402 research outputs found

### Quantum Mechanical Breaking of Local GL(4) Invariance

We consider the gravitational coupling of a scalar field, in a reformulation
of General Relativity exhibiting local GL(4) invariance at the classical level.
We compute the one-loop contribution of the scalar to the quantum effective
potential of the vierbein and find that it does not have GL(4) invariance. The
minima of the effective potential occur for a vierbein which is proportional to
the unit matrix.Comment: 9 pages, plain-TeX, no figure

### 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

### Tests of Complete Positivity in Fiber Optics

We consider the propagation of polarized photons in optical fibers under the
action of randomly generated noise. In such situation, the change in time of
the photon polarization can be described by a quantum dynamical semigroup. We
show that the hierarchy among the decay constants of the polarization density
matrix elements as prescribed by complete positivity can be experimentally
probed using standard laboratory set-ups.Comment: 10 pages, LaTe

### Open system approach to neutrino oscillations

Neutrino oscillations are studied in the general framework of open quantum
systems by means of extended dynamics that take into account possible
dissipative effects. These new phenomena induce modifications in the neutrino
oscillation pattern that in general can be parametrized by means of six
phenomenological constants. Although very small, stringent bounds on these
parameters are likely to be given by future planned neutrino experiments.Comment: 15 pages, plain-TeX, to appear in JHE

### Complete positivity and neutron interferometry

We analyze the dynamics of neutron beams in interferometry experiments using
quantum dynamical semigroups. We show that these experiments could provide
stringent limits on the non-standard, dissipative terms appearing in the
extended evolution equations.Comment: 12 pages, plain Te

### More on the q-oscillator algebra and q-orthogonal polynomials

Properties of certain $q$-orthogonal polynomials are connected to the
$q$-oscillator algebra. The Wall and $q$-Laguerre polynomials are shown to
arise as matrix elements of $q$-exponentials of the generators in a
representation of this algebra. A realization is presented where the continuous
$q$-Hermite polynomials form a basis of the representation space. Various
identities are interpreted within this model. In particular, the connection
formula between the continuous big $q$-Hermite polynomials and the continuous
$q$-Hermite polynomials is thus obtained, and two generating functions for
these last polynomials are algebraically derived

### Massless neutrino oscillations

Quantum dynamical semigroups provide a general framework for studying the
evolution of open systems. Neutrino propagation both in vacuum and in matter
can be analyzed using these techniques: they allow a consistent treatment of
non-standard, dissipative effects that can alter the pattern of neutrino
oscillations. In particular, initially massless neutrinos can give rise to a
nonvanishing flavour transition probability, involving in addition the Majorana
CP-violating mixing phase.Comment: 27 pages, plain-TeX, no figure

### Asymptotic Entanglement of Two Independent Systems in a Common Bath

Two, non-interacting systems immersed in a common bath and evolving with a
Markovian, completely positive dynamics can become initially entangled via a
purely noisy mechanism. Remarkably, for certain, phenomenologically relevant
environments, the quantum correlations can persist even in the asymptotic
long-time regime.Comment: 10 pages, LaTe

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