[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] Li and Rosmej derived analytical fits for the energy level shifts due to plasma screening on the basis of a free-electron potential published by Rosmej et al. one year earlier. The derivation of the fits, which were shown by Iglesias to be inconsistent with the fundamental premise of the ion-sphere model, was motivated by the belief that no analytical expression exists for the expectation value 3/2>, an assertion that was also contradicted by Iglesias. In this short note, I point out that a simple expression for the latter quantity can be obtained as a particular case of a formula published by Shertzer, and I provide a corresponding compact analytical expression for the level shifts in the framework of Rosmej's formalism. (authors)

[en] Moments are expectation values of products of powers of position and momentum, taken over quantum states (or averages over a set of classical particles). For free particles, the evolution in the quantum case is closely related to that of a set of classical particles. Here we consider the evolution of symmetrized moments for free particles in one dimension, first examining the geometric properties of the evolution for moments up to the fourth order, as determined by their extrema and inflections. These properties are specified by combinations of the moments that are invariant in that they remain constant under free evolution. An inequality constrains the fourth-order moments and shows that some geometric types of evolution are possible for a quantum particle but not possible classically, and some examples are examined. Explicit expressions are found for the moments of any order in terms of their initial values, for the invariant combinations, and for the moments in terms of these invariants. (paper)

[en] The 'Stieltjes moment problem' technique together with the positivity and monotonic decreasing properties of the electronic density of an atom is used to find new and more accurate lower bounds for the charge density at the nucleus and the momentum density at the origin, in terms of radial and momentum expectation values, respectively. Bounds depending on two and three expectation values are given explicitly and a Hartree-Fock study of their quality is carried out. Also, the behavior of the new bounds at large Z's is discussed. The Stieltjes technique allows to find lower bounds of better accuracy by including expectation values of higher order. (orig.)

[en] Using the scattering approach to quantization, we define an appropriate representation of the billiard wavefunction on the scattering Poincare section. The expectation values of smooth operators in terms of these Poincare section wavefunctions are expressed as sums over periodic orbits. A special operator is used to define scars on the section and the relation to scars in configuration space is discussed and demonstrated numerically. (author)