59,234 research outputs found
Non-ergodic states induced by impurity levels in quantum spin chains
The semi-infinite XY spin chain with an impurity at the boundary has been
chosen as a prototype of interacting many-body systems to test for non-ergodic
behavior. The model is exactly solvable in analytic way in the thermodynamic
limit, where energy eigenstates and the spectrum are obtained in closed form.
In addition of a continuous band, localized states may split off from the
continuum, for some values of the impurity parameters. In the next step, after
the preparation of an arbitrary non-equilibrium state, we observe the time
evolution of the site magnetization. Relaxation properties are described by the
long-time behavior, which is estimated using the stationary phase method.
Absence of localized states defines an ergodic region in parameter space, where
the system relaxes to a homogeneous magnetization. Out of this region, impurity
levels split from the band, and localization phenomena may lead to
non-ergodicity.Comment: 10 pages, 5 figures. arXiv admin note: substantial text overlap with
arXiv:1703.0344
Symmetry limit properties of a priori mixing amplitudes for non-leptonic and weak radiative decays of hyperons
We show that the so-called parity-conserving amplitudes predicted in the a
priori mixing scheme for non-leptonic and weak radiative decays of hyperons
vanish in the strong-flavor symmetry limit
Equivalence between the real time Feynman histories and the quantum shutter approaches for the "passage time" in tunneling
We show the equivalence of the functions and
for the ``passage time'' in tunneling. The former, obtained within the
framework of the real time Feynman histories approach to the tunneling time
problem, using the Gell-Mann and Hartle's decoherence functional, and the
latter involving an exact analytical solution to the time-dependent
Schr\"{o}dinger equation for cutoff initial waves
Oversampling in shift-invariant spaces with a rational sampling period
8 pages, no figures.It is well known that, under appropriate hypotheses, a sampling formula allows us to recover any function in a principal shift-invariant space from its samples taken with sampling period one. Whenever the generator of the shift-invariant space satisfies the Strang-Fix conditions of order r, this formula also provides an approximation scheme of order r valid for smooth functions. In this paper we obtain sampling formulas sharing the same features by using a rational sampling period less than one. With the use of this oversampling technique, there is not one but an infinite number of sampling formulas. Whenever the generator has compact support, among these formulas it is possible to find one whose associated reconstruction functions have also compact support.This work has been supported by the Grant MTM2009-08345 from the D.G.I. of the Spanish Ministerio de Ciencia y TecnologĂa
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