Regularized Renormalization Group Reduction of Symplectic Map

By means of the perturbative renormalization group method, we study a long-time behaviour of some symplectic discrete maps near elliptic and hyperbolic fixed points. It is shown that a naive renormalization group (RG) map breaks the symplectic symmetry and fails to describe a long-time behaviour. In order to preserve the symplectic symmetry, we present a regularization procedure, which gives a regularized symplectic RG map describing an approximate long-time behaviour succesfully

Geometric Approach to Lyapunov Analysis in Hamiltonian Dynamics

As is widely recognized in Lyapunov analysis, linearized Hamilton's equations of motion have two marginal directions for which the Lyapunov exponents vanish. Those directions are the tangent one to a Hamiltonian flow and the gradient one of the Hamiltonian function. To separate out these two directions and to apply Lyapunov analysis effectively in directions for which Lyapunov exponents are not trivial, a geometric method is proposed for natural Hamiltonian systems, in particular. In this geometric method, Hamiltonian flows of a natural Hamiltonian system are regarded as geodesic flows on the cotangent bundle of a Riemannian manifold with a suitable metric. Stability/instability of the geodesic flows is then analyzed by linearized equations of motion which are related to the Jacobi equations on the Riemannian manifold. On some geometric setting on the cotangent bundle, it is shown that along a geodesic flow in question, there exist Lyapunov vectors such that two of them are in the two marginal directions and the others orthogonal to the marginal directions. It is also pointed out that Lyapunov vectors with such properties can not be obtained in general by the usual method which uses linearized Hamilton's equations of motion. Furthermore, it is observed from numerical calculation for a model system that Lyapunov exponents calculated in both methods, geometric and usual, coincide with each other, independently of the choice of the methods.Comment: 22 pages, 14 figures, REVTeX

Photon Mass Bound Destroyed by Vortices

The Particle Data Group gives an upper bound on the photon mass $m < 2 \times 10^{-16}$eV from a laboratory experiment and lists, but does not adopt, an astronomical bound $m < 3 \times 10^{-27}$eV, both of which are based on the plausible assumption of large galactic vector-potential. We argue that the interpretations of these experiments should be changed, which alters significantly the bounds on $m$. If $m$ arises from a Higgs effect, both limits are invalid because the Proca vector-potential of the galactic magnetic field may be neutralized by vortices giving a large-scale magnetic field that is effectively Maxwellian. In this regime, experiments sensitive to the Proca potential do not yield a useful bound on $m$. As a by-product, the non-zero photon mass from Higgs effect predicts generation of a primordial magnetic field in the early universe. If, on the other hand, the galactic magnetic field is in the Proca regime, the very existence of the observed large-scale magnetic field gives $m^{-1}\gtrsim 1$kpc, or $m\lesssim 10^{-26}$eV.Comment: 9 pages, discussion of primordial magnetic field adde

Energy Storage in a Hamiltonian System in Partial Contact with a Heat Bath

To understand the mechanism allowing for the long-term storage of excess energy in proteins, we study a Hamiltonian system consisting of several coupled pendula in partial contact with a heat bath. It is found that energy storage is possible when the motion of each pendulum switches between oscillatory (vibrational) and rotational (phase-slip) modes. The storage time increases almost exponentially to the square root of the injected energy. The relevance of our mechanism to protein motors is discussed.Comment: 8 pages, 4 figures, to appear in J.Phys.Soc.Jp

Failure processes of cemented granular materials

The mechanics of cohesive or cemented granular materials is complex, combining the heterogeneous responses of granular media, like force chains, with clearly defined material properties. Here, we use a discrete element model (DEM) simulation, consisting of an assemblage of elastic particles connected by softer but breakable elastic bonds, to explore how this class of material deforms and fails under uniaxial compression. We are particularly interested in the connection between the microscopic interactions among the grains or particles and the macroscopic material response. To this end, the properties of the particles and the stiffness of the bonds are matched to experimental measurements of a cohesive granular media with tunable elasticity. The criterion for breaking a bond is also based on an explicit Griffith energy balance, with realistic surface energies. By varying the initial volume fraction of the particle assembles we show that this simple model reproduces a wide range of experimental behaviors, both in the elastic limit and beyond it. These include quantitative details of the distinct failure modes of shear-banding, ductile failure and compaction banding or anti-cracks, as well as the transitions between these modes. The present work, therefore, provides a unified framework for understanding the failure of porous materials such as sandstone, marble, powder aggregates, snow and foam

Symmetry of high-piezoelectric Pb-based complex perovskites at the morphotropic phase boundary II. Theoretical treatment

The structural characteristics of the perovskite- based ferroelectric Pb(Zn1/3Nb2/3)O3-9%PbTiO3 at the morphotropic phase boundary (MPB) region (x&#8771;0.09) have been analyzed. The analysis is based on the symmetry adapted free energy functions under the assumption that the total polarization and the unit cell volume are conserved during the transformations between various morphotropic phases. Overall features of the relationships between the observed lattice constants at various conditions have been consistently explained. The origin of the anomalous physical properties at MPB is discussed

Quantum Algorithm for Molecular Properties and Geometry Optimization

It is known that quantum computers, if available, would allow an exponential decrease in the computational cost of quantum simulations. We extend this result to show that the computation of molecular properties (energy derivatives) could also be sped up using quantum computers. We provide a quantum algorithm for the numerical evaluation of molecular properties, whose time cost is a constant multiple of the time needed to compute the molecular energy, regardless of the size of the system. Molecular properties computed with the proposed approach could also be used for the optimization of molecular geometries or other properties. For that purpose, we discuss the benefits of quantum techniques for Newton's method and Householder methods. Finally, global minima for the proposed optimizations can be found using the quantum basin hopper algorithm, which offers an additional quadratic reduction in cost over classical multi-start techniques.Comment: 6 page

Non-local Control of the Kondo Effect in a Double Quantum Dot-Quantum Wire Coupled System

We have performed low-temperature transport measurements on a double quantum dot-quantum wire coupled device and demonstrated non-local control of the Kondo effect in one dot by manipulating the electronic spin states of the other. We discuss the modulation of the local density of states in the wire region due to the Fano-Kondo antiresonance, and the Ruderman-Kittel-Kasuya-Yoshida (RKKY) exchange interaction as the mechanisms responsible for the observed features.Comment: 4 pages, 4 figure

Basaltic Clasts in Y-86032 Feldspathic Lunar Meteorite: Ancient Volcanism far from the Procellarum Kreep Terrane

Lunar meteorite, Y-86032 is a fragmental or regolith breccia enriched in Al2O3 (28-31 wt%) and having very low concentrations of REEs and Th, U [e.g., 1]. Nyquist et al. [2] suggested that Y- 86032 contains a variety of lithologies not represented by the Apollo samples. They found clasts with old Ar-Ar ages and an ancient Sm-Nd age, and negative Nd indicating a direct link to the primordial magma ocean. Importantly, the final lithification of the Y-86032 breccia was likely >3.8-4.1 Ga ago. Therefore, any lithic components in the breccia formed prior to 3.8 Ga, and lithic components in breccia clasts in the parent breccia formed even earlier. Here we report textures and mineralogy of basaltic and gabbroic clasts in Y- 86032 to better understand the nature of ancient lunar volcanism far from the Procellarum KREEP Terrain (PKT) [3] and the central nearside