Closure of the Monte Carlo dynamical equation in the spherical Sherrington-Kirkpatrick model

We study the analytical solution of the Monte Carlo dynamics in the spherical Sherrington-Kirkpatrick model using the technique of the generating function. Explicit solutions for one-time observables (like the energy) and two-time observables (like the correlation and response function) are obtained. We show that the crucial quantity which governs the dynamics is the acceptance rate. At zero temperature, an adiabatic approximation reveals that the relaxational behavior of the model corresponds to that of a single harmonic oscillator with an effective renormalized mass.

Chaotic dynamics of electric-field domains in periodically driven superlattices

Self-sustained time-dependent current oscillations under dc voltage bias have been observed in recent experiments on n-doped semiconductor superlattices with sequential resonant tunneling. The current oscillations are caused by the motion and recycling of the domain wall separating low- and high-electric-field regions of the superlattice, as the analysis of a discrete drift model shows and experimental evidence supports. Numerical simulation shows that different nonlinear dynamical regimes of the domain wall appear when an external microwave signal is superimposed on the dc bias and its driving frequency and driving amplitude vary. On the frequency-amplitude parameter plane, there are regions of entrainment and quasiperiodicity forming Arnold tongues. Chaos is demonstrated to appear at the boundaries of the tongues and in the regions where they overlap. Coexistence of up to four electric-field domains randomly nucleated in space is detected under ac+dc driving.

The role of dynamical polarization of the ligand-to-metal charge transfer excitations in the ab initio determination of effective exchange parameters

The role of the bridging ligand on the effective Heisenberg coupling parameters is analyzed in detail. This analysis strongly suggests that the ligand-to-metal charge transfer excitations are responsible for a large part of the final value of the magnetic coupling constant. This permits us to suggest a variant of the difference dedicated configuration interaction (DDCI) method, presently one of the most accurate and reliable for the evaluation of magnetic effective interactions. This method treats the bridging ligand orbitals mediating the interaction at the same level than the magnetic orbitals and preserves the high quality of the DDCI results while being much less computationally demanding. The numerical accuracy of the new approach is illustrated on various systems with one or two magnetic electrons per magnetic center. The fact that accurate results can be obtained using a rather reduced configuration interaction space opens the possibility to study more complex systems with many magnetic centers and/or many electrons per center.

First principles LDA+U and GGA+U study of cerium oxides: Dependence on the effective U-parameter

The electronic structure and properties of cerium oxides (CeO2 and Ce2O3) have been studied in the framework of the LDA+U and GGA(PW91)+U implementations of density functional theory. The dependence of selected observables of these materials on the effective U parameter has been investigated in detail. The examined properties include lattice constants, bulk moduli, density of states, and formation energies of CeO2 and Ce2O3. For CeO2, the LDA+U results are in better agreement with experiment than the GGA+U results whereas for the computationally more demanding Ce2O3 both approaches give comparable accuracy. Furthermore, as expected, Ce2O3 is much more sensitive to the choice of the U value. Generally, the PW91 functional provides an optimal agreement with experiment at lower U energies than LDA does. In order to achieve a balanced description of both kinds of materials, and also of nonstoichiometric CeO2¿x phases, an appropriate choice of U is suggested for LDA+U and GGA+U schemes. Nevertheless, an optimum value appears to be property dependent, especially for Ce2O3. Optimum U values are found to be, in general, larger than values determined previously in a self-consistent way.