Anticommutative extension of the Adler map

We construct a noncommutative (Grassmann) extension of the well-known Adler Yang–Baxter map. It satisfies the Yang–Baxter equation, it is reversible and birational. Our extension preserves all the properties of the original map except the involutivity

Materials processing with tightly focused femtosecond vortex laser beams

This letter is the first demonstration of material modification using tightly focused femtosecond laser vortex beams. Double-charge femtosecond vortices were synthesized with the polarization-singularity beam converter described in Ref [1] and then focused using moderate and high numerical aperture optics (viz., NA = 0.45 and 0.9) to ablate fused silica and soda-lime glasses. By controlling the pulse energy we consistently machine high-quality micron-size ring-shaped structures with less than 100 nm uniform groove thickness.Comment: 8 pages, 3 figures, 10 references; submitted to Appl. Phys. Lett. on May 31, 201

Dynamical Casimir Effect for a Swinging Cavity

The resonant scalar particle generation for a swinging cavity resonator in the Casimir vacuum is examined. It is shown that the number of particles grows exponentially when the cavity rotates at some specific external frequency.Comment: to appear in J. Phys. A: Math. Theo

Comment on "Two Phase Transitions in the Fully frustrated XY Model"

The conclusions of a recent paper by Olsson (Phys. Rev. Lett. 75, 2758 (1995), cond-mat/9506082) about the fully frustrated XY model in two dimensions are questioned. In particular, the evidence presented for having two separate chiral and U(1) phase transitions are critically considered.Comment: One page one table, to Appear in Physical Review Letter

Reentrant Peak Effect in an anisotropic superconductor 2H-NbSe_2 : Role of disorder

The reentrant nature of Peak Effect is established in a single crystal of 2H-NbSe_2 via electrical transport and dc magnetisation studies. The role of disorder on the reentrant branch of PE has been examined in three single crystals with varying levels of quenched random disorder. Increasing disorder presumably shrinks the (H,T) parameter space over which vortex array retains spatial order. Although, the upper branch of the PE curve is somewhat robust, the lower reentrant branch of the same curve is strongly affected by disorder.Comment: 5 Pages of text, 4 figure

Coarse-Graining the Lin-Maldacena Geometries

The Lin-Maldacena geometries are nonsingular gravity duals to degenerate vacuum states of a family of field theories with SU(2|4) supersymmetry. In this note, we show that at large N, where the number of vacuum states is large, there is a natural `macroscopic' description of typical states, giving rise to a set of coarse-grained geometries. For a given coarse-grained state, we can associate an entropy related to the number of underlying microstates. We find a simple formula for this entropy in terms of the data that specify the geometry. We see that this entropy function is zero for the original microstate geometries and maximized for a certain ``typical state'' geometry, which we argue is the gravity dual to the zero-temperature limit of the thermal state of the corresponding field theory. Finally, we note that the coarse-grained geometries are singular if and only if the entropy function is non-zero.Comment: 29 pages, LaTeX, 3 figures; v2 references adde

String-Net Models with ZNZ_N Fusion Algebra

We study the Levin-Wen string-net model with a $Z_N$ type fusion algebra. Solutions of the local constraints of this model correspond to $Z_N$ gauge theory and double Chern-simons theories with quantum groups. For the first time, we explicitly construct a spin-$(N-1)/2$ model with $Z_N$ gauge symmetry on a triangular lattice as an exact dual model of the string-net model with a $Z_N$ type fusion algebra on a honeycomb lattice. This exact duality exists only when the spins are coupled to a $Z_N$ gauge field living on the links of the triangular lattice. The ungauged $Z_N$ lattice spin models are a class of quantum systems that bear symmetry-protected topological phases that may be classified by the third cohomology group $H^3(Z_N,U(1))$ of $Z_N$. Our results apply also to any case where the fusion algebra is identified with a finite group algebra or a quantusm group algebra.Comment: 16 pages, 2 figures, publishe

Operator-sum representation of time-dependent density operators and its applications

We show that any arbitrary time-dependent density operator of an open system can always be described in terms of an operator-sum representation regardless of its initial condition and the path of its evolution in the state space, and we provide a general expression of Kraus operators for arbitrary time-dependent density operator of an $N$-dimensional system. Moreover, applications of our result are illustrated through several examples.Comment: 4 pages, no figure, brief repor