WZW orientifolds and finite group cohomology

The simplest orientifolds of the WZW models are obtained by gauging a Z_2 symmetry group generated by a combined involution of the target Lie group G and of the worldsheet. The action of the involution on the target is by a twisted inversion g \mapsto (\zeta g)^{-1}, where \zeta is an element of the center of G. It reverses the sign of the Kalb-Ramond torsion field H given by a bi-invariant closed 3-form on G. The action on the worldsheet reverses its orientation. An unambiguous definition of Feynman amplitudes of the orientifold theory requires a choice of a gerbe with curvature H on the target group G, together with a so-called Jandl structure introduced in hep-th/0512283. More generally, one may gauge orientifold symmetry groups \Gamma = Z_2 \ltimes Z that combine the Z_2-action described above with the target symmetry induced by a subgroup Z of the center of G. To define the orientifold theory in such a situation, one needs a gerbe on G with a Z-equivariant Jandl structure. We reduce the study of the existence of such structures and of their inequivalent choices to a problem in group-\Gamma cohomology that we solve for all simple simply-connected compact Lie groups G and all orientifold groups \Gamma = Z_2 \ltimes Z.Comment: 48+1 pages, 11 figure

Fidelity balance in quantum operations

I derive a tight bound between the quality of estimating the state of a single copy of a $d$-level system, and the degree the initial state has to be altered in course of this procedure. This result provides a complete analytical description of the quantum mechanical trade-off between the information gain and the quantum state disturbance expressed in terms of mean fidelities. I also discuss consequences of this bound for quantum teleportation using nonmaximally entangled states.Comment: 4 pages, REVTeX. Revised versio

Leading-effect vs. Risk-taking in Dynamic Tournaments: Evidence from a Real-life Randomized Experiment

Two 'order effects' may emerge in dynamic tournaments with information feedback. First, participants adjust effort across stages, which could advantage the leading participant who faces a larger 'effective prize' after an initial victory (leading-effect). Second, participants lagging behind may increase risk at the final stage as they have 'nothing to lose' (risk-taking). We use a randomized natural experiment in professional two-game soccer tournaments where the treatment (order of a stage-specific advantage) and team characteristics, e.g. ability, are independent. We develop an identification strategy to test for leading-effects controlling for risk-taking. We find no evidence of leading-effects and negligible risk-taking effects

A sequence of unsharp measurements enabling a real time visualization of a quantum oscillation

The normalized state $\ket{\psi(t)}=c_1(t)\ket{1}+c_2(t)\ket{2}$ of a single two-level system performs oscillations under the influence of a resonant driving field. It is assumed that only one realization of this process is available. We show that it is possible to approximately visualize in real time the evolution of the system as far as it is given by $|c_2(t)|^2$. For this purpose we use a sequence of particular unsharp measurements separated in time. They are specified within the theory of generalized measurements in which observables are represented by positive operator valued measures (POVM). A realization of the unsharp measurements may be obtained by coupling the two-level system to a meter and performing the usual projection measurements on the meter only.Comment: 17 pages, 3 figures, accepted for publication in Phys. Rev. A. Some typographical corrections are made and a short treatmeant of the fidelity of our measurements (N-series) is adde

How metal films de-wet substrates - identifying the kinetic pathways and energetic driving forces

We study how single-crystal chromium films of uniform thickness on W(110) substrates are converted to arrays of three-dimensional (3D) Cr islands during annealing. We use low-energy electron microscopy (LEEM) to directly observe a kinetic pathway that produces trenches that expose the wetting layer. Adjacent film steps move simultaneously uphill and downhill relative to the staircase of atomic steps on the substrate. This step motion thickens the film regions where steps advance. Where film steps retract, the film thins, eventually exposing the stable wetting layer. Since our analysis shows that thick Cr films have a lattice constant close to bulk Cr, we propose that surface and interface stress provide a possible driving force for the observed morphological instability. Atomistic simulations and analytic elastic models show that surface and interface stress can cause a dependence of film energy on thickness that leads to an instability to simultaneous thinning and thickening. We observe that de-wetting is also initiated at bunches of substrate steps in two other systems, Ag/W(110) and Ag/Ru(0001). We additionally describe how Cr films are converted into patterns of unidirectional stripes as the trenches that expose the wetting layer lengthen along the W[001] direction. Finally, we observe how 3D Cr islands form directly during film growth at elevated temperature. The Cr mesas (wedges) form as Cr film steps advance down the staircase of substrate steps, another example of the critical role that substrate steps play in 3D island formation

Sabotage in Contests: A Survey

A contest is a situation in which individuals expend irretrievable resources to win valuable prize(s). ‘Sabotage’ is a deliberate and costly act of damaging a rival’s' likelihood of winning the contest. Sabotage can be observed in, e.g., sports, war, promotion tournaments, political or marketing campaigns. In this article, we provide a model and various perspectives on such sabotage activities and review the economics literature analyzing the act of sabotage in contests. We discuss the theories and evidence highlighting the means of sabotage, why sabotage occurs, and the effects of sabotage on individual players and on overall welfare, along with possible mechanisms to reduce sabotage. We note that most sabotage activities are aimed at the ablest player, the possibility of sabotage reduces productive effort exerted by the players, and sabotage may lessen the effectiveness of public policies, such as affirmative action, or information revelation in contests. We discuss various policies that a designer may employ to counteract sabotage activities. We conclude by pointing out some areas of future research

Fidelity trade-off for finite ensembles of identically prepared qubits

We calculate the trade-off between the quality of estimating the quantum state of an ensemble of identically prepared qubits and the minimum level of disturbance that has to be introduced by this procedure in quantum mechanics. The trade-off is quantified using two mean fidelities: the operation fidelity which characterizes the average resemblance of the final qubit state to the initial one, and the estimation fidelity describing the quality of the obtained estimate. We analyze properties of quantum operations saturating the achievability bound for the operation fidelity versus the estimation fidelity, which allows us to reduce substantially the complexity of the problem of finding the trade-off curve. The reduced optimization problem has the form of an eigenvalue problem for a set of tridiagonal matrices, and it can be easily solved using standard numerical tools.Comment: 26 pages, REVTeX, 2 figures. Few minor corrections, accepted for publication in Physical Review

Phase separation in a lattice model of a superconductor with pair hopping

We have studied the extended Hubbard model with pair hopping in the atomic limit for arbitrary electron density and chemical potential. The Hamiltonian considered consists of (i) the effective on-site interaction U and (ii) the intersite charge exchange interactions I, determining the hopping of electron pairs between nearest-neighbour sites. The model can be treated as a simple effective model of a superconductor with very short coherence length in which electrons are localized and only electron pairs have possibility of transferring. The phase diagrams and thermodynamic properties of this model have been determined within the variational approach, which treats the on-site interaction term exactly and the intersite interactions within the mean-field approximation. We have also obtained rigorous results for a linear chain (d=1) in the ground state. Moreover, at T=0 some results derived within the random phase approximation (and the spin-wave approximation) for d=2 and d=3 lattices and within the low density expansions for d=3 lattices are presented. Our investigation of the general case (as a function of the electron concentration and as a function of the chemical potential) shows that, depending on the values of interaction parameters, the system can exhibit not only the homogeneous phases: superconducting (SS) and nonordered (NO), but also the phase separated states (PS: SS-NO). The system considered exhibits interesting multicritical behaviour including tricritical points.Comment: 15 pages, 9 figures; pdf-ReVTeX, final version, corrected typos; submitted to Journal of Physics: Condensed Matte