1,139 research outputs found
Bound states in the one-dimensional two-particle Hubbard model with an impurity
We investigate bound states in the one-dimensional two-particle Bose-Hubbard
model with an attractive () impurity potential. This is a
one-dimensional, discrete analogy of the hydrogen negative ion H problem.
There are several different types of bound states in this system, each of which
appears in a specific region. For given , there exists a (positive) critical
value of , below which the ground state is a bound state.
Interestingly, close to the critical value (), the ground
state can be described by the Chandrasekhar-type variational wave function,
which was initially proposed for H. For , the ground state is no
longer a bound state. However, there exists a second (larger) critical value
of , above which a molecule-type bound state is established and
stabilized by the repulsion. We have also tried to solve for the eigenstates of
the model using the Bethe ansatz. The model possesses a global \Zz_2-symmetry
(parity) which allows classification of all eigenstates into even and odd ones.
It is found that all states with odd-parity have the Bethe form, but none of
the states in the even-parity sector. This allows us to identify analytically
two odd-parity bound states, which appear in the parameter regions
and , respectively. Remarkably, the latter one can be \textit{embedded}
in the continuum spectrum with appropriate parameters. Moreover, in part of
these regions, there exists an even-parity bound state accompanying the
corresponding odd-parity bound state with almost the same energy.Comment: 18 pages, 18 figure
Integrability and weak diffraction in a two-particle Bose-Hubbard model
A recently introduced one-dimensional two-particle Bose-Hubbard model with a
single impurity is studied on finite lattices. The model possesses a discrete
reflection symmetry and we demonstrate that all eigenstates odd under this
symmetry can be obtained with a generalized Bethe ansatz if periodic boundary
conditions are imposed. Furthermore, we provide numerical evidence that this
holds true for open boundary conditions as well. The model exhibits
backscattering at the impurity site -- which usually destroys integrability --
yet there exists an integrable subspace. We investigate the non-integrable even
sector numerically and find a class of states which have almost the Bethe
ansatz form. These weakly diffractive states correspond to a weak violation of
the non-local Yang-Baxter relation which is satisfied in the odd sector. We
bring up a method based on the Prony algorithm to check whether a numerically
obtained wave function is in the Bethe form or not, and if so, to extract
parameters from it. This technique is applicable to a wide variety of other
lattice models.Comment: 13.5 pages, 11 figure
Bound States in the Continuum Realized in the One-Dimensional Two-Particle Hubbard Model with an Impurity
We report a bound state of the one-dimensional two-particle (bosonic or
fermionic) Hubbard model with an impurity potential. This state has the
Bethe-ansatz form, although the model is nonintegrable. Moreover, for a wide
region in parameter space, its energy is located in the continuum band. A
remarkable advantage of this state with respect to similar states in other
systems is the simple analytical form of the wave function and eigenvalue. This
state can be tuned in and out of the continuum continuously.Comment: A semi-exactly solvable model (half of the eigenstates are in the
Bethe form
Non-perturbative approaches to magnetism in strongly correlated electron systems
The microscopic basis for the stability of itinerant ferromagnetism in
correlated electron systems is examined. To this end several routes to
ferromagnetism are explored, using both rigorous methods valid in arbitrary
spatial dimensions, as well as Quantum Monte Carlo investigations in the limit
of infinite dimensions (dynamical mean-field theory). In particular we discuss
the qualitative and quantitative importance of (i) the direct Heisenberg
exchange coupling, (ii) band degeneracy plus Hund's rule coupling, and (iii) a
high spectral density near the band edges caused by an appropriate lattice
structure and/or kinetic energy of the electrons. We furnish evidence of the
stability of itinerant ferromagnetism in the pure Hubbard model for appropriate
lattices at electronic densities not too close to half-filling and large enough
. Already a weak direct exchange interaction, as well as band degeneracy, is
found to reduce the critical value of above which ferromagnetism becomes
stable considerably. Using similar numerical techniques the Hubbard model with
an easy axis is studied to explain metamagnetism in strongly anisotropic
antiferromagnets from a unifying microscopic point of view.Comment: 11 pages, Latex, and 6 postscript figures; Z. Phys. B, in pres
The moduli space of hypersurfaces whose singular locus has high dimension
Let be an algebraically closed field and let and be integers with
and Consider the moduli space of
hypersurfaces in of fixed degree whose singular locus is
at least -dimensional. We prove that for large , has a unique
irreducible component of maximal dimension, consisting of the hypersurfaces
singular along a linear -dimensional subspace of . The proof
will involve a probabilistic counting argument over finite fields.Comment: Final version, including the incorporation of all comments by the
refere
Fundamental groups of open K3 surfaces, Enriques surfaces and Fano 3-folds
We investigate when the fundamental group of the smooth part of a K3 surface
or Enriques surface with Du Val singularities, is finite. As a corollary we
give an effective upper bound for the order of the fundamental group of the
smooth part of a certain Fano 3-fold. This result supports Conjecture A below,
while Conjecture A (or alternatively the rational connectedness conjecture in
[KoMiMo] which is still open when the dimension is at least 4) would imply that
every log terminal Fano variety has a finite fundamental group (now a Theorem
of S. Takayama).Comment: Journal of Pure and Applied Algebra, to appear; 24 page
Tone-activated, remote, alert communication system
Pocket sized transmitter, frequency modulated by crystal derived tones, with integral loop antenna provides police with easy operating alert signal communicator which uses patrol car radio to relay signal. Communication channels are time shared by several patrol units
Telescopic actions
A group action H on X is called "telescopic" if for any finitely presented
group G, there exists a subgroup H' in H such that G is isomorphic to the
fundamental group of X/H'.
We construct examples of telescopic actions on some CAT[-1] spaces, in
particular on 3 and 4-dimensional hyperbolic spaces. As applications we give
new proofs of the following statements:
(1) Aitchison's theorem: Every finitely presented group G can appear as the
fundamental group of M/J, where M is a compact 3-manifold and J is an
involution which has only isolated fixed points;
(2) Taubes' theorem: Every finitely presented group G can appear as the
fundamental group of a compact complex 3-manifold.Comment: +higher dimension
Directly Indecomposables in Semidegenerate Varieties of Connected po-Groupoids
We study varieties with a term-definable poset structure, "po-groupoids". It
is known that connected posets have the "strict refinement property" (SRP). In
[arXiv:0808.1860v1 [math.LO]] it is proved that semidegenerate varieties with
the SRP have definable factor congruences and if the similarity type is finite,
directly indecomposables are axiomatizable by a set of first-order sentences.
We obtain such a set for semidegenerate varieties of connected po-groupoids and
show its quantifier complexity is bounded in general
Viking X-band telemetry experiment
In order to uncover operational and design problems in the use of X-band by the 1977 Mariner Jupiter-Saturn mission and future spacecraft using the Deep Space Network, the Viking X-band telemetry experiment was conducted. The experiment was conducted during the months of December 1975 and January 1976. During each of the five successful passes, a periodic sequence (in lieu of ranging) was transmitted to the spacecraft and returned by the spacecraft transponder on both S- and X-bands. These telemetry-like signals were received, demodulated, and detected. From a variety of measurements at the station, four independent measurements were made of the received signal-to-noise ratio (SNR). These four SNRs were later compared with each other and the predicted SNR. The principal result of the experiment is that X-band telemetry works as expected. That is, the measured SNRs were consistent relative to each other and to the predicted values within the accuracy of the experiment
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