Product Vacua with Boundary States and the Classification of Gapped Phases

We address the question of the classification of gapped ground states in one dimension that cannot be distinguished by a local order parameter. We introduce a family of quantum spin systems on the one-dimensional chain that have a unique gapped ground state in the thermodynamic limit that is a simple product state, but which on the left and right half-infinite chains have additional zero energy edge states. The models, which we call Product Vacua with Boundary States, form phases that depend only on two integers corresponding to the number of edge states at each boundary. They can serve as representatives of equivalence classes of such gapped ground states phases and we show how the AKLT model and its SO(2J + 1)-invariant generalizations fit into this classification.     

Coherence-based axial point-spread function engineering for two-photon excited polymerization

We show in proof-of-principle experiments an axial resolution improvement in two-photon-excited fluorescence and polymerization enabled by the short coherence length of two counter-propagating ultrashort laser pulses. The interference of these pulses generate a spatial interference fringe pattern, whose width scales inversely to the spectral bandwidth and is therefore considerably shorter than the effective focal length of a laser beam conventionally focused from only one side.     

Macroscopic behavior of systems with an axial dynamic preferred direction

We present the derivation of the macroscopic equations for systems with an axial dynamic preferred direction. In addition to the usual hydrodynamic variables, we introduce the time derivative of the local preferred direction as a new variable and discuss its macroscopic consequences including new cross-coupling terms. Such an approach is expected to be useful for a number of systems for which orientational degrees of freedom are important including, for example, the formation of dynamic macroscopic patterns shown by certain bacteria such a Proteus mirabilis. We point out similarities in symmetry between the additional macroscopic variable discussed here, and the magnetization density in magnetic systems as well as the so-called [^(l)]\hat l vector in superfluid ³He-A. Furthermore we investigate the coupling to a gel-like system for which one has the strain tensor and relative rotations between the new variable and the network as additional macroscopic variables.     

In-medium operator product expansion for heavy-light-quark pseudoscalar mesons

The operator product expansion (OPE) for heavy-light-quark pseudoscalar mesons (D -mesons and B -mesons) in medium is determined, both for a moving meson with respect to the surrounding medium as well as for a meson at rest. First of all, the OPE is given in terms of normal-ordered operators up to mass dimension 5, and the mass of the heavy quark and the mass of the light quark are kept finite. The Wilson coefficients of such an expansion are infrared (IR) divergent in the limit of a vanishing light-quark mass. A consistent separation of scales necessitates an OPE in terms of non-normal-ordered operators, which implies operator mixing, where the IR-divergences are absorbed into the operators. It is shown that the Wilson coefficients of such an expansion are IR-stable, and the limit of a vanishing light-quark mass is perfomed. Details of the major steps for the calculation of the Wilson coefficients are presented. By a comparison with previous results obtained by other theoretical groups we have found serious disagreements.     

Inductive linearization for binary quadratic programs with linear constraints

4OR - A linearization technique for binary quadratic programs (BQPs) that comprise linear constraints is presented. The technique, called “inductive linearization”, extends concepts for...     

Synthesis and Structural Characterization of Bis(tetrahydro­pyran)calcium Bis[bis(trimethylsilyl)amide]

Transmetalation of Sn[N(SiMe₃)₂]₂ with calcium granules in tetrahydropyran (thp) yields colorless [(thp)₂Ca{N(SiMe₃)₂}₂] ( 1 ) which is soluble in common organic solvents. The calcium center is in a distorted tetrahedral environment with Ca–N and Ca–O bond lengths of 231.08(11) and 240.23(9) pm, respectively. The molecular structure is dominated by steric factors leading to a NCaN bond angle of 119.43(6)°.