[en] We first present, by using exclusivity principle, a brief proof of the complementarity principle: the sum of squared expectation values of dichotomic (±1) mutually complementary observables can not be greater than 1. Then we prove that the complementarity principle yields tight quantum bounds of violations of N-qubit Svetlichny's inequalities. This result not only demonstrates that exclusivity principle can give tight quantum bound for certain type of genuine multipartite correlations, but also illustrates the subtle relationship between quantum complementarity and quantum genuine multipartite correlations. (general)

[en] We consider models of anomaly-mediated supersymmetry breaking (AMSB) in which the grand unification (GUT) scale is determined by the vacuum expectation value of a chiral superfield. If the anomaly-mediated contributions to the potential are balanced by gravitational-strength interactions, a GUT scale of M_Planck/(16π²) can be generated. The GUT threshold also affects superpartner masses, and can easily give rise to realistic predictions if the GUT gauge group is asymptotically free. We give an explicit example of a model with these features, in which the doublet-triplet splitting problem is solved. The resulting superpartner spectrum is very different from that of previously considered AMSB models, with gaugino masses typically unifying at the GUT scale

[en] We show that Abelian discrete symmetries Z_N and Z_nR from string orbifolds result by assigning vacuum expectation values (VEVs) only to specified singlets. These singlets obtaining VEVs carry the gauge charges (of the covering U(1) gauge group) as multiples of N for Z_N and n for Z_nR. We explicitly show this realization in a Z_12−I orbifold model

[en] By using the function representation of self-adjoint operators, the expectation and variance of physical quantities (self-adjoint operators) are defined, and it is shown that the so-called uncertainty principle does not hold.

[en] We study the behaviour of generalized random Fibonacci sequences defined by the relation g_n = |λg_n-1 ± g_n-2|, where the ± sign is given by tossing an unbalanced coin, giving probability p to the + sign. We prove that the expected value of g_n grows exponentially fast for any 0 < p ≤ 1 when λ ≥ 2, and for any p > (2 - λ)/4 when λ is of the form 2cos(π/k) for some fixed integer k ≥ 3. In both cases, we give an algebraic expression for the growth rate

[en] I propose a scheme for reconstructing the weak value of an observable without the need for weak measurements. The post-selection in weak measurements is replaced by an initial projector measurement. The observable can be measured using any form of interaction, including projective measurements. The reconstruction is effected by measuring the change in the expectation value of the observable due to the projector measurement. The weak value may take nonclassical values if the projector measurement disturbs the expectation value of the observable

[en] We present an octonionic N=1 superfield action that reproduces in components the action of Bagger and Lambert for M2 branes. By giving an expectation value to one of the scalars we obtain the maximally supersymmetric superfield action for D2 branes

[en] We show how to provide suitable gauge invariant prescriptions for the classical spatial averages (resp. quantum expectation values) that are needed in the evaluation of classical (resp. quantum) backreaction effects. We also present examples illustrating how the use of gauge invariant prescriptions can avoid interpretation problems and prevent misleading conclusions

[en] Direct application of Bayes' theorem to generalized data yields a posterior probability distribution function (PDF) that is a product of a prior PDF of generalized data and a likelihood function, where generalized data consists of model parameters, measured data, and model defect data. The prior PDF of generalized data is defined by prior expectation values and a prior covariance matrix of generalized data that naturally includes covariance between any two components of generalized data. A set of constraints imposed on the posterior expectation values and covariances of generalized data via a given model is formally solved by the method of Lagrange multipliers. Posterior expectation values of the constraints and their covariance matrix are conventionally set to zero, leading to a likelihood function that is a Dirac delta function of the constraining equation. It is shown that setting constraints to values other than zero is analogous to introducing a model defect. Since posterior expectation values of any function of generalized data are integrals of that function over all generalized data weighted by the posterior PDF, all elements of generalized data may be viewed as nuisance parameters marginalized by this integration. One simple form of posterior PDF is obtained when the prior PDF and the likelihood function are normal PDFs. For linear models without a defect this PDF becomes equivalent to constrained least squares (CLS) method, that is, the χ² minimization method. (authors)

[en] We present a new scheme to detect and visualize oscillations of a single quantum system in real time. The scheme is based upon a sequence of very weak generalized measurements, distinguished by their low disturbance and low information gain. Accumulating the information from the single measurements by means of an appropriate Bayesian estimator, the actual oscillations can be monitored nevertheless with high accuracy and low disturbance. For this purpose only the minimum and the maximum expected oscillation frequency need to be known. The accumulation of information is based on a general derivation of the optimal estimator of the expectation value of a Hermitian observable for a sequence of measurements. At any time it takes into account all the preceding measurement results