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991.
James K. Freericks Elliott H. Lieb Daniel Ueltschi 《Communications in Mathematical Physics》2002,227(2):243-279
The Falicov–Kimball model is a simple quantum lattice model that describes light and heavy electrons interacting with an
on-site repulsion; alternatively, it is a model of itinerant electrons and fixed nuclei. It can be seen as a simplification
of the Hubbard model; by neglecting the kinetic (hopping) energy of the spin up particles, one gets the Falicov–Kimball model.
We show that away from half-filling, i.e. if the sum of the densities of both kinds of particles differs from 1, the particles
segregate at zero temperature and for large enough repulsion. In the language of the Hubbard model, this means creating two
regions with a positive and a negative magnetization.
Our key mathematical results are lower and upper bounds for the sum of the lowest eigenvalues of the discrete Laplace operator
in an arbitrary domain, with Dirichlet boundary conditions. The lower bound consists of a bulk term, independent of the shape
of the domain, and of a term proportional to the boundary. Therefore, one lowers the kinetic energy of the itinerant particles
by choosing a domain with a small boundary. For the Falicov- Kimball model, this corresponds to having a single “compact”
domain that has no heavy particles.
Received: 21 June 2001 / Accepted: 4 January 2002 相似文献
992.
A.R. DegheidyM.T. Attia M. Sallah 《Journal of Quantitative Spectroscopy & Radiative Transfer》2002,74(3):285-297
The time-independent radiative transfer problem in a scattering and absorbing planar random medium with general boundary conditions and internal energy source is considered. The medium is assumed to consist of two randomly mixed immiscible fluids, with the mixing statistics described as a two-state homogeneous Markov process. The problem is solved in terms of the solution of the corresponding free-source problem with simple boundary conditions which is solved using Pomraning-Eddington approximation in the deterministic case. A formalism, developed to treat radiative transfer in statistical mixtures, is used to obtain the ensemble-averaged solution. The average partial heat fluxes are calculated in terms of the albedoes of the source-free problem. Results are obtained for isotropic and anisotropic scattering for specular and diffused reflecting boundaries. 相似文献
993.
L.V. Zolotukhina Ye.V. ZabolotskayaYe.V. Arkhipova M.G. Zuev 《Journal of Physics and Chemistry of Solids》2002,63(3):415-418
Phase equilibria in the Sc2O3-V2O5-Nb2O5-Ta2O5 system and properties of ScNb2−2xTa2xVO9 phases were studied by X-ray phase analysis, optical and radio spectroscopy. A continuous series of solid solutions was shown to exist at 0≤x≤1. V(IV) centers with different crystallographic surrounding were detected for all the considered compositions. A correlation between the number of V(IV) ions and the width of the forbidden gap in the solid solutions was found. 相似文献
994.
We prove that the diffusion semigroups generated by the second order differential ultraspherical (Gegenbauer) operator are pseudomeasure operators. 相似文献
995.
A method for stabilizing frequency based on using the soliton state of the Bose-Einstein condensate of alkali metal atoms as an atomic source was suggested. The critical total number of lithium condensate particles at which the existence of a quasi-one-dimensional soliton in the condensate was possible and the lifetime of such a soliton were estimated. The attainable accuracy of measuring reference transition frequencies in the suggested standard was shown to be substantially higher than with the known quantum frequency standards. 相似文献
996.
D. Yafaev 《Proceedings Mathematical Sciences》2002,112(1):245-255
We find an explicit function approximating at high energies the kernel of the scattering matrix with arbitrary accuracy. Moreover,
the same function gives all diagonal singularities of the kernel of the scattering matrix in the angular variables.
This paper is dedicated to Jean-Michel Combes on the occasion of his sixtieth birthday. 相似文献
997.
J. Tabor 《Aequationes Mathematicae》2002,63(1-2):18-25
998.
We consider Markov processes built from pasting together pieces of strong Markov processes which are killed at a position
dependent rate and connected via a transition kernel. We give necessary and sufficient conditions for local absolute continuity
of probability laws for such processes on a suitable path space and derive an explicit formula for the corresponding likelihood
ratio process. The main tool is the consideration of the process between successive jumps – what we call ‘elementary experiments’
– and criteria for absolute continuity of laws of the process there. We apply our results to systems of branching diffusions
with interactions and immigrations.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
999.
1000.