The solution to nonlinear Fokker-Planck equation is constructed in terms of the minimal Markov semigroup generated by the equation. The semigroup is obtained by a purely functional analytical method via Hille-Yosida theorem. The existence of the positive invariant measure with density is established and a weak form of Foguel alternative proven. We show the equivalence among self-adjoint of the ...

We examine the spin-wave (SW) dynamics of Dy/Y multilayers in order to separate the contribution of the Dy-Y interface from that of bulk Dy. The SW frequencies and intensities of bulk Dy are determined analytically. When the Dy layers in a multilayer geometry are decoupled, the SW dispersion relations are discontinuous with discrete excitations. With a Ruderman-Kittel-Kasuya-Yosida (RKKY) inter...

We study finite delay evolution equation { x′(t) = Ax(t) + F (t, xt), t ≥ 0, x0 = φ ∈ C ([−r, 0] , E) , where linear operator A is non-densely defined and satisfies the Hille-Yosida condition. First we obtain some properties of “integral solutions” in this case, and prove the compactness of an operator determined by integral solutions. This allows us to apply Horn’s fixed point theorem to prove...

We consider a one-dimensional Allen–Cahn equation with constraint from the view-point of numerical analysis. Our constraint is the subdifferential of the indicator function on the closed interval, which is the multivalued function. Therefore, it is very difficult to make numerical experiments of our equation. In this paper we approximate our constraint by Yosida approximation. Then, we study th...

The effect of the Zeeman field on the defect-induced Kondo effect in graphene is investigated. The effective model of the Kondo effect is derived, and is analyzed on the basis of the numerical renormalization group method. It is found that, under the Zeeman field, at the border of the spin polarized state and the Kondo-Yosida singlet state, there is an unusual fixed point where the entropy of t...

Exact-sparsity inducing prior distributions in high-dimensional Bayesian analysis typically lead to posterior distributions that are very challenging to handle by standard Markov Chain Monte Carlo methods. We propose a methodology to derive a smooth approximation of such posterior distributions. The approximation is obtained from the forward-backward approximation of the Moreau-Yosida regulariz...

We propose a new criterion for distinguishing the Hertz-Millis (HM) and the local quantum critical (LQC) mechanism in heavy-fermion systems with a magnetic quantum phase transition (QPT). The criterion is based on our finding that the complete spin screening of Kondo ions can be suppressed by the Ruderman-Kittel-Kasuya-Yosida (RKKY) coupling to the surrounding magnetic ions even without magneti...

Elastic backscattering of electrons moving along the helical edge is prohibited by time-reversal symmetry. We demonstrate, however, that an ensemble of magnetic impurities may cause time-reversal symmetry-preserving quasielastic backscattering, resulting in interference effects in the conductance. The characteristic energy transferred in a backscattering event is suppressed due to the Ruderman-...

In this work, we prove the existence of a center manifold for some partial functional differential equations, whose linear part is not necessarily densely defined but satisfies the Hille-Yosida condition. When the unstable space is reduced to zero, we also show the attractiveness of the center manifold. We prove that the flow on the center manifold is completely determined by an ordinary differ...

In this paper, we focus on a family of backward stochastic differential equations (BSDEs) with subdifferential operators that are driven by infinite-dimensional martingales. We shall show the solution to such BSDEs exists and is unique. The existence uniqueness established using Yosida approximations. Furthermore, as an application main result, partial equation martingales continuous linear ope...