Direct CP-violation as a test of quantum mechanics

Direct CP-violating effects in the neutral kaon system result in violations of certain Bell-like inequalities. The new experimental results on the determination of the phenomenological parameter epsilon' allow to dismiss a large class of ``hidden variable'' alternatives to quantum mechanics.Comment: 15 pages, Te

A model for the continuous q-ultraspherical polynomials

We provide an algebraic interpretation for two classes of continuous $q$-polynomials. Rogers' continuous $q$-Hermite polynomials and continuous $q$-ultraspherical polynomials are shown to realize, respectively, bases for representation spaces of the $q$-Heisenberg algebra and a $q$-deformation of the Euclidean algebra in these dimensions. A generating function for the continuous $q$-Hermite polynomials and a $q$-analog of the Fourier-Gegenbauer expansion are naturally obtained from these models

An algebraic interpretation of the continuous big q-Hermite polynomials

The continuous big $q$-Hermite polynomials are shown to realize a basis for a representation space of an extended $q$-oscillator algebra. An expansion formula is algebraically derived using this model

Non-markovian mesoscopic dissipative dynamics of open quantum spin chains

We study the dissipative dynamics of $N$ quantum spins with Lindblad generator consisting of operators scaling as fluctuations, namely with the inverse square-root of $N$. In the large $N$ limit, the microscopic dissipative time-evolution converges to a non-Markovian unitary dynamics on strictly local operators, while at the mesoscopic level of fluctuations it gives rise to a dissipative non-Markovian dynamics. The mesoscopic time-evolution is Gaussian and exhibits either a stable or an unstable asymptotic character; furthermore, the mesoscopic dynamics builds correlations among fluctuations that survive in time even when the original microscopic dynamics is unable to correlate local observables.Comment: 18 page

Quantum algebra approach to q -Gegenbauer polynomials

Abstract Quantum algebras provide a natural algebraic setting for q special functions. The matrix elements of certain algebra generators in irreducible representations are in fact expressible in terms of q hypergeometric series. Taking the quantum algebra U( (1,1) ) as example, we shall show that its metaplectic representation provides a group-theoretic setting for certain basic orthogonal polynomials generalizing the usual Gegenbauer polynomials

q -Gamma and q -beta functions in quantum algebra representation theory

AbstractIntegral representations and addition formulas for the q-generalizations of the gamma and beta functions are obtained by studying function space models of a simple quantum algebra

Quantum contextuality in N-boson systems

Quantum contextuality in systems of identical bosonic particles is explicitly exhibited via the maximum violation of a suitable inequality of Clauser-Horne-Shimony-Holt type. Unlike the approaches considered so far, which make use of single-particle observables, our analysis involves collective observables constructed using multi-boson operators. An exemplifying scheme to test this violation with a quantum optical setup is also discussed.Comment: 4 pages, 1 figure, LaTe

Exact steady state of the open XX-spin chain: entanglement and transport properties

We study the reduced dynamics of open quantum spin chains of arbitrary length $N$ with nearest neighbour $XX$ interactions, immersed within an external constant magnetic field along the $z$ direction, whose end spins are weakly coupled to heat baths at different temperatures, via energy preserving couplings. We find the analytic expression of the unique stationary state of the master equation obtained in the so-called global approach based on the spectralization of the full chain Hamiltonian. Hinging upon the explicit stationary state, we reveal the presence of sink and source terms in the spin-flow continuity equation and compare their behaviour with that of the stationary heat flow. Moreover, we also obtain analytic expressions for the steady state two-spin reduced density matrices and for their concurrence. We then set up an algorithm suited to compute the stationary bipartite entanglement along the chain and to study its dependence on the Hamiltonian parameters and on the bath temperatures

Testing complete positivity

We study the modified dynamical evolution of the neutral kaon system under the condition of complete positivity. The accuracy of the data from planned future experiments is expected to be sufficiently precise to test such a hypothesis.Comment: 12 pages, latex, no figures, to appear in Mod. Phys. Lett.