Statistics of branched flow in a weak correlated random potential

Recent images of electron flow through a two-dimensional electron gas device show branching behavior that is reproduced in numerical simulations of motion in a correlated random potential [M. A. Topinka, Nature 410, 183 (2001)]]. We show how such branching arises from caustics in the classical flow and find a simple scaling behavior of the branching under variation of the random potential strength. Analytic results describing statistical properties of the branching are confirmed by classical and quantum numerical tests.     

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.