Study the Heavy Molecular States in Quark Model with Meson Exchange Interaction

Some charmonium-like resonances such as X(3872) can be interpreted as possible $D^{(*)}D^{(*)}$ molecular states. Within the quark model, we study the structure of such molecular states and the similar $B^{(*)}B^{(*)}$ molecular states by taking into account of the light meson exchange ($\pi$, $\eta$, $\rho$, $\omega$ and $\sigma$) between two light quarks from different mesons

Spectral analysis for preconditioning of multi-dimensional Riesz fractional diffusion equations

In this paper, we analyze the spectra of the preconditioned matrices arising from discretized multi-dimensional Riesz spatial fractional diffusion equations. The finite difference method is employed to approximate the multi-dimensional Riesz fractional derivatives, which will generate symmetric positive definite ill-conditioned multi-level Toeplitz matrices. The preconditioned conjugate gradient method with a preconditioner based on the sine transform is employed to solve the resulting linear system. Theoretically, we prove that the spectra of the preconditioned matrices are uniformly bounded in the open interval (1/2,3/2) and thus the preconditioned conjugate gradient method converges linearly. The proposed method can be extended to multi-level Toeplitz matrices generated by functions with zeros of fractional order. Our theoretical results fill in a vacancy in the literature. Numerical examples are presented to demonstrate our new theoretical results in the literature and show the convergence performance of the proposed preconditioner that is better than other existing preconditioners

Electrically-controllable RKKY interaction in semiconductor quantum wires

We demonstrate in theory that it is possible to all-electrically manipulate the RKKY interaction in a quasi-one-dimensional electron gas embedded in a semiconductor heterostructure, in the presence of Rashba and Dresselhaus spin-orbit interaction. In an undoped semiconductor quantum wire where intermediate excitations are gapped, the interaction becomes the short-ranged Bloembergen-Rowland super-exchange interaction. Owing to the interplay of different types of spin-orbit interaction, the interaction can be controlled to realize various spin models, e.g., isotropic and anisotropic Heisenberg-like models, Ising-like models with additional Dzyaloshinsky-Moriya terms, by tuning the external electric field and designing the crystallographic directions. Such controllable interaction forms a basis for quantum computing with localized spins and quantum matters in spin lattices.Comment: 5 pages, 1 figur

Universal role of correlation entropy in critical phenomena

In statistical physics, if we successively divide an equilibrium system into two parts, we will face a situation that, within a certain length $\xi$, the physics of a subsystem is no longer the same as the original system. Then the extensive properties of the thermal entropy $S($AB$)= S($A$)+S($B$)$ is violated. This observation motivates us to introduce the concept of correlation entropy between two points, as measured by mutual information in the information theory, to study the critical phenomena. A rigorous relation is established to display some drastic features of the non-vanishing correlation entropy of the subsystem formed by any two distant particles with long-range correlation. This relation actually indicates the universal role of the correlation entropy in understanding critical phenomena. We also verify these analytical studies in terms of two well-studied models for both the thermal and quantum phase transitions: two-dimensional Ising model and one-dimensional transverse field Ising model. Therefore, the correlation entropy provides us with a new physical intuition in critical phenomena from the point of view of the information theory.Comment: 10 pages, 9 figure

Levinson's Theorem for the Klein-Gordon Equation in Two Dimensions

The two-dimensional Levinson theorem for the Klein-Gordon equation with a cylindrically symmetric potential $V(r)$ is established. It is shown that $N_{m}\pi=\pi (n_{m}^{+}-n_{m}^{-})= [\delta_{m}(M)+\beta_{1}]-[\delta_{m}(-M)+\beta_{2}]$, where $N_{m}$ denotes the difference between the number of bound states of the particle $n_{m}^{+}$ and the ones of antiparticle $n_{m}^{-}$ with a fixed angular momentum $m$, and the $\delta_{m}$ is named phase shifts. The constants $\beta_{1}$ and $\beta_{2}$ are introduced to symbol the critical cases where the half bound states occur at $E=\pm M$.Comment: Revtex file 14 pages, submitted to Phys. Rev.

Chiral Lagrangians for Radiative Decays of Heavy Hadrons

The radiative decays of heavy mesons and heavy baryons are studied in a formalism which incorporates both the heavy quark symmetry and the chiral symmetry. The chiral Lagrangians for the electromagnetic interactions of heavy hadrons consist of two pieces: one from gauging electromagnetically the strong-interaction chiral Lagrangian, and the other from the anomalous magnetic moment interactions of the heavy baryons and mesons. Due to the heavy quark spin symmetry, the latter contains only one independent coupling constant in the meson sector and two in the baryon sector. These coupling constants only depend on the light quarks and can be calculated in the nonrelativistic quark model. However, the charm quark is not heavy enough and the contribution from its magnetic moment must be included. Applications to the radiative decays $D^\ast \rightarrow D \gamma~,~B^\ast \rightarrow B \gamma~,~ \Xi^\prime_c \rightarrow \Xi_c \gamma~, \Sigma_c \rightarrow \Lambda_c \gamma$ and $\Sigma_c \rightarrow \Lambda_c \pi \gamma$ are given. Together with our previous results on the strong decay rates of $D^\ast \rightarrow D \pi$ and $\Sigma_c \rightarrow \Lambda_c \pi$, predictions are obtained for the total widths and branching ratios of $D^\ast$ and $\Sigma_c$. The decays $\Sigma^+_c \rightarrow \Lambda^+_c \pi^0 \gamma$ and $\Sigma^0_c \rightarrow \Lambda^+_c \pi^- \gamma$ are discussed to illustrate the important roles played by both the heavy quark symmetry and the chiral symmetry.Comment: 30 pages (one figure, available on request), CLNS 92/1158 and IP-ASTP-13-9

Corrections to Chiral Dynamics of Heavy Hadrons: (I) 1/M Correction

In earlier publications we have analyzed the strong and radiative decays of heavy hadrons in a formalism which incorporates both heavy-quark and chiral symmetries. In particular, we have derived a heavy-hadron chiral Lagrangian whose coupling constants are related by the heavy-quark flavor-spin symmetry arising from the QCD Lagrangian with infinitely massive quarks. In this paper, we re-examine the structure of the above chiral Lagrangian by including the effects of $1/m_Q$ corrections in the heavy quark effective theory. The relations among the coupling constants, originally derived in the heavy-quark limit, are modified by heavy quark symmetry breaking interactions in QCD. Some of the implications are discussed.Comment: PHYZZX, 45 pages, 1 figure (not included), CLNS 93/1192, IP-ASTP-02-93, ITP-SB-93-0