Enhanced charge fluctuations due to competitions between intersite and Kondo-Yosida singlet formations in heavy-fermion systems

We investigate f-electron charge susceptibility in a two-impurity Anderson model on the basis of Wilson's numerical renormalization group method. The f-electron charge susceptibility diverges logarithmically at the critical point of this model when conduction-electron bands exhibit particle-hole symmetry. Although the critical point disappears without the particle-hole symmetry, the f-electron charge fluctuation is much more enhanced near the crossover regime between the Kondo-Yosida singlet and intersite spin-singlet states than that in the single-impurity case. This result shows that charge fluctuations are enhanced owing to the competition between intersite and Kondo-Yosida spin singlets. A possible scenario for the enhanced residual resistivity near the region where the Kondo temperature becomes comparable with the N\'eel temperatures under pressure in some heavy-fermion compounds is proposed.Comment: 5 pages, 4 figures, J. Phys. Soc. Jpn. 79 (2010) in pres

On uniqueness of maximal coupling for diffusion processes with a reflection

A maximal coupling of two diffusion processes makes two diffusion particles meet as early as possible. We study the uniqueness of maximal couplings under a sort of "reflection structure" which ensures the existence of such couplings. In this framework, the uniqueness in the class of Markovian couplings holds for the Brownian motion on a Riemannian manifold whereas it fails in more singular cases. We also prove that a Kendall-Cranston coupling is maximal under the reflection structure.Comment: 23 page

On deformations of isolated singularities of polar weighted homogeneous mixed polynomials

In the present paper, we deform isolated singularities of a certain class of polar weighted homogeneous mixed polynomials, and show that there exists a deformation which has only definite fold singularities and mixed Morse singularities.Comment: 19 page

Continuous-time Quantum Monte Carlo Approach for Impurity Anderson Models with Phonon-assisted Hybridizations

We develop a continuous-time quantum Monte Carlo method based on a strong-coupling expansion for Anderson impurity models with phonon-assisted hybridizations for arbitrary number of phonon modes. As a benchmark, we investigate the two-channel Anderson model with a single phonon, and numerically demonstrate that an SO(5) susceptibility composed of localized-electron charge and phonon-parity operators diverges logarithmically at the non-Fermi liquid critical point in the model, which verifies the predictions by the boundary conformal field theory[K. Hattori: Phys. Rev. B {\bf 85} (2012) 214411].Comment: 6 pages, 5 figure

On the number of cusps of deformations of complex polynomials

Let f be a 1-variable complex polynomial such that f has a singularity at the origin. In the present paper, we show that there exists a deformation of f which has only fold singularities and cusps as singularities of a real polynomial map from the plane to the plane. We then calculate the number of cusps of a deformation in a sufficiently small neighborhood of the origin.Comment: 12 page

Coupling by reflection of diffusion processes via discrete approximation under a backward Ricci flow

A coupling by reflection of a time-inhomogeneous diffusion process on a manifold are studied. The condition we assume is a natural time-inhomogeneous extension of lower Ricci curvature bounds. In particular, it includes the case of backward Ricci flow. As in time-homogeneous cases, our coupling provides a gradient estimate of the diffusion semigroup which yields the strong Feller property. To construct the coupling via discrete approximation, we establish the convergence in law of geodesic random walks as well as a uniform non-explosion type estimate.Comment: 29 page

An LR pair that can be extended to an LR triple

Fix an integer $d \geq 0$, a field $\mathbb{F}$, and a vector space $V$ over $\mathbb{F}$ with dimension $d+1$. By a decomposition of $V$ we mean a sequence $\{V_i\}_{i=0}^d$ of $1$-dimensional $\mathbb{F}$-subspaces of $V$ such that $V = \sum_{i=0}^d V_i$ (direct sum). Consider $\mathbb{F}$-linear transformations $A$, $B$ from $V$ to $V$. Then $A,B$ is called an LR pair whenever there exists a decomposition $\{V_i\}_{i=0}^d$ of $V$ such that $A V_i = V_{i-1}$ and $B V_i = V_{i+1}$ for $0 \leq i \leq d$, where $V_{-1}=0$ and $V_{d+1}=0$. By an LR triple we mean a $3$-tuple $A,B,C$ of $\mathbb{F}$-linear transformations from $V$ to $V$ such that any two of them form an LR pair. In the present paper, we consider how an LR pair $A,B$ can be extended to an LR triple $A,B,C$.Comment: 21 page

Can the Ising critical behavior survive in non-equilibrium synchronous cellular automata?

Universality classes of Ising-like phase transitions are investigated in series of two-dimensional synchronously updated probabilistic cellular automata (PCAs), whose time evolution rules are either of Glauber type or of majority-vote type, and degrees of anisotropy are varied. Although early works showed that coupled map lattices and PCAs with synchronously updating rules belong to a universality class distinct from the Ising class, careful calculations reveal that synchronous Glauber PCAs should be categorized into the Ising class, regardless of the degree of anisotropy. Majority-vote PCAs for the system size considered yield exponents $\nu$ which are between those of the two classes, closer to the Ising value, with slight dependence on the anisotropy. The results indicate that the Ising critical behavior is robust with respect to anisotropy and synchronism for those types of non-equilibrium PCAs. There are no longer any PCAs known to belong to the non-Ising class.Comment: 10 pages, 6 figures, 1 table; title slightly changed, references and supplementary information added, layout change

The end-parameters of a Leonard pair

Fix an algebraically closed field \F and an integer $d \geq 3$. Let $V$ be a vector space over \F with dimension $d+1$. A Leonard pair on $V$ is a pair of diagonalizable linear transformations $A: V \to V$ and $A^* : V \to V$, each acting in an irreducible tridiagonal fashion on an eigenbasis for the other one. There is an object related to a Leonard pair called a Leonard system. It is known that a Leonard system is determined up to isomorphism by a sequence of scalars (\{\th_i\}_{i=0}^d, \{\th^*_i\}_{i=0}^d, \{\vphi_i\}_{i=1}^d, \{\phi_i\}_{i=1}^d), called its parameter array. The scalars $\{\th_i\}_{i=0}^d$ (resp.\ $\{\th^*_i\}_{i=0}^d$) are mutually distinct, and the expressions $(\th_{i-2} - \th_{i+1})/(\th_{i-1}-\th_{i})$, $(\th^*_{i-2} - \th^*_{i+1})/(\th^*_{i-1}-\th^*_{i})$ are equal and independent of $i$ for $2 \leq i \leq d-1$. Write this common value as $\beta+1$. In the present paper, we consider the "end-parameters" $\th_0$, $\th_d$, $\th^*_0$, $\th^*_d$, \vphi_1, \vphi_d, $\phi_1$, $\phi_d$ of the parameter array. We show that a Leonard system is determined up to isomorphism by the end-parameters and $\beta$. We display a relation between the end-parameters and $\beta$. Using this relation, we show that there are up to inverse at most $\lfloor (d-1)/2 \rfloor$ Leonard systems that have specified end-parameters. The upper bound $\lfloor (d-1)/2 \rfloor$ is best possible

A note for the global non-existence of semirelativistic equations with non-gauge invariant power type nonlinearity

The non-existence of global solutions for semirelativistic equations with non-gauge invariant power type nonlinearity is revisited by a relatively direct way with a pointwise estimate of fractional derivative of some test functions.Comment: 11 pages, no figur