The inhomogeneous extended Bose-Hubbard model: A mean-field theory

We develop an inhomogeneous mean-field theory for the extended Bose-Hubbard model with a quadratic, confining potential. In the absence of this potential, our mean-field theory yields the phase diagram of the homogeneous extended Bose-Hubbard model. This phase diagram shows a superfluid (SF) phase and lobes of Mott-insulator (MI), density-wave (DW), and supersolid (SS) phases in the plane of the chemical potential mu and on-site repulsion U; we present phase diagrams for representative values of V, the repulsive energy for bosons on nearest-neighbor sites. We demonstrate that, when the confining potential is present, superfluid and density-wave order parameters are nonuniform; in particular, we obtain, for a few representative values of parameters, spherical shells of SF, MI, DW, and SS phases. We explore the implications of our study for experiments on cold-atom dipolar condensates in optical lattices in a confining potential.

Asymptotics of the invariant measure in mean field models with jumps

We consider the asymptotics of the invariant measure for the process of spatial distribution of N coupled Markov chains in the limit of a large number of chains. Each chain reflects the stochastic evolution of one particle. The chains are coupled through the dependence of transition rates on the spatial distribution of particles in the various states. Our model is a caricature for medium access interactions in wireless local area networks. Our model is also applicable in the study of spread of epidemics in a network. The limiting process satisfies a deterministic ordinary differential equation called the McKean-Vlasov equation. When this differential equation has a unique globally asymptotically stable equilibrium, the spatial distribution converges weakly to this equilibrium. Using a control-theoretic approach, we examine the question of a large deviation from this equilibrium.

Improved quasiparticle wave functions and mean field for G(0)W(0) calculations: Initialization with the COHSEX operator

The GW approximation to the electron self-energy has become a standard method for ab initio calculation of excited-state properties of condensed-matter systems. In many calculations, the G W self-energy operator, E, is taken to be diagonal in the density functional theory (DFT) Kohn-Sham basis within the G0 W0 scheme. However, there are known situations in which this diagonal Go Wo approximation starting from DFT is inadequate. We present two schemes to resolve such problems. The first, which we called sc-COHSEX-PG W, involves construction of an improved mean field using the static limit of GW, known as COHSEX (Coulomb hole and screened exchange), which is significantly simpler to treat than GW W. In this scheme, frequency-dependent self energy E(N), is constructed and taken to be diagonal in the COHSEX orbitals after the system is solved self-consistently within this formalism. The second method is called off diagonal-COHSEX G W (od-COHSEX-PG W). In this method, one does not self-consistently change the mean-field starting point but diagonalizes the COHSEX Hamiltonian within the Kohn-Sham basis to obtain quasiparticle wave functions and uses the resulting orbitals to construct the G W E in the diagonal form. We apply both methods to a molecular system, silane, and to two bulk systems, Si and Ge under pressure. For silane, both methods give good quasiparticle wave functions and energies. Both methods give good band gaps for bulk silicon and maintain good agreement with experiment. Further, the sc-COHSEX-PGW method solves the qualitatively incorrect DFT mean-field starting point (having a band overlap) in bulk Ge under pressure.

Multi-field simulations and characterization of CMOS-MEMS high-temperature smart gas sensors based on SOI technology

This paper describes multiple field-coupled simulations and device characterization of fully CMOS-MEMS-compatible smart gas sensors. The sensor structure is designated for gas/vapour detection at high temperatures (>300 °C) with low power consumption, high sensitivity and competent mechanic robustness employing the silicon-on-insulator (SOI) wafer technology, CMOS process and micromachining techniques. The smart gas sensor features micro-heaters using p-type MOSFETs or polysilicon resistors and differentially transducing circuits for in situ temperature measurement. Physical models and 3D electro-thermo-mechanical simulations of the SOI micro-hotplate induced by Joule, self-heating, mechanic stress and piezoresistive effects are provided. The electro-thermal effect initiates and thus affects electronic and mechanical characteristics of the sensor devices at high temperatures. Experiments on variation and characterization of micro-heater resistance, power consumption, thermal imaging, deformation interferometry and dynamic thermal response of the SOI micro-hotplate have been presented and discussed. The full integration of the smart gas sensor with automatically temperature-reading ICs demonstrates the lowest power consumption of 57 mW at 300 °C and fast thermal response of 10 ms. © 2008 IOP Publishing Ltd.

The effects of disorder in dimerized quantum magnets in mean field approximations

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Relativistic mean field theory: methods and applications

We develop a method for performing one-loop calculations in finite systems that is based on using the WKB approximation for the high energy states. This approximation allows us to absorb all the counterterms analytically and thereby avoids the need for extreme numerical precision that was required by previous methods. In addition, the local approximation makes this method well suited for self-consistent calculations. We then discuss the application of relativistic mean field methods to the atomic nucleus. Self-consistent, one loop calculations in the Walecka model are performed and the role of the vacuum in this model is analyzed. This model predicts that vacuum polarization effects are responsible for up to five percent of the local nucleon density. Within this framework the possible role of strangeness degrees of freedom is studied. We find that strangeness polarization can increase the kaon-nucleus scattering cross section by ten percent. By introducing a cutoff into the model, the dependence of the model on short-distance physics, where its validity is doubtful, is calculated. The model is very sensitive to cutoffs around one GeV.

Mean-field study of Fe2+- and Co2+-doped diluted magnetic semiconductors

Based on a modified mean-field model, we calculate the Curie temperatures of Fe2+- and Co2+-doped diluted magnetic semiconductors (DMSs) and their dependence on the hole concentration. We find that the Curie temperatures increase with an increase in hole concentration and the relationship T(C)proportional to p(1/3) also approximately holds for Fe2+- and Co2+-doped systems with moderate hole concentration. For either low or high hole concentrations, however, the p(1/3) law is violated due to the anomalous magnetization of the Fe2+ and Co2+ ions, and the nonparabolic nature of the hole bands. Further, the values of T-C for Fe2+- and Co2+-doped DMSs are significantly higher than those for Mn2+-doped DMSs, due to the larger exchange interaction strength.

Electronic structure of Mn-doped ZnO quantum wires: A mean-field theory study

Based on the effective-mass model and the mean-field approximation, we investigate the energy levels of the electron and hole states of the Mn-doped ZnO quantum wires (x=0.0018) in the presence of the external magnetic field. It is found that either twofold degenerated electron or fourfold degenerated hole states split in the field. The splitting energy is about 100 times larger than those of undoped cases. There is a dark exciton effect when the radius R is smaller than 16.6 nm, and it is independent of the effective doped Mn concentration. The lowest state transitions split into six Zeeman components in the magnetic field, four sigma(+/-) and two pi polarized Zeeman components, their splittings depend on the Mn-doped concentration, and the order of pi and sigma(+/-) polarized Zeeman components is reversed for thin quantum wires (R < 2.3 nm) due to the quantum confinement effect.