Cumulant approach to weakly doped antiferromagnets

We present a new approach to static and dynamical properties of holes and spins in weakly doped antiferromagnets in two dimensions. The calculations are based on a recently introduced cumulant approach to ground--state properties of correlated electronic systems. The present method allows to evaluate hole and spin--wave dispersion relations by considering hole or spin excitations of the ground state. Usually, these dispersions are found from time--dependent correlation functions. To demonstrate the ability of the approach we first derive the dispersion relation for the lowest single hole excitation at half--filling. However, the main purpose of this paper is to focus on the mutual influence of mobile holes and spin waves in the weakly doped system. It is shown that low-energy spin excitations strongly admix to the ground--state. The coupling of spin waves and holes leads to a strong suppression of the staggered magnetization which can not be explained by a simple rigid--band picture for the hole quasiparticles. Also the experimentally observed doping dependence of the spin--wave excitation energies can be understood within our formalism.Comment: REVTEX, 25 pages, 7 figures (EPS), to be published in Phys. Rev.

Stochastic framework for evaluating the effect of displaced antenna elements on DOA estimation

We establish a statistical framework for investigating the influence of correlated random displacements of antenna elements in a uniform circular antenna array (UCA) on the distribution of direction-of-arrival (DOA) estimates. More specifically, we apply a stochastic collocation method formodeling the sparse UCA root-MUSIC-DOA estimates as polynomial expansions of the random displacements. Compared to Monte-Carlo simulations, this approach yields a speedup of about 40 for the case of a displacement of two antenna elements

Transfer Entropy and Cumulant Based Cost as Measures of Nonlinear Causal Relationships in Space Plasmas: Applications to D St.

It is well known that the magnetospheric response to the solar wind is nonlinear. Information theoretical tools such as mutual information, transfer entropy, and cumulant based analysis are able to characterize the nonlinearities in the system. Using cumulant based cost, we show that nonlinear significance of D st peaks at 3–12 hours lags that can be attributed to VBs which also exhibit similar behavior. However, the nonlinear significance that peaks at lags 25, 50, and 90 hours can be attributed to internal dynamics, which may be related to the relaxation of the ring current. These peaks are absent in the linear and nonlinear self-significance of VBs . Our analysis with mutual information and transfer entropy show that both methods can establish that there are a strong correlation and transfer of information from V sw to D st at a time scale that is consistent with that obtained from the cumulant based analysis. However, mutual information also shows that there is a strong correlation in the backward direction, from D st to V sw , which is counterintuitive. In contrast, transfer entropy shows that there is no or little transfer of information from D st to V sw , as expected because it is the solar wind that drives the magnetosphere, not the other way around. Our case study demonstrates that these information theoretical tools are quite useful for space physics studies because these tools can uncover nonlinear dynamics that cannot be seen with the traditional analyses and models that assume linear relationships

Replica Symmetry Breaking in Short-Range Spin Glasses: Theoretical Foundations and Numerical Evidences

We discuss replica symmetry breaking (RSB) in spin glasses. We update work in this area, from both the analytical and numerical points of view. We give particular attention to the difficulties stressed by Newman and Stein concerning the problem of constructing pure states in spin glass systems. We mainly discuss what happens in finite-dimensional, realistic spin glasses. Together with a detailed review of some of the most important features, facts, data, and phenomena, we present some new theoretical ideas and numerical results. We discuss among others the basic idea of the RSB theory, correlation functions, interfaces, overlaps, pure states, random field, and the dynamical approach. We present new numerical results for the behaviors of coupled replicas and about the numerical verification of sum rules, and we review some of the available numerical results that we consider of larger importance (for example, the determination of the phase transition point, the correlation functions, the window overlaps, and the dynamical behavior of the system).Comment: 48 pages, 21 figures. v2: the published versio

Van der Waals interaction between flux lines in High-T_c Superconductors

In anisotropic or layered superconductors thermal fluctuations as well as impurities induce a van der Waals (vdW) attraction between flux lines, as has recently been shown by Blatter and Geshkenbein in the thermal case [Phys. Rev. Lett. 77, 4958 (1996)] and by Mukherji and Nattermann in the disorder dominated case [Phys. Rev. Lett. 79, 139 (1997)]. This attraction together with the entropic or disorder induced repulsion has interesting consequences for the low field phase diagram. We present two derivations of the vdW attraction, one of which is based on an intuitive picture, the other one following from a systematic expansion of the free energy of two interacting flux lines. Both the thermal and the disorder dominated case are considered. In the thermal case in the absence of disorder, we use scaling arguments as well as a functional renormalization of the vortex-vortex interaction energy to calculate the effective Gibbs free energy on the scale of the mean flux line distance. We discuss the resulting low field phase diagram and make quantitative predictions for pure BiSCCO (Bi_2-Sr_2-CaCu_2-O_8). In the case with impurities, the Gibbs free energy is calculated on the basis of scaling arguments, allowing for a semi-quantitative discussion of the low-field, low-temperature phase diagram in the presence of impurities.Comment: 19 pages EPJ style, 9 PostScript figures. Minor additions to the first submission. Accepted for publication in EPJ