7,802 research outputs found
Harnack Type Inequalities and Applications for SDE Driven by Fractional Brownian Motion
For stochastic differential equation driven by fractional Brownian motion
with Hurst parameter , Harnack type inequalities are established by
constructing a coupling with unbounded time-dependent drift. These inequalities
are applied to the study of existence and uniqueness of invariant measure for a
discrete Markov semigroup constructed in terms of the distribution of the
solution. Furthermore, we show that entropy-cost inequality holds for the
invariant measure
Metal-insulator transition in three-band Hubbard model with strong spin-orbit interaction
Recent investigations suggest that both spin-orbit coupling and electron
correlation play very crucial roles in the transition metal oxides. By
using the generalized Gutzwiller variational method and dynamical mean-field
theory with the hybridization expansion continuous time quantum Monte Carlo as
impurity solver, the three-band Hubbard model with full Hund's rule coupling
and spin-orbit interaction terms, which contains the essential physics of
partially filled sub-shell of materials, is studied
systematically. The calculated phase diagram of this model exhibits three
distinct phase regions, including metal, band insulator and Mott insulator
respectively. We find that the spin-orbit coupling term intends to greatly
enhance the tendency of the Mott insulator phase. Furthermore, the influence of
the electron-electron interaction on the effective strength of spin-orbit
coupling in the metallic phase is studied in detail. We conclude that the
electron correlation effect on the effective spin-orbit coupling is far beyond
the mean-field treatment even in the intermediate coupling region.Comment: 8 pages, 8 figure
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Understanding size dependence of phase stability and band gap in CsPbI3 perovskite nanocrystals.
Inorganic halide perovskites CsPbX3 (X = Cl, Br, I) have been widely studied as colloidal quantum dots for their excellent optoelectronic properties. Not only is the long-term stability of these materials improved via nanostructuring, their optical bandgaps are also tunable by the nanocrystal (NC) size. However, theoretical understanding of the impact of the NC size on the phase stability and bandgap is still lacking. In this work, the relative phase stability of CsPbI3 as a function of the crystal size and the chemical potential is investigated by density functional theory. The optically active phases (α- and γ-phase) are found to be thermodynamically stabilized against the yellow δ-phase by reducing the size of the NC below 5.6 nm in a CsI-rich environment. We developed a more accurate quantum confinement model to predict the change in bandgaps at the sub-10 nm regime by including a finite-well effect. These predictions have important implications for synthesizing ever more stable perovskite NCs and bandgap engineering
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