208 research outputs found
New coherent states and a new proof of the Scott correction
We introduce new coherent states and use them to prove semi-classical
estimates for Schr\"odinger operators with regular potentials. This can be
further applied to the Thomas-Fermi potential yielding a new proof of the Scott
correction for molecules. This is the short version of a paper by the authors
archived at math-ph/0208044.Comment: A misprint in definition of new coherent states corrected. To appear
in Proceedings of the UAB 2002 Int'l Conference on Differential Equations and
Mathematics Physic
Droplet Excitations for the Spin-1/2 XXZ Chain with Kink Boundary Conditions
We give a precise definition for excitations consisting of a droplet of size
n in the XXZ chain with various choices of boundary conditions, including kink
boundary conditions and prove that, for each n, the droplet energies converge
to a boundary condition independent value in the thermodynamic limit. We
rigorously compute an explicit formula for this limiting value using the Bethe
ansatz.Comment: 36 pages, figures included as eps file
Counterexamples to Ferromagnetic Ordering of Energy Levels
The Heisenberg ferromagnet has symmetry group . The property
known as ferromagnetic ordering of energy levels (FOEL) states that the minimum
energy eigenvalue among eigenvectors with total spin is monotone decreasing
as a function of . While this property holds for certain graphs such as open
chains, in this note we demonstrate some counterexamples. We consider the spin
1/2 model on rings of length for , and show that the minimum
energy among all spin singlets is less than or equal to the minimum energy
among all spin triplets, which violates FOEL. This also shows some
counterexamples to the "Aldous ordering" for the symmetric exclusion process.
We also review some of the literature related to these examples.Comment: We corrected an earlier misinterpretation we made of a famous result
of Sutherland, which an anonymous referee corrected us on. 29 page
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