodinger perturbation theory so that any coefficient of the perturbation series is obtained from a simple and compact recursion relationship. The Zeeman effect in hydrogen and the hydrogen molecule-ion are used to illustrate the procedure.     

Robust discretizations versus increase of the time step for the Lorenz system

When continuous systems are discretized, their solutions depend on the time step chosen a priori. Such solutions are not necessarily spurious in the sense that they can still correspond to a solution of the differential equations but with a displacement in the parameter space. Consequently, it is of great interest to obtain discrete equations which are robust even when the discretization time step is large. In this paper, different discretizations of the Lorenz system are discussed versus the values of the discretization time step. It is shown that the sets of difference equations proposed are more robust versus increases of the time step than conventional discretizations built with standard schemes such as the forward Euler, backward Euler, or centered finite difference schemes. The nonstandard schemes used here are Mickens' scheme and Monaco and Normand-Cyrot's scheme.     

Anomalous transport in scale-free networks

To study transport properties of scale-free and Erdos-Rényi networks, we analyze the conductance G between two arbitrarily chosen nodes of random scale-free networks with degree distribution P(k)-k(-lambda) in which all links have unit resistance. We predict a broad range of values of G, with a power-law tail distribution phi(SF)(G)-G(-g(G)), where g(G)=2lambda-1, and confirm our predictions by simulations. The power-law tail in phi(SF)(G) leads to large values of G, signaling better transport in scale-free networks compared to Erdos-Rényi networks where the tail of the conductivity distribution decays exponentially. Based on a simple physical "transport backbone" picture we show that the conductances of scale-free and Erdos-Rényi networks are well approximated by ck(A)k(B)/(k(A)+k(B)) for any pair of nodes A and B with degrees k(A) and k(B), where c emerges as the main parameter characterizing network transport.     

Melting of the nanocrystalline vortex matter in highly anisotropic high-temperature superconductors

Multilevel Monte Carlo simulations of the vortex matter in the highly anisotropic high-temperature superconductor Bi2Sr2CaCu2O8 were performed. We introduced low concentration of columnar defects satisfying Bphi < or = B. Both the electromagnetic and Josephson interactions among pancake vortices were included. The nanocrystalline, nanoliquid, and homogeneous liquid phases were identified in agreement with experiments. We observed the two-step melting process and also noted an enhancement of the structure factor just prior to the melting transition. A proposed theoretical model is in agreement with our findings.     

An inorganic iron complex that inhibits wild-type and an isoniazid-resistant mutant 2-trans-enoyl-ACP (CoA) reductase from Mycobacterium tuberculosis

The in vitro kinetics of inactivation of both wild-type and I21V InhA enzymes by [FeII(CN)5(INH)]3- indicate that this process requires no activation by KatG, and no need for the presence of NADH. This inorganic complex may represent a new class of lead compounds to the development of anti-tubercular agents aiming at inhibition of a validated target.     

Double exchange model for magnetic hexaborides

A microscopic theory for rare-earth ferromagnetic hexaborides, such as Eu1-xCaxB6, is proposed on the basis of the double-exchange Hamiltonian. In these systems, the reduced carrier concentrations place the Fermi level near the mobility edge, introduced in the spectral density by the disordered spin background. We show that the transport properties such as the Hall effect, magnetoresistance, frequency dependent conductivity, and dc resistivity can be quantitatively described within the model. We also make specific predictions for the behavior of the Curie temperature T(C) as a function of the plasma frequency omega(p).     

Frobenius Modules and Hodge Asymptotics

We exhibit a direct correspondence between the potential defining the H^1,1 small quantum module structure on the cohomology of a Calabi-Yau manifold and the asymptotic data of the A-model variation of Hodge structure. This is done in the abstract context of polarized variations of Hodge structure and Frobenius modules. E. Cattani was partially supported by NSF Grant DMS-0099707