9,715 research outputs found
Stability of three-fermion clusters with finite range of attraction
Three quantum particles with on-site repulsion and nearest-neighbour
attraction on a one-dimensional lattice are considered. The three-body
Schroedinger equation is reduced to a set of single-variable integral
equations. Energies of three-particle bound complexes (trions) are found from
self-consistency of the approximating matrix equation. In the case of spin-1/2
fermions, the ground state trion energy, the excited state energies, the trion
spectra and stability regions are obtained for total spins S = 1/2 and S = 3/2.
In the S = 1/2 sector, a narrow but finite parameter region is identified where
the ground state consists of a stable fermion pair and an unbound fermion. Also
presented is the reference case of spin-0 bosons.Comment: 6 pages, 5 figures, plus 3 pages of supplementary materia
Separation of variables in one partial integrable case of Goryachev
We show that the equations of motion in one partial integrable case of
Goryachev in the rigid body dynamics can be separated by the appropriate change
of variables, the new variables x, y being hyperelliptic functions of time. The
natural phase variables (components of coordinates and momenta) are expressed
via x,y explicitly in elementary algebraic functions.Comment: LaTex, 6 page
Identification of stochastic operators
Based on the here developed functional analytic machinery we extend the
theory of operator sampling and identification to apply to operators with
stochastic spreading functions. We prove that identification with a delta train
signal is possible for a large class of stochastic operators that have the
property that the autocorrelation of the spreading function is supported on a
set of 4D volume less than one and this support set does not have a defective
structure. In fact, unlike in the case of deterministic operator
identification, the geometry of the support set has a significant impact on the
identifiability of the considered operator class. Also, we prove that,
analogous to the deterministic case, the restriction of the 4D volume of a
support set to be less or equal to one is necessary for identifiability of a
stochastic operator class
Sampling of stochastic operators
We develop sampling methodology aimed at determining stochastic operators
that satisfy a support size restriction on the autocorrelation of the operators
stochastic spreading function. The data that we use to reconstruct the operator
(or, in some cases only the autocorrelation of the spreading function) is based
on the response of the unknown operator to a known, deterministic test signal
Estimation of Overspread Scattering Functions
In many radar scenarios, the radar target or the medium is assumed to possess
randomly varying parts. The properties of a target are described by a random
process known as the spreading function. Its second order statistics under the
WSSUS assumption are given by the scattering function. Recent developments in
operator sampling theory suggest novel channel sounding procedures that allow
for the determination of the spreading function given complete statistical
knowledge of the operator echo from a single sounding by a weighted pulse
train.
We construct and analyze a novel estimator for the scattering function based
on these findings. Our results apply whenever the scattering function is
supported on a compact subset of the time-frequency plane. We do not make any
restrictions either on the geometry of this support set, or on its area. Our
estimator can be seen as a generalization of an averaged periodogram estimator
for the case of a non-rectangular geometry of the support set of the scattering
function
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