Chaotic Evolution in Quantum Mechanics

A quantum system is described, whose wave function has a complexity which increases exponentially with time. Namely, for any fixed orthonormal basis, the number of components required for an accurate representation of the wave function increases exponentially.Comment: 8 pages (LaTeX 16 kB, followed by PostScript 2 kB for figure

Evolution of Liouville density of a chaotic system

An area-preserving map of the unit sphere, consisting of alternating twists and turns, is mostly chaotic. A Liouville density on that sphere is specified by means of its expansion into spherical harmonics. That expansion initially necessitates only a finite number of basis functions. As the dynamical mapping proceeds, it is found that the number of non-negligible coefficients increases exponentially with the number of steps. This is to be contrasted with the behavior of a Schr\"odinger wave function which requires, for the analogous quantum system, a basis of fixed size.Comment: LaTeX 4 pages (27 kB) followed by four short PostScript files (2 kB + 2 kB + 1 kB + 4 kB

Asymmetry of bipartite quantum discord

It is known from the analysis of the density matrix for bipartite systems that the quantum discord (as a measure of quantum correlations) depends on the particular subsystem chosen for the projective measurements. We study asymmetry of the discord in a simple physical model of two spin-1/2 particles with the dipole-dipole interaction governed by the XY Hamiltonian in the inhomogeneous magnetic field. The dependence of the above discord asymmetry on the Larmour frequencies at both T=0 (the ground state) and $T>0$ has been investigated. It is demonstrated, in particular, that the asymmetry is negligible for high temperatures but it may become significant with the decrease in temperature.Comment: 5 pages 3 figure

Wigner's little group and Berry's phase for massless particles

The ``little group'' for massless particles (namely, the Lorentz transformations $\Lambda$ that leave a null vector invariant) is isomorphic to the Euclidean group E2: translations and rotations in a plane. We show how to obtain explicitly the rotation angle of E2 as a function of $\Lambda$ and we relate that angle to Berry's topological phase. Some particles admit both signs of helicity, and it is then possible to define a reduced density matrix for their polarization. However, that density matrix is physically meaningless, because it has no transformation law under the Lorentz group, even under ordinary rotations.Comment: 4 pages revte

All multipartite Bell correlation inequalities for two dichotomic observables per site

We construct a set of 2^(2^n) independent Bell correlation inequalities for n-partite systems with two dichotomic observables each, which is complete in the sense that the inequalities are satisfied if and only if the correlations considered allow a local classical model. All these inequalities can be summarized in a single, albeit non-linear inequality. We show that quantum correlations satisfy this condition provided the state has positive partial transpose with respect to any grouping of the n systems into two subsystems. We also provide an efficient algorithm for finding the maximal quantum mechanical violation of each inequality, and show that the maximum is always attained for the generalized GHZ state.Comment: 11 pages, REVTe

Serological prevalence of Brucella spp. in feral pigs and sympatric cattle in the Pantanal of Mato Grosso do Sul, Brazil.

The aim of this study was to estimate the prevalence of anti-Brucella antibodies in feral pigs and sympatric cattle in the Pantanal sub-regions of Paiaguás and Nhecolândia. The study was conducted in Corumbá, State of Mato Grosso do Sul, Brazil. A total of 105 feral pigs and 256 cattle were sampled on 12 farms. Blood samples were collected from all the animals for serological diagnosis with buffered acidified antigen (BAA) for screening, confirmatory 2-Mercaptoethanol (2-ME) test, and comparative fluorescent polarization assay (FPA). The positive prevalence of feral pigs was 1% (1/105) in BAA and FPT, with no positive result confirmed of BAA in 2-ME. The prevalence of positive sampled cattle was 11.32% (29/256), 4.3% (10/256), and 7.42% (19/256) in the BAA, 2-ME, and FPT tests, respectively. The degree of agreement obtained among the serological tests in cattle was Kappa = 0.506 (p < 0.001), 95% CI (0.282-0.729). The results of serological tests showed that brucellosis is widespread in cattle herds of the studied region, but the same type of exposure to the agent did not occur in feral pigs according to the used diagnostic tests

Finite precision measurement nullifies the Kochen-Specker theorem

Only finite precision measurements are experimentally reasonable, and they cannot distinguish a dense subset from its closure. We show that the rational vectors, which are dense in S^2, can be colored so that the contradiction with hidden variable theories provided by Kochen-Specker constructions does not obtain. Thus, in contrast to violation of the Bell inequalities, no quantum-over-classical advantage for information processing can be derived from the Kochen-Specker theorem alone.Comment: 7 pages, plain TeX; minor corrections, interpretation clarified, references update

Analytical study of non-linear transport across a semiconductor-metal junction

In this paper we study analytically a one-dimensional model for a semiconductor-metal junction. We study the formation of Tamm states and how they evolve when the semi-infinite semiconductor and metal are coupled together. The non-linear current, as a function of the bias voltage, is studied using the non-equilibrium Green's function method and the density matrix of the interface is given. The electronic occupation of the sites defining the interface has strong non-linearities as function of the bias voltage due to strong resonances present in the Green's functions of the junction sites. The surface Green's function is computed analytically by solving a quadratic matrix equation, which does not require adding a small imaginary constant to the energy. The wave function for the surface states is given

Representations of Coherent and Squeezed States in a ff-deformed Fock Space

We establish some of the properties of the states interpolating between number and coherent states denoted by $| n >_{\lambda}$; among them are the reproducing of these states by the action of an operator-valued function on $| n>$ (the standard Fock space) and the fact that they can be regarded as $f$-deformed coherent bound states. In this paper we use them, as the basis of our new Fock space which in this case are not orthogonal but normalized. Then by some special superposition of them we obtain new representations for coherent and squeezed states in the new basis. Finally the statistical properties of these states are studied in detail.Comment: 13 pages, 4 Figure

Quantum Computation with Quantum Dots

We propose a new implementation of a universal set of one- and two-qubit gates for quantum computation using the spin states of coupled single-electron quantum dots. Desired operations are effected by the gating of the tunneling barrier between neighboring dots. Several measures of the gate quality are computed within a newly derived spin master equation incorporating decoherence caused by a prototypical magnetic environment. Dot-array experiments which would provide an initial demonstration of the desired non-equilibrium spin dynamics are proposed.Comment: 12 pages, Latex, 2 ps figures. v2: 20 pages (very minor corrections, substantial expansion), submitted to Phys. Rev.