Coherent states for a quantum particle on a Möbius strip

The coherent states for a quantum particle on a Möbius strip are constructed and the relation with the natural phase space for fermionic fields is shown. The explicit comparison of the obtained states with previous works where the cylinder quantization was used and the spin 1/2 was introduced by hand is given.     

Möbius and super-Möbius gauge fixing for the closed string amplitudes on the desk

We systematically study the gauge fixing of the Möbius and the super-Möbius transformations for the N-point closed-string amplitudes on the disk. Using the Faddeev-Popov method, we obtain the explicit formulas for the Koba-Nielsen factors for these amplitudes.     

Möbius invariance and classical solutions of SU(2) gauge theory

We use quaterniomic Möbius transformations to construct classical solutions of pure SU(2) gauge theory which correspond to two generalized merons and to two “excited” merons. We discuss how such transformations can yield distinct gauge invariant quantities and point out the limitations for generating further solutions by these techniques.     

A symmetry reduction scheme of the Dirac algebra without dimensional defects

In relating the Dirac algebra to homogeneous coordinates of a projective geometry, we present a simple geometric scheme which allows to identify various Lie algebras and Lie groups well-known from classical physics as well as from quantum field theory. We introduce a 1 -point-compactification and quaternionic Möbius transformations, and we use SU* (4) and a symmetry reduction scheme without dimensional defects to identify transformations and particle representations thoroughly. As such, two subsequent nonlinear σ models SU*(4)/U Sp(4) and U Sp(4)/SU(2) × U(1) emerge as well as a possible double coset decomposition of SU*(4) with respect to SU(2) × U(1). Whereas the first model leads to equivalence classes of hyperbolic manifolds and naturally introduces coordinates and velocities, the second coset model leads to a Hermitian symmetric (vector) space (Kählerian space) of real dimension 6, i.e., to a 3-dimensional complex space with a global symplectic and a local SU(2) × U(1) symmetry which allows to identify the (local) gauge group of electroweak interactions as well as under certain assumptions it admits compact SU(3) transformations as automorphisms of this 3-dimensional (hyper)complex vector space. In the limit of low energies, this geometric SU*(4) scheme naturally yields the (compact) group SU(4) to describe “chiral symmetry” and conserved isospin of hadrons as well as the low-dimensional hadron representations. Last not least, with respect to some of the SU*(4) generators we find a multiplication table which (up to signs) is identical with the octonions represented in the Fano plane.     

Electronic, energy, and thermal properties of the Möbius strip and related ring nanostructures of NbS3

The electronic structure and energy characteristics of the Möbius strip and related ring nanostructures of niobium trisulfide NbS₃ are investigated using the density functional tight-binding (DFTB) method. The results obtained are analyzed and compared with those obtained for the crystal and planar ribbon structures of NbS₃. The formation of NbS₃ ring structures leads to a considerable increase in the density of Nb 4d states at the Fermi level. The simulation of the behavior of the ring structures in the temperature range T = 0–700 K demonstrates that the Möbius strip has a lower thermal stability as compared to the NbS₃ ring.     

Dimer statistics on the Möbius strip and the Klein bottle

Closed-form expressions are obtained for the generating function of close-packed dimers on a 2M×2N simple quartic lattice embedded on a Möbius strip and a Klein bottle. Finite-size corrections are also analyzed and compared with those under cylindrical and free boundary conditions. Particularly, it is found that, for large lattices of the same size and with a square symmetry, the number of dimer configurations on a Möbius strip is 70.2% of that on a cylinder. We also establish two identities relating dimer generating functions for Möbius strips and cylinders.     

Möbius invariant integrable lattice equations associated with KP and 2DTL hierarchies

The integrable lattice equations arising in the context of singular manifold equations for scalar, multicomponent KP hierarchies and 2D Toda lattice hierarchy are considered. They generate the corresponding continuous hierarchy of singular manifold equations, its Bäcklund transformations and different forms of superposition principles; their distinctive feature is invariance under the action of Möbius transformation. Geometric interpretation of these discrete equations is given.     

