The projected SO(5) (pSO(5)) Hamiltonian incorporates the quantum spin and superconducting fluctuations of underdoped cuprates in terms of four bosons moving on a coarse grained lattice. A simple mean field approximation can explain some key features of the experimental phase diagram: (i) The Mott transition between antiferromagnet and superconductor, (ii) the increase of T c and superfluid stiffness with hole concentration x and (iii) the increase of antiferromagnetic resonance energy as [Formula: see text] in the superconducting phase. We apply this theory to explain the "two gaps" problem in underdoped cuprate SNS junctions. In particular we explain the sharp subgap Andreev peaks of the differential resistance, as signatures of the antiferromagnetic resonance (the magnon mass gap). A critical test of this theory is proposed. The tunneling charge, as measured by shot noise, should change by increments of ΔQ=2e at the Andreev peaks, rather than by ΔQ=e as in conventional superconductors.
We discuss the mean-field approximation for a trapped weakly-interacting Bose–Einstein condensate (BEC) and its connection with the exact many-body problem by deriving the Gross–Pitaevskii action of the condensate. The mechanics of the BEC in a harmonic potential is studied by using a variational approach with time-dependent Gaussian trial wave-functions. In particular, we analyze the static configurations, the stability and the collective oscillations for both ground-state and vortices.
Based on the mean field approximation, a model has been worked out for the description of evolution of carbonitride precipitate ensemble with various composition in steels at the stages of their growth, dissolution and coarsening. Based on the numerical realization of this model, the calculations of growth and dissolution kinetics of carbonitrides in a Fe-Nb-V-C-N system have been carried out.
AbstractWhenever an alloy changes composition because of metal to metal transmutations, as is the case in Ag-In-Cd alloys undergoing (n, −) actions in the control rods of Pressurised Water Reactors, unique features may develop.A simple model shows that in a two components alloy more than two phases can coexist under appropriate irradiation conditions i.e. temperature, which scales diffusivities and solubilities, and flux, which scales the transmutations rate; because second phase precipitation occurs at the grain boundaries, the grain size in the underlying matrix is found to be one important parameter of the process.The above ideas are illustrated on a multicomponent alloy, the thermodynamics and the kinetics of which are treated at the same level of sophistication in a mean field approximation.
Abstract
In the present work, the magnetoelectric coupling coefficient, from the temperature dependences of the dielectric permittivity for the multiferroic composite was determined. The research material was ferroelectric-ferromagnetic composite on the based PZT and ferrite. We investigated the temperature dependences of the dielectric permittivity (") for the different frequency of measurement’s field. From the dielectric measurements we determined the temperature of phase transition from ferroelectric to paraelectric phase. For the theoretical description of the temperature dependence of the dielectric constant, the Hamiltonian of Alcantara, Gehring and Janssen was used. To investigate the dielectric properties of the multiferroic composite this Hamiltonian was expressed under the mean-field approximation. Based on dielectric measurements and theoretical considerations, the values of the magnetoelectric coupling coefficient were specified.
The properties of spin crossover (SCO) nanoparticles were studied for five 2D hexagonal lattice structures of increasing sizes embedded in a matrix, thus affecting the thermal properties of the SCO region. These effects were modeled using the Ising-like model in the framework of local mean field approximation (LMFA). The systematic combined effect of the different types of couplings, consisting of (i) bulk short- and long-range interactions and (ii) edge and corner interactions at the surface mediated by the matrix environment, were investigated by using parameter values typical of SCO complexes. Gradual two and three hysteretic transition curves from the LS to HS states were obtained. The results were interpreted in terms of the competition between the structure-dependent order and disorder temperatures (TO.D.) of internal coupling origin and the ligand field-dependent equilibrium temperatures (Teq) of external origin.
We study novel geometrical and transport properties of a 2D model of disordered fibre networks. To assess the geometrical structure we determine, analytically, the probability distribution for the number of fibre intersections and resulting segment sizes in the network as a function of fibre density and length. We also determine, numerically, the probability distribution of pore perimeters and areas. We find a non-monotonous behavior of the perimeter distribution whose main features can be explained by solving for two simplified models of the line network. Finally we formulate a mean field approximation to conduction, above the percolation threshold, using the derived results. Relevance of the results to fracture networks will be discussed.
PROJECTED SO(5) HAMILTONIAN FOR CUPRATES AND ITS APPLICATIONS