Recoil-free spectroscopy of neutral Sr atoms in the Lamb-Dicke regime

We have demonstrated a recoil-free spectroscopy on the ${}^1S_0-{}^3P_1$ transition of strontium atoms confined in a one-dimensional optical lattice. By investigating the wavelength and polarization dependence of the ac Stark shift acting on the ${}^1S_0$ and ${}^3P_1(m_J=0)$ states, we determined the {\it magic wavelength} where the Stark shifts for both states coincide. The Lamb-Dicke confinement provided by this Stark-free optical lattice enabled the measurement of the atomic spectrum free from Doppler as well as recoil shifts.Comment: 5pages, 4figure

Angular momentum at null infinity in higher dimensions

We define the angular momentum at null infinity in higher dimensions. The asymptotic symmetry at null infinity becomes the Poincare group in higher dimensions. This fact implies that the angular momentum can be defined without any ambiguities such as supertranslation in four dimensions. Indeed we can show that the angular momentum in our definition is transformed covariantly with respect to the Poincare group.Comment: 13 page

Reaction Path Hamiltonian Based on a Reaction Coordinate and a Curvature Coordinate

We propose a reaction path‐based Hamiltonian in terms of the reaction coordinate, the curvature coordinate, the remaining 3N−8 transverse normal coordinates (whose directions are orthogonal to the path tangent and curvature vectors), and their conjugate momenta, for an Natomic reaction system. The 3N−8 transverse vibrational modes are independent of the motion along the reaction path, although they have coupling terms with the curvature direction in the harmonic approximation. A two‐dimensional plane determined by the path tangent and curvature vectors is termed the ‘‘reaction plane.’’ We introduce a function that estimates changes of the reaction plane along the reaction path, and analyze the reaction path based on this function for an abstraction reaction, CH3+H2→CH4+H. The scheme proposed here should be effective when a reaction path has a sharply curved region

Dynamic Reaction Path Analysis Based on an Intrinsic Reaction Coordinate

We propose two methods that may be used to describe the dynamic reaction path (DRP) based on an intrinsic reaction coordinate (IRC) or minimum energy path, to examine how the actual dynamics proceeds relative to the IRC path. In the first of these, any point on the DRP is expressed in terms of the IRC and the distance from the IRC path. In the second method, any DRP point is expressed in terms of the IRC, the curvature coordinate, and the distance from a two‐dimensional ‘‘reaction plane’’ determined by the IRC path tangent and curvature vectors. The latter representation is based on the fact that the 3N−8 dimensional space orthogonal to the reaction plane is independent of an internal centrifugal force caused by the motion along the IRC path. To analyze the relation between geometrical features of the IRC path and the dynamics, we introduce a function that estimates the variation of the reaction plane along the IRC path. As demonstrations, the methods are applied to the dissociationreaction of thiofolmaldehyde (H2CS→H2+CS)

Finite volume QCD at fixed topological charge

In finite volume the partition function of QCD with a given $\theta$ is a sum of different topological sectors with a weight primarily determined by the topological susceptibility. If a physical observable is evaluated only in a fixed topological sector, the result deviates from the true expectation value by an amount proportional to the inverse space-time volume 1/V. Using the saddle point expansion, we derive formulas to express the correction due to the fixed topological charge in terms of a 1/V expansion. Applying this formula, we propose a class of methods to determine the topological susceptibility in QCD from various correlation functions calculated in a fixed topological sector.Comment: 22pages, references adde