861 research outputs found
Antiferromagnetism in the Exact Ground State of the Half Filled Hubbard Model on the Complete-Bipartite Graph
As a prototype model of antiferromagnetism, we propose a repulsive Hubbard
Hamiltonian defined on a graph \L={\cal A}\cup{\cal B} with and bonds connecting any element of with all the
elements of . Since all the hopping matrix elements associated with
each bond are equal, the model is invariant under an arbitrary permutation of
the -sites and/or of the -sites. This is the Hubbard model
defined on the so called -complete-bipartite graph,
() being the number of elements in (). In this
paper we analytically find the {\it exact} ground state for at
half filling for any ; the repulsion has a maximum at a critical
-dependent value of the on-site Hubbard . The wave function and the
energy of the unique, singlet ground state assume a particularly elegant form
for N \ra \inf. We also calculate the spin-spin correlation function and show
that the ground state exhibits an antiferromagnetic order for any non-zero
even in the thermodynamic limit. We are aware of no previous explicit analytic
example of an antiferromagnetic ground state in a Hubbard-like model of
itinerant electrons. The kinetic term induces non-trivial correlations among
the particles and an antiparallel spin configuration in the two sublattices
comes to be energetically favoured at zero Temperature. On the other hand, if
the thermodynamic limit is taken and then zero Temperature is approached, a
paramagnetic behavior results. The thermodynamic limit does not commute with
the zero-Temperature limit, and this fact can be made explicit by the analytic
solutions.Comment: 19 pages, 5 figures .ep
Some exact results for the multicomponent t-J model
We present a generalization of the Sutherland's multicomponent model. Our
extension includes both the ferromagnetic and the antiferromagnetic t-J model
for any value of the exchange coupling J and the hopping parameter t. We prove
rigorously that for one dimensional chains the ground-state of the generalized
model is non-degenerate. As a consequence, the ordering of energy levels of the
antiferromagnetic t-J model is determined. Our result rigorously proves and
extends the analysis carried out by Sutherland in establishing the phase
diagram of the model as a function of the number of components.Comment: 11 pages, RevTeX 3.0, no figure
Skyrmions in Higher Landau Levels
We calculate the energies of quasiparticles with large numbers of reversed
spins (``skyrmions'') for odd integer filling factors 2k+1, k is greater than
or equals 1. We find, in contrast with the known result for filling factor
equals 1 (k = 0), that these quasiparticles always have higher energy than the
fully polarized ones and hence are not the low energy charged excitations, even
at small Zeeman energies. It follows that skyrmions are the relevant
quasiparticles only at filling factors 1, 1/3 and 1/5.Comment: 10 pages, RevTe
Opial-Type Integral Inequalities Involving Several Arbitrary Increasing Convex Functions
AbstractSome new Opial-type integral inequalities involving several arbitrary increasing convex functions on both sides are proved. These results generalise and yield important complementary results of some known integral inequalities established by G. I. Rozanova, B. G. Pachpatte, E. K. Godunova and V. I. Levin, and T. S. Hwang and G. S. Yang
Thermodynamical Bethe Ansatz and Condensed Matter
The basics of the thermodynamic Bethe ansatz equation are given. The simplest
case is repulsive delta function bosons, the thermodynamic equation contains
only one unknown function. We also treat the XXX model with spin 1/2 and the
XXZ model and the XYZ model. This method is very useful for the investigation
of the low temperature thermodynamics of solvable systems.Comment: 52 pages, 6 figures, latex, lamuphys.st
REMOVED: Optimization of VMD Process as Draw Solution Recovery Unit in FO Process
This article has been removed: please see Elsevier Policy on Article Withdrawal (http://www.elsevier.com/locate/withdrawalpolicy).This article has been removed at the request of the Executive Publisher.This article has been removed because it was published without the permission of the author(s)
Asymptotics of basic Bessel functions and q-Laguerre polynomials
AbstractWe establish a large n complete asymptotic expansion for q-Laguerre polynomials and a complete asymptotic expansion for a q-Bessel function of large argument. These expansions are needed in our study of an exactly solvable random transfer matrix model for disordered electronic systems. We also give a new derivation of an asymptotic formula due to Littlewood (1907)
Wave Mechanics of Two Hard Core Quantum Particles in 1-D Box
The wave mechanics of two impenetrable hard core particles in 1-D box is
analyzed. Each particle in the box behaves like an independent entity
represented by a {\it macro-orbital} (a kind of pair waveform). While the
expectation value of their interaction, ,
satisfies (or , with being the size
of the box). The particles in their ground state define a close-packed
arrangement of their wave packets (with , phase position
separation and momentum ) and experience a
mutual repulsive force ({\it zero point repulsion}) which
also tries to expand the box. While the relative dynamics of two particles in
their excited states represents usual collisional motion, the same in their
ground state becomes collisionless. These results have great significance in
determining the correct microscopic understanding of widely different many body
systems.Comment: 12 pages, no figur
Tau-Function Constructions of the Recurrence Coefficients of Orthogonal Polynomials
AbstractIn this paper we compute the recurrence coefficients of orthogonal polynomials using τ-function techniques. It is shown that for polynomials orthogonal with respect to positive weight functions on a noncompact interval, the recurrence coefficient can be expressed as the change in the chemical potential which, for sufficiently largeNis the second derivative of the free energy with respect toN, the particle number. We give three examples using this technique: Freud weights, Erdős weights, and weak exponential weights
Effects of etchants in the transfer of chemical vapor deposited graphene
The quality of graphene can be strongly modified during the transfer process following chemical vapor deposition (CVD) growth. Here, we transferred CVD-grown graphene from a copper foil to a SiO2/Si substrate using wet etching with four different etchants: HNO3, FeCl3, (NH4)2S2O8, and a commercial copper etchant. We then compared the quality of graphene after the transfer process in terms of surface modifications, pollutions (residues and contaminations), and electrical properties (mobility and density). Our tests and analyses showed that the commercial copper etchant provides the best structural integrity, the least amount of residues, and the smallest doping carrier concentration
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