495 research outputs found
Phase Space Derivation of a Variational Principle for One Dimensional Hamiltonian Systems
We consider the bifurcation problem u'' + \lambda u = N(u) with two point
boundary conditions where N(u) is a general nonlinear term which may also
depend on the eigenvalue \lambda. A new derivation of a variational principle
for the lowest eigenvalue \lambda is given. This derivation makes use only of
simple algebraic inequalities and leads directly to a more explicit expression
for the eigenvalue than what had been given previously.Comment: 2 pages, Revtex, no figure
A Variational Principle for Eigenvalue Problems of Hamiltonian Systems
We consider the bifurcation problem with two point
boundary conditions where is a general nonlinear term which may also
depend on the eigenvalue . We give a variational characterization of
the bifurcating branch as a function of the amplitude of the
solution. As an application we show how it can be used to obtain simple
approximate closed formulae for the period of large amplitude oscillations.Comment: 10 pages Revtex, 2 figures include
Validity of the Brunet-Derrida formula for the speed of pulled fronts with a cutoff
We establish rigorous upper and lower bounds for the speed of pulled fronts
with a cutoff. We show that the Brunet-Derrida formula corresponds to the
leading order expansion in the cut-off parameter of both the upper and lower
bounds. For sufficiently large cut-off parameter the Brunet-Derrida formula
lies outside the allowed band determined from the bounds. If nonlinearities are
neglected the upper and lower bounds coincide and are the exact linear speed
for all values of the cut-off parameter.Comment: 8 pages, 3 figure
A simple proof of a theorem of Laptev and Weidl
A new and elementary proof of a recent result of Laptev and Weidl is given.
It is a sharp Lieb-Thirring inequality for one dimensional Schroedinger
operators with matrix valued potentials.Comment: Replaces the version of June 28, 1999. A technical error in the proof
has been correcte
On Some Open Problems in Many-Electron Theory
Mel Levy and Elliott Lieb are two of the most prominent researchers who have
dedicated their efforts to the investigation of fundamental questions in
many-electron theory. Their results have not only revolutionized the
theoretical approach of the field, but, directly or indirectly, allowed for a
quantum jump in the computational treatment of realistic systems as well. For
this reason, at the conclusion of our book where the subject is treated across
different disciplines, we have asked Mel Levy and Elliott Lieb to provide us
with some open problems, which they believe will be a worth challenge for the
future also in the perspective of a synergy among the various disciplines.Comment: "Epilogue" chapter in "Many-Electron Approaches in Physics, Chemistry
and Mathematics: A Multidisciplinary View", Volker Bach and Luigi Delle Site
Eds. pages 411-416; Book Series: Mathematical Physics Studies, Springer
International Publishing Switzerland, 2014. The original title has been
modified in order to clarify the subject of the chapter out of the context of
the boo
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