Mechanisms and Möbius strips: understanding dynamic processes in annulenes

Exploratory computational studies on annulenes with planar, Möbius, and two‐twist topologies have resulted in new mechanisms to explain facile thermal configuration change (cis‐trans isomerization) for medium‐sized annulenes ([12]‐ to [16]annulene). Möbius π‐bond shifting through both aromatic and antiaromatic transition states, two‐twist π‐bond shifting, and planar nondegenerate π‐bond shifting can all be invoked to explain experimental results. Moreover, a simple bond‐shift rule, which is based on the change in number of trans C?C double bonds (Δtrans), was developed that predicts the topology of the transition state(s) necessary to effect the desired cis‐trans isomerization. The bond‐shift rule was also applied to configuration change in dehydro[12]annulene. Finally, extensive investigation of the [14]annulene hypersurface revealed that numerous Möbius minima exist within 10 kcal/mol of the global minimum. Copyright © 2012 John Wiley & Sons, Ltd.     

Quasiprimary fields: An approach to positivity of 2D conformal quantum field theory

Among the “secondary fields” of Belavin, Polyakov, and Zamolodchikov, the quasiprimary fields are distinguished by their covariant behaviour under infinitesimal Möbius transformations. Local n-point functions can be described in terms of the numerical amplitudes of 3-point functions of quasiprimary fields. The positivity of the full field theory is guaranteed if certain nonlinear consistency conditions among these constants can be satisfied by real numbers. Constraints arising from these conditions are discussed.     

Topology induced anomalous plasmon modes in metallic Möbius nanorings

We report on the theoretical investigation of plasmonic resonances in metallic Möbius nanorings. Half‐integer numbers of resonant modes are observed due to the presence of an extra phase π provided by the topology of the Möbius nanostrip. Anomalous plasmon modes located at the non‐orientable surface of the Möbius nanoring break the symmetry that exist in conventional ring cavities, thus enable far‐field excitation and emission as bright modes. The far‐field resonant wavelength as well as the feature of half‐integer mode numbers is constant to the change of charge distribution on the Möbius nanoring due to the topology of Möbius ring. Owing to the ultra‐small mode volume induced by the remaining dark feature, an extremely high sensitivity as well as a remarkable figure of merit is obtained in our numerical calculations for sensing performance. The topological metallic nanostructure provides a novel platform for the investigation of localized surface plasmon modes exhibiting unique phenomena for potential plasmonic applications.

     

Robust scheme for the preparation of symmetric Dicke states with coherence state via cross-Kerr nonlinearity

A scheme is proposed for generating multiphoton maximally entangled states among four modes. These schemes only use Kerr medium and polarization beam splitters and P homodyne measurements on coherent light fields, which can be efficiently implemented in quantum optical laboratories. It's comparatively easy to realize symmetric Dicke state of light fields in the scheme. The scheme can be generalized to produce N-qubit maximally entangled states.     

Winding Clusters in Percolation on the Torus and the Möbius Strip

Using a simulation technique introduced recently, we study winding clusters in percolation on the torus and the Möbius strip for different aspect ratios. The asynchronous parallelization of the simulation makes very large system and sample sizes possible. Our high accuracy results are fully consistent with predictions from conformal field theory. The numerical results for the Möbius strip and the number distribution of winding clusters on the torus await theoretical explanation. To our knowledge, this study is the first of its kind.     

Plasmonic microcavity formed by the Möbius strip

We propose a Möbius-strip-type plasmonic cavity with a silver Möbius strip sandwiched between dielectric layers. By brief theoretical and simulation analyses, we obtain that the Q factor of the cavity remains about 40 and the mode volume is ultrasmall (less than 1 μm³) which is more compact than that of the cylindric cavity. This Möbius-strip-type plasmonic cavity supporting the propagation of surface plasmon polaritons owns some unusual properties such as more effective volume and the spatial separation. More potential applications based on this cavity remain to be explored in future nanophotonics.     

