228,525 research outputs found

### On universal decoherence under gravity: a perspective through the Equivalence Principle

In Nature Phys. 11, 668 (2015) (Ref. [1]), a composite particle prepared in a
pure initial quantum state and propagated in a uniform gravitational field is
shown to undergo a decoherence process at a rate determined by the
gravitational acceleration. By assuming Einstein's Equivalence Principle to be
valid, we demonstrate, first in a Lorentz frame with accelerating detectors,
and then directly in the Lab frame with uniform gravity, that the dephasing
between the different internal states arise not from gravity but rather from
differences in their rest mass, and the mass dependence of the de Broglie
wave's dispersion relation. We provide an alternative view to the situation
considered by Ref. [1], where we propose that gravity plays a kinematic role in
the loss of fringe visibility by giving the detector a transverse velocity
relative to the particle beam; visibility can be easily recovered by giving the
screen an appropriate uniform velocity. We finally propose that dephasing due
to gravity may in fact take place for certain modifications to the
gravitational potential where the Equivalence Principle is violated.Comment: 5 pages, 3 figure

### Marginally Trapped Surfaces in the Nonsymmetric Gravitational Theory

We consider a simple, physical approach to the problem of marginally trapped
surfaces in the Nonsymmetric Gravitational Theory (NGT). We apply this approach
to a particular spherically symmetric, Wyman sector gravitational field,
consisting of a pulse in the antisymmetric field variable. We demonstrate that
marginally trapped surfaces do exist for this choice of initial data.Comment: REVTeX 3.0 with epsf macros and AMS symbols, 3 pages, 1 figur

### Eigenvalues of Ruijsenaars-Schneider models associated with $A_{n-1}$ root system in Bethe ansatz formalism

Ruijsenaars-Schneider models associated with $A_{n-1}$ root system with a
discrete coupling constant are studied. The eigenvalues of the Hamiltonian are
givein in terms of the Bethe ansatz formulas. Taking the "non-relativistic"
limit, we obtain the spectrum of the corresponding Calogero-Moser systems in
the third formulas of Felder et al [20].Comment: Latex file, 25 page

### The Cauchy Operator for Basic Hypergeometric Series

We introduce the Cauchy augmentation operator for basic hypergeometric
series. Heine's ${}_2\phi_1$ transformation formula and Sears' ${}_3\phi_2$
transformation formula can be easily obtained by the symmetric property of some
parameters in operator identities. The Cauchy operator involves two parameters,
and it can be considered as a generalization of the operator $T(bD_q)$. Using
this operator, we obtain extensions of the Askey-Wilson integral, the Askey-Roy
integral, Sears' two-term summation formula, as well as the $q$-analogues of
Barnes' lemmas. Finally, we find that the Cauchy operator is also suitable for
the study of the bivariate Rogers-Szeg\"o polynomials, or the continuous big
$q$-Hermite polynomials.Comment: 21 pages, to appear in Advances in Applied Mathematic

- â€¦