The Meaning of Elements of Reality and Quantum Counterfactuals: Reply to Kastner

This paper is an answer to the preceding paper by Kastner, in which she continued the criticism of the counterfactual usage of the Aharonov-Bergman-Lebowitz rule in the framework of the time-symmetrized quantum theory, in particular, by analyzing the three-box paradox. It is argued that the criticism is not sound. Paradoxical features of the three-box example are discussed. It is explained that the elements of reality in the framework of time-symmetrized quantum theory are counterfactual statements, and therefore, even conflicting elements of reality can be associated with a single system. It is shown how such counterfactual elements of reality can be useful in the analysis of a physical experiment (the three-box example). The validity of Kastner's application of the consistent histories approach to the time-symmetrized counterfactuals is questioned.     

Zero-one programming with many variables and few constraints

One of the more successful techniques for solving zero-one integer programs has been the implicit enumeration strategy first introduced by E. Balas. However, experience has shown that the efficiency of these enumerative techniques depends critically upon the bumber of variables. In this paper an algorithm is developed and computational experience provided for solving zero-one integer programs with many variables and few constraints. Sub-problems solved via implicit enumeration are generated from the linear programming relaxation and the variables in these sub-problems correspond to the fractional variables obtained in the linear program. Since the number of fractional variables in the linear program is bounded by the number of constraints in the linear program, the sub-problems will in general contain many fewer variables than the original zero-one integer program.     

Manganese(I) poly(mercaptoimidazolyl)borate complexes: spectroscopic and structural characterization of Mn...H-B interactions in solution and in the solid state

The manganese(I) tricarbonyl complexes (Bm(R))Mn(CO)3(R = Me, Bz, But, p-Tol) and (PhBmMe)Mn(CO)3, the first bis(mercaptoimidazolyl)borate derivatives for this metal, have been readily prepared and fully characterized. In particular, the presence of three-center-two-electron Mn...H-B interactions in these species, both in solution and in the solid state, has been investigated using a combination of IR and NMR spectroscopies and, in the case of the methyl-, tert-butyl- and para-tolyl-substituted derivatives, by X-ray crystallography. To complement these synthetic and structural studies, the tris(mercaptoimidazolyl)borate complexes (TmMe)Mn(CO)3(R = Me, Bz, But, p-Tol) and (PhTm(Me))Mn(CO)3, as well as the related pyrazolylbis(mercaptoimidazolyl)borate (pzBmMe)Mn(CO)3, have also been synthesized and characterized by a combination of analytical and spectroscopic techniques.     

Information and Distinguishability of Ensembles of Identical Quantum States

We consider a fixed quantum measurement performed over n identical copies of quantum states. Using a rigorous notion of distinguishability based on Shannon’s 12th theorem, we show that in the case of a single qubit, the number of distinguishable states is , where (α₁,α₂) is the angle interval from which the states are chosen. In the general case of an N-dimensional Hilbert space and an area Ω of the domain on the unit sphere from which the states are chosen, the number of distinguishable states is . The optimal distribution is uniform over the domain in Cartesian coordinates.     

The Reality in Bohmian Quantum Mechanics or Can You Kill with an Empty Wave Bullet?

Several situations, in which an empty wave causes an observable effect, are reviewed. They include an experiment showing surrealistic trajectories proposed by Englert et al. and protective measurement of the density of the quantum state. Conditions for observable effects due to empty waves are derived. The possibility (in spite of the existence of these examples) of minimalistic interpretation of Bohmian quantum mechanics in which only Bohmian positions supervene on our experience is discussed.     

New asymptotic behavior of the surface-atom force out of thermal equilibrium

The Casimir-Polder-Lifshitz force felt by an atom near the surface of a substrate is calculated out of thermal equilibrium in terms of the dielectric function of the material and of the atomic polarizability. The new force decays like 1/z3 at large distances (i.e., slower than at equilibrium), exhibits a sizable temperature dependence, and is attractive or repulsive depending on whether the temperature of the substrate is higher or smaller than the one of the environment. Our predictions can be relevant for experiments with ultracold atomic gases. Both dielectric and metal substrates are considered.     

Facile formation of molybdenum(VI) monooxo aryloxides MoO(OAr)4-nCln from molybdenum dioxo dichloride

Molybdenum monooxo compoundsMoO(OAr)4-nCln (n=0-2, Ar=2,6-Me2C6H3 or 2,6-i-Pr2C6H3) have been synthesized starting from the dioxo precursor MoO2Cl2. The complexes are characterized spectroscopically and by X-ray diffraction. The formation mechanism likely involves phenol precoordination followed by addition across the Mo=O bond.     

Inside or outside a ligand cleft? Synthetic, structural, and kinetic inertness studies of zinc, cadmium, and mercury complexes of cross-bridged cyclam and cyclen

Ethylene cross-bridging of the popular tetraazamacrocyclic ligand cyclam has led to metal complexes with enhanced kinetic inertness. The synthesis and spectral characterization of zinc(II), cadmium(II), and mercury(II) complexes of cross-bridged cyclam (L1) as well as cross-bridged cyclen (L2) are reported along with the details of our synthetic route to L2. X-ray structural studies revealed that all Zn(II) and Cd(II) cations are fully kappa(4)N-coordinated inside the respective ligand's molecular cleft with L1 providing the better fit for Zn(II). While Hg(II) is similarly coordinated to L2, it has been found to complex L1 outside the ligand cleft in a novel exo-kappa(2)N-mode. Solution NMR data of the kappa(4)N complexes are consistent with the presence of only a single cis-folded isomer in each case. Ligand (1)H and (13)C coupling to both (111,113)Cd and (199)Hg in their complexes can be clearly discerned. The relative kinetic inertness of representative cross-bridged complexes in acidic aqueous solution has been assessed and found to be in the following order: Zn(II) > Cd(II)[dbl greater-than] Hg(II). The data also reaffirm that cross-bridged cyclam ligand L1 forms a substantially more inert complex with zinc(II) than either the smaller cyclen analogue L2 or the unbridged 1,4,8,11-tetramethyl-cyclam L3.     

"Eclipse" effect in the scattering of weakly bound helium clusters

The total cross sections of the helium dimer, trimer, and tetramer for scattering from Kr atoms have been measured for cluster beam velocities between 250 and 820 m/s. The dimer cross section is twice that of the atom within 5% indicating that the Kr atoms scatter from the He atoms independently, which is consistent with the large dimer bond distance of about 50 A. The trimer and tetramer cross sections are somewhat larger and can be described by an impulse approximation with a multiple "eclipse" correction, extending ideas of Glauber for high energy collisions with the deuteron.