Gravitational anomaly cancellation type I superstring theory

By explicit calculations we show that the gravitational anomaly of type I superstring theory vanishes at the string level. There are contributions from four topologically different diagrams to the anomaly: annulus, Möbius strip, torus, and Klein bottle. We explicitly show how the non-trivial cancellation occurs between the open (annulus and Möbius strip) and closed (Klein bottle) sectors. The anomaly of the torus diagram has the same form of type II superstring theory and vanishes because of the modular invariance.     

Comprehensive study of the correlations that exist among the members of the [n]cyclacene series and the Möbius[n]cyclacene series

Cyclacenes are the smallest substructures of carbon nanotubes used in modelling studies. The systematics that exists between Hückel molecular orbital eigenvalues and eigenvectors of cyclacenes are delineated. This study of cyclacenes combines the interconnection of concepts of complementarity theorem, characteristic and matching polynomial recursion equations, embedding, greater than twofold symmetry and doubly degenerate eigenvalues, open-shell singlet character, and pairing theorem. Proof that cyclacenes have more open-shell (diradical) character than do polyacenes is also provided by the sum total of this work. Mirror-plane scission of even-ring cyclacenes gives linear polyacene fragments. This shows that the properties of the successor linear polyacene must be contained in the precursor cyclacene. Corresponding Möbius[n]cyclacene isomers display contrasting and unusual comparative properties. A partial list of contrasting properties include alternant (cyclacenes) versus nonalternant (Möbius[n]cyclacene) polyenes, presence of Hamiltonian circuits in Möbius[n]cyclacene and presence of oscillatory electronic properties in cyclacenes.     

The Klein-Gordon Operator on Möbius Strip Domains and the Klein Bottle in ℝ n

In this paper we present explicit formulas for the fundamental solution to the Klein-Gordon operator on some higher dimensional generalizations of the Möbius strip and the Klein bottle with values in distinct pinor bundles. The fundamental solution is described in terms of generalizations of the Weierstraß $\wp $ -function that are adapted to the context of these geometries. The explicit formulas for the kernel then allow us to express all solutions to the homogeneous and inhomogeneous Klein-Gordon problem with given boundary data in the context of these manifolds. In the case of the Klein bottle we are able to describe all null solutions of the Klein-Gordon equation in terms of finite linear combinations of the fundamental solution and its partial derivatives.     

Prospects for emission Mössbauer spectroscopy in chemical investigations

Emission Mössbauer spectroscopy is a radiochemical method for investigating materials and the consequences of nuclear transformations taking place in them. Isotopes are traditionally used as structural probes, and the sensitivity of the method is 2–3 orders of magnitude higher than that of absorption Mössbauer spectroscopy. The elements of Mössbauer isotopes with parent nuclei that undergo electron capture or a converted isomeric transition (i.e., lead to high Auger ionization) are the best-studied elements. The electron processes that accompany ionization and their effect on the state of daughter Mössbauer atoms in qualitatively different compounds, from elementary oxides, superconductors, insulators and magnetics to sophisticated bioorganic complexes, are considered.     

Covariant string amplitudes on exotic topologies to one loop

Rules are provided for the calculation of string amplitudes on all exotic topologies to one loop. These topologies include the real projective plane, the disk, the annulus, the Möbius strip, the torus and the Klein bottle. The rules are valid for bosonic strings, superstrings, and heterotic strings either in their critical dimensions or toroidally compactified, and they are applicable to amplitudes with arbitrary external bosonic and fermionic states, including mixed open- and closed-string transitions. The modular invariance of the torus amplitudes is discussed.     

Reversed Radial SLE and the Brownian Loop Measure

The Brownian loop measure is a conformally invariant measure on loops in the plane that arises when studying the Schramm–Loewner evolution (SLE). When an SLE curve in a domain evolves from an interior point, it is natural to consider the loops that hit the curve and leave the domain, but their measure is infinite. We show that there is a related normalized quantity that is finite and invariant under Möbius transformations of the plane. We estimate this quantity when the curve is small and the domain simply connected. We then use this estimate to prove a formula for the Radon–Nikodym derivative of reversed radial SLE with respect to whole-plane SLE.