Nuclear force in Lattice QCD

We perform the quenched lattice QCD analysis on the nuclear force (baryon-baryon interactions). We employ $20^3\times 24$ lattice at $\beta=5.7$ ($a\simeq 0.19$ fm) with the standard gauge action and the Wilson quark action with the hopping parameters $\kappa=0.1600, 0.1625, 0.1650$, and generate about 200 gauge configurations. We measure the temporal correlators of the two-baryon system which consists of heavy-light-light quarks. We extract the inter-baryon force as a function of the relative distance $r$. We also evaluate the contribution to the nuclear force from each ``Feynman diagram'' such as the quark-exchange diagram individually, and single out the roles of Pauli-blocking effects or quark exchanges in the inter-baryon interactions.Comment: Presented at Particles and Nuclei International Conference (PANIC05), Santa Fe, NM, Oct. 24-28, 2005; 3 pages, 2figure

Classical and Quantum Gravity in 1+1 Dimensions, Part II: The Universal Coverings

A set of simple rules for constructing the maximal (e.g. analytic) extensions for any metric with a Killing field in an (effectively) two-dimensional spacetime is formulated. The application of these rules is extremely straightforward, as is demonstrated at various examples and illustrated with numerous figures. Despite the resulting simplicity we also comment on some subtleties concerning the concept of Penrose diagrams. Most noteworthy among these, maybe, is that (smooth) spacetimes which have both degenerate and non-degenerate (Killing) horizons do not allow for globally smooth Penrose diagrams. Physically speaking this obstruction corresponds to an infinite relative red/blueshift between observers moving across the two horizons. -- The present work provides a further step in the classification of all global solutions of the general class of two-dimensional gravity-Yang-Mills systems introduced in Part I, comprising, e.g., all generalized (linear and nonlinear) dilaton theories. In Part I we constructed the local solutions, which were found to always have a Killing field; in this paper we provide all universal covering solutions (the simply connected maximally extended spacetimes). A subsequent Part III will treat the diffeomorphism inequivalent solutions for all other spacetime topologies. -- Part II is kept entirely self-contained; a prior reading of Part I is not necessary.Comment: 29 pages, 14 Postscript figures; one figure, some paragraphs, and references added; to appear in Class. Quantum Gra

Navier-Stokes Equation by Stochastic Variational Method

We show for the first time that the stochastic variational method can naturally derive the Navier-Stokes equation starting from the action of ideal fluid. In the frame work of the stochastic variational method, the dynamical variables are extended to stochastic quantities. Then the effect of dissipation is realized as the direct consequence of the fluctuation-dissipation theorem. The present result reveals the potential availability of this approach to describe more general dissipative processes.Comment: 5 pages, no figure, discussions and references are added, errors in Sec. IV were correcte

Fluctuations of the one-dimensional polynuclear growth model with external sources

The one-dimensional polynuclear growth model with external sources at edges is studied. The height fluctuation at the origin is known to be given by either the Gaussian, the GUE Tracy-Widom distribution, or certain distributions called GOE$^2$ and $F_0$, depending on the strength of the sources. We generalize these results and show that the scaling limit of the multi-point equal time height fluctuations of the model are described by the Fredholm determinant, of which the limiting kernel is explicitly obtained. In particular we obtain two new kernels, describing transitions between the above one-point distributions. One expresses the transition from the GOE$^2$ to the GUE Tracy-Widom distribution or to the Gaussian; the other the transition from $F_0$ to the Gaussian. The results specialized to the fluctuation at the origin are shown to be equivalent to the previously obtained ones via the Riemann-Hilbert method.Comment: 43 pages, 4 figure

Z2_2 index theorem for Majorana zero modes in a class D topological superconductor

We propose a Z$_2$ index theorem for a generic topological superconductor in class D. Introducing a particle-hole symmetry breaking term depending on a parameter and regarding it as a coordinate of an extra dimension, we define the index of the zero modes and corresponding topological invariant for such an extended Hamiltonian. It is shown that these are related with the number of the zero modes of the original Hamiltonian modulo two.Comment: 5 pages, 3 figures. v2: typos correcte

Real-time simulation of finite frequency noise from a single electron emitter

We study the real-time emission of single electrons from a quantum dot coupled to a one dimensional conductor, using exact diagonalization on a discrete tight-binding chain. We show that from the calculation of the time-evolution of the one electron states, we have a simple access to all the relevant physical quantities in the system. In particular, we are able to compute accurately the finite frequency current autocorrelation noise. The method which we use is general and versatile, allowing to study the impact of many different parameters like the dot transparency or level position. Our results can be directly compared with existing experiments, and can also serve as a basis for future calculations including electronic interactions using the time dependent density-matrix renormalisation group and other techniques based on tight-binding models.Comment: 10 page