Circulating-current states and ring-exchange interactions in cuprates

We consider the consequences for circulating-current states of a cyclic, four-spin, ``ring-exchange'' interaction of the type shown recently to be significant in cuprate systems. The real-space Hartree-Fock approach is used to establish the existence of charge-current and spin-current phases in a generalized Hubbard model for the CuO_2 planes in cuprates. We compare the results of the Hartree-Fock approximation with the correlated states renormalized by Gutzwiller projection factors which allows us to gauge the qualitative effects of projection to no double site occupancy. We find that charge flux states may be competitive in cuprates, whereas spin flux states are suppressed in the strongly correlated regime. We then include the ring-exchange interaction and demonstrate its effect on current-carrying states both at and away from half-filling.Comment: 14 pages, 11 figure

Ballistic (precessional) contribution to the conventional magnetic switching

We consider a magnetic moment with an easy axis anisotropy energy, switched by an external field applied along this axis. Additional small, time-independent bias field is applied perpendicular to the axis. It is found that the magnet's switching time is a non-monotonic function of the rate at which the field is swept from "up" to "down". Switching time exhibits a minimum at a particular optimal sweep time. This unusual behavior is explained by the admixture of a ballistic (precessional) rotation of the moment caused by the perpendicular bias field in the presence of a variable switching field. We derive analytic expressions for the optimal switching time, and for the entire dependence of the switching time on the field sweep time. The existence of the optimal field sweep time has important implications for the optimization of magnetic memory devices

Stability of tetrons

We consider the interactions in a mesonic system, referred here to as `tetron', consisting of two heavy quarks and two lighter antiquarks (which may still be heavy in the scale of QCD), i.e. generally $Q_a Q_b \bar q_c \bar q_d$, and study the existence of bound states below the threshold for decay into heavy meson pairs. At a small ratio of the lighter to heavier quark masses an expansion parameter arises for treatment of the binding in such systems. We find that in the limit where all the quarks and antiquarks are so heavy that a Coulomb-like approximation can be applied to the gluon exchange between all of them, such bound states arise when this parameter is below a certain critical value. We find the parametric dependence of the critical mass ratio on the number of colors $N_c$, and confirm this dependence by numerical calculations. In particular there are no stable tetrons when all constituents have the same mass. We discuss an application of a similar expansion in the large $N_c$ limit to realistic systems where the antiquarks are light and their interactions are nonperturbative. In this case our findings are in agreement with the recent claims from a phenomenological analysis that a stable $b b \bar u \bar d$ tetron is likely to exist, unlike those where one or both bottom quarks are replaced by the charmed quark.Comment: 10 pages, 2 figure

Dipole Excitation of Dipositronium

The energy interval between the ground and the P-wave excited states of the recently discovered positronium molecule Ps_2 is evaluated, including the relativistic and the leading logarithmic radiative corrections, E_P-E_S = 0.181 586 7(8) a.u. The P-state, decaying usually via annihilation, is found to decay into the ground state by an electric dipole transition 19 percent of the time. Anticipated observation of this transition will provide insight into this exotic system.Comment: 5 page

An analytical treatment of in-plane magnetotransport in the Falicov-Sievert model

We derive an analytical expression which allows efficient computation of the effect of all the Fermi surface trajectories induced by a combination of Bragg scattering and magnetic breakdown on the in-plane components of the resistivity tensor. The particular network of coupled orbits which we consider was first formulated by Falicov and Sievert, who studied the problem numerically. Our approach, based upon a method used previously to derive an analytical solution for interlayer transport, allows us to show that the conductivity tensor can be written as a sum of a matrix representing the effect of total magnetic breakdown and one representing a combination of complex electronic trajectories, and we find a compact expression for the in-plane components of the resistivity tensor that can be evaluated straightforwardly.Comment: 4 pages, 4 figure

Modelling communities and populations: An introduction to computational social science

In sociology, interest in modelling has not yet become widespread. However, the methodology has been gaining increased attention in parallel with its growing popularity in economics and other social sciences, notably psychology and political science, and the growing volume of social data being measured and collected. In this paper, we present representative computational methodologies from both data-driven (such as “black box”) and rule-based (such as “per analogy”) approaches. We show how to build simple models, and discuss both the greatest successes and the major limitations of modelling societies. We claim that the end goal of computational tools in sociology is providing meaningful analyses and calculations in order to allow making causal statements in sociological explanation and support decisions of great importance for society