Cascades of Dynamical Transitions in an Adaptive Population

In an adaptive population which models financial markets and distributed control, we consider how the dynamics depends on the diversity of the agents' initial preferences of strategies. When the diversity decreases, more agents tend to adapt their strategies together. This change in the environment results in dynamical transitions from vanishing to non-vanishing step sizes. When the diversity decreases further, we find a cascade of dynamical transitions for the different signal dimensions, supported by good agreement between simulations and theory. Besides, the signal of the largest step size at the steady state is likely to be the initial signal.Comment: 4 pages, 8 figure

Experimental observation of negative differential resistance from an InAs/GaSb interface

We have observed negative differential resistance at room temperature from devices consisting of a single interface between n-type InAs and p-type GaSb. InAs and GaSb have a type II staggered band alignment; hence, the negative differential resistance arises from the same mechanism as in a p+-n+ tunnel diode. Room-temperature peak current densities of 8.2×10^4 A/cm^2 and 4.2×10^4 A/cm^2 were measured for structures with and without undoped spacer layers at the heterointerface, respectively

Perturbed Three Vortex Dynamics

It is well known that the dynamics of three point vortices moving in an ideal fluid in the plane can be expressed in Hamiltonian form, where the resulting equations of motion are completely integrable in the sense of Liouville and Arnold. The focus of this investigation is on the persistence of regular behavior (especially periodic motion) associated to completely integrable systems for certain (admissible) kinds of Hamiltonian perturbations of the three vortex system in a plane. After a brief survey of the dynamics of the integrable planar three vortex system, it is shown that the admissible class of perturbed systems is broad enough to include three vortices in a half-plane, three coaxial slender vortex rings in three-space, and `restricted' four vortex dynamics in a plane. Included are two basic categories of results for admissible perturbations: (i) general theorems for the persistence of invariant tori and periodic orbits using Kolmogorov-Arnold-Moser and Poincare-Birkhoff type arguments; and (ii) more specific and quantitative conclusions of a classical perturbation theory nature guaranteeing the existence of periodic orbits of the perturbed system close to cycles of the unperturbed system, which occur in abundance near centers. In addition, several numerical simulations are provided to illustrate the validity of the theorems as well as indicating their limitations as manifested by transitions to chaotic dynamics.Comment: 26 pages, 9 figures, submitted to the Journal of Mathematical Physic

Perturbation Calculation of the Axial Anomaly of a Ginsparg-Wilson lattice Dirac operator

A recent proposal suggests that even if a Ginsparg-Wilson lattice Dirac operator does not possess any topological zero modes in topologically-nontrivial gauge backgrounds, it can reproduce correct axial anomaly for sufficiently smooth gauge configurations, provided that it is exponentially-local, doublers-free, and has correct continuum behavior. In this paper, we calculate the axial anomaly of this lattice Dirac operator in weak coupling perturbation theory, and show that it recovers the topological charge density in the continuum limit.Comment: 25 pages, v2: calculation up to O(g^4) for nonabelian gauge backgroun

Two-body charmed baryon decays involving decuplet baryon in the quark-diagram scheme

In the quark-diagram scheme, we study the charmed baryon decays of ${\bf B}_c\to {\bf B}^* M$, where ${\bf B}_c$ is $\Lambda_c^+$ or $\Xi_c^{+(0)}$, together with ${\bf B}^*$ ($M$) the decuplet baryon (pseudoscalar meson). It is found that only two $W$-exchange processes are allowed to contribute to ${\bf B}_c\to {\bf B}^* M$. Particularly, we predict ${\cal B}(\Lambda_c^+ \to \Sigma^{*0(+)} \pi^{+(0)})=(2.8\pm 0.4)\times 10^{-3}$, which respects the isospin symmetry. Besides, we take into account the $SU(3)$ flavor symmetry breaking, in order to explain the observation of ${\cal B}(\Lambda_c^+\to \Sigma^{*+}\eta)$. For the decays involving $\Delta^{++}(uuu)$, we predict ${\cal B}(\Lambda_c^+\to \Delta^{++} \pi^-,\Xi_c^+ \to \Delta^{++} K^-) =(7.0\pm 1.4,13.5\pm 2.7)\times 10^{-4}$ as the largest branching fractions in the singly Cabibbo-suppressed $\Lambda_c^+,\Xi_c^+\to{\bf B}^*M$ decay channels, respectively, which are accessible to the LHCb, BELLEII and BESIII experiments.Comment: 12 pages, 1 figure, 3 tables, version to appear in EPJ

Local tunneling spectroscopy as signatures of the Fulde-Ferrell-Larkin-Ovchinnikov state in s- and d-wave Superconductors

The Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states for two-dimensional s- and d-wave superconductors (s- and d-SC) are self-consistently studied under an in-plane magnetic field. While the stripe solution of the order parameter (OP) is found to have lower free energy in s-SC, a square lattice solution appears to be energetically more favorable in the case of d-SC. At certain symmetric sites, we find that the features in the local density of states (LDOS) can be ascribed to two types of bound states. We also show that the LDOS maps for d-SC exhibit bias-energy-dependent checkerboard patterns. These characteristics can serve as signatures of the FFLO states.Comment: 5 pages, 5 figures Type and grammaratic errors corrected. Last figure replaced by colored one. To appear in PR