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Dendrophidion paucicarinatum
Number of Pages: 2Integrative BiologyGeological Science
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Dendrophidion vinitor
Number of Pages: 2Integrative BiologyGeological Science
Existence of Solutions to the Bethe Ansatz Equations for the 1D Hubbard Model: Finite Lattice and Thermodynamic Limit
In this work, we present a proof of the existence of real and ordered
solutions to the generalized Bethe Ansatz equations for the one dimensional
Hubbard model on a finite lattice, with periodic boundary conditions. The
existence of a continuous set of solutions extending from any positive U to the
limit of large interaction is also shown. This continuity property, when
combined with the proof that the wavefunction obtained with the generalized
Bethe Ansatz is normalizable, is relevant to the question of whether or not the
solution gives us the ground state of the finite system, as suggested by Lieb
and Wu. Lastly, for the absolute ground state at half-filling, we show that the
solution converges to a distribution in the thermodynamic limit. This limit
distribution satisfies the integral equations that led to the well known
solution of the 1D Hubbard model.Comment: 18 page
Stability of Relativistic Matter With Magnetic Fields
Stability of matter with Coulomb forces has been proved for non-relativistic
dynamics, including arbitrarily large magnetic fields, and for relativistic
dynamics without magnetic fields. In both cases stability requires that the
fine structure constant alpha be not too large. It was unclear what would
happen for both relativistic dynamics and magnetic fields, or even how to
formulate the problem clearly. We show that the use of the Dirac operator
allows both effects, provided the filled negative energy `sea' is defined
properly. The use of the free Dirac operator to define the negative levels
leads to catastrophe for any alpha, but the use of the Dirac operator with
magnetic field leads to stability.Comment: This is an announcement of the work in cond-mat/9610195 (LaTeX
The Lieb-Liniger Model as a Limit of Dilute Bosons in Three Dimensions
We show that the Lieb-Liniger model for one-dimensional bosons with repulsive
-function interaction can be rigorously derived via a scaling limit
from a dilute three-dimensional Bose gas with arbitrary repulsive interaction
potential of finite scattering length. For this purpose, we prove bounds on
both the eigenvalues and corresponding eigenfunctions of three-dimensional
bosons in strongly elongated traps and relate them to the corresponding
quantities in the Lieb-Liniger model. In particular, if both the scattering
length and the radius of the cylindrical trap go to zero, the
Lieb-Liniger model with coupling constant is derived. Our bounds
are uniform in in the whole parameter range , and apply
to the Hamiltonian for three-dimensional bosons in a spectral window of size
above the ground state energy.Comment: LaTeX2e, 19 page
The Ground States of Large Quantum Dots in Magnetic Fields
The quantum mechanical ground state of a 2D -electron system in a
confining potential ( is a coupling constant) and a homogeneous
magnetic field is studied in the high density limit , with fixed. It is proved that the ground state energy and
electronic density can be computed {\it exactly} in this limit by minimizing
simple functionals of the density. There are three such functionals depending
on the way varies as : A 2D Thomas-Fermi (TF) theory applies
in the case ; if the correct limit theory
is a modified -dependent TF model, and the case is described
by a ``classical'' continuum electrostatic theory. For homogeneous potentials
this last model describes also the weak coupling limit for arbitrary
. Important steps in the proof are the derivation of a new Lieb-Thirring
inequality for the sum of eigenvalues of single particle Hamiltonians in 2D
with magnetic fields, and an estimation of the exchange-correlation energy. For
this last estimate we study a model of classical point charges with
electrostatic interactions that provides a lower bound for the true quantum
mechanical energy.Comment: 57 pages, Plain tex, 5 figures in separate uufil
Stability and Instability of Relativistic Electrons in Classical Electro magnetic Fields
The stability of matter composed of electrons and static nuclei is
investigated for a relativistic dynamics for the electrons given by a suitably
projected Dirac operator and with Coulomb interactions. In addition there is an
arbitrary classical magnetic field of finite energy. Despite the previously
known facts that ordinary nonrelativistic matter with magnetic fields, or
relativistic matter without magnetic fields is already unstable when the fine
structure constant, is too large it is noteworthy that the combination of the
two is still stable provided the projection onto the positive energy states of
the Dirac operator, which defines the electron, is chosen properly. A good
choice is to include the magnetic field in the definition. A bad choice, which
always leads to instability, is the usual one in which the positive energy
states are defined by the free Dirac operator. Both assertions are proved here.Comment: LaTeX fil
Applied thermionic research Quarterly progress report, 25 Jan. - 25 Mar. 1965
Cesium fluoride and argon plasma additive effects in thermionic converter
Checkerboards, stripes and corner energies in spin models with competing interactions
We study the zero temperature phase diagram of Ising spin systems in two
dimensions in the presence of competing interactions, long range
antiferromagnetic and nearest neighbor ferromagnetic of strength J. We first
introduce the notion of a "corner energy" which shows, when the
antiferromagnetic interaction decays faster than the fourth power of the
distance, that a striped state is favored with respect to a checkerboard state
when J is close to J_c, the transition to the ferromagnetic state, i.e., when
the length scales of the uniformly magnetized domains become large. Next, we
perform detailed analytic computations on the energies of the striped and
checkerboard states in the cases of antiferromagnetic interactions with
exponential decay and with power law decay r^{-p}, p>2, that depend on the
Manhattan distance instead of the Euclidean distance. We prove that the striped
phase is always favored compared to the checkerboard phase when the scale of
the ground state structure is very large. This happens for J\lesssim J_c if
p>3, and for J sufficiently large if 2<p<=3. Many of our considerations
involving rigorous bounds carry over to dimensions greater than two and to more
general short-range ferromagnetic interactions.Comment: 21 pages, 3 figure
The q-deformed Bose gas: Integrability and thermodynamics
We investigate the exact solution of the q-deformed one-dimensional Bose gas
to derive all integrals of motion and their corresponding eigenvalues. As an
application, the thermodynamics is given and compared to an effective field
theory at low temperatures.Comment: 10 pages, 6 figure
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