204 research outputs found
Global Continua of Positive Equilibria for some Quasilinear Parabolic Equation with a Nonlocal Initial Condition
This paper is concerned with a quaslinear parabolic equation including a
nonlinear nonlocal initial condition. The problem arises as equilibrium
equation in population dynamics with nonlinear diffusion. We make use of global
bifurcation theory to prove existence of an unbounded continuum of positive
solutions
Semiclassical theory of spin-orbit interactions using spin coherent states
We formulate a semiclassical theory for systems with spin-orbit interactions.
Using spin coherent states, we start from the path integral in an extended
phase space, formulate the classical dynamics of the coupled orbital and spin
degrees of freedom, and calculate the ingredients of Gutzwiller's trace formula
for the density of states. For a two-dimensional quantum dot with a spin-orbit
interaction of Rashba type, we obtain satisfactory agreement with fully
quantum-mechanical calculations. The mode-conversion problem, which arose in an
earlier semiclassical approach, has hereby been overcome.Comment: LaTeX (RevTeX), 4 pages, 2 figures, accepted for Physical Review
Letters; final version (v2) for publication with minor editorial change
Semiclassical trace formulae for systems with spin-orbit interactions: successes and limitations of present approaches
We discuss the semiclassical approaches for describing systems with
spin-orbit interactions by Littlejohn and Flynn (1991, 1992), Frisk and Guhr
(1993), and by Bolte and Keppeler (1998, 1999). We use these methods to derive
trace formulae for several two- and three-dimensional model systems, and
exhibit their successes and limitations. We discuss, in particular, also the
mode conversion problem that arises in the strong-coupling limit.Comment: LaTeX2e, 25 pages incl. 9 figures, version 3: final version in print
for J. Phys.
Semiclassical coherent state propagator for systems with spin
We derive the semiclassical limit of the coherent state propagator for
systems with two degrees of freedom of which one degree of freedom is canonical
and the other a spin. Systems in this category include those involving
spin-orbit interactions and the Jaynes-Cummings model in which a single
electromagnetic mode interacts with many independent two-level atoms. We
construct a path integral representation for the propagator of such systems and
derive its semiclassical limit. As special cases we consider separable systems,
the limit of very large spins and the case of spin 1/2.Comment: 19 pages, no figure
Effect of pitchfork bifurcations on the spectral statistics of Hamiltonian systems
We present a quantitative semiclassical treatment of the effects of
bifurcations on the spectral rigidity and the spectral form factor of a
Hamiltonian quantum system defined by two coupled quartic oscillators, which on
the classical level exhibits mixed phase space dynamics. We show that the
signature of a pitchfork bifurcation is two-fold: Beside the known effect of an
enhanced periodic orbit contribution due to its peculiar -dependence at
the bifurcation, we demonstrate that the orbit pair born {\em at} the
bifurcation gives rise to distinct deviations from universality slightly {\em
above} the bifurcation. This requires a semiclassical treatment beyond the
so-called diagonal approximation. Our semiclassical predictions for both the
coarse-grained density of states and the spectral rigidity, are in excellent
agreement with corresponding quantum-mechanical results.Comment: LaTex, 25 pp., 14 Figures (26 *.eps files); final version 3, to be
published in Journal of Physics
Semiclassical theory of spin-orbit interaction in the extended phase space
We consider the semiclassical theory in a joint phase space of spin and
orbital degrees of freedom. The method is developed from the path integrals
using the spin-coherent-state representation, and yields the trace formula for
the density of states. We discuss special cases, such as weak and strong
spin-orbit coupling, and relate the present theory to the earlier approaches.Comment: 36 pages, 8 figures. Version 2: revised Sec. 4.4 and Appendix B;
minor corrections elsewher
On the canonically invariant calculation of Maslov indices
After a short review of various ways to calculate the Maslov index appearing
in semiclassical Gutzwiller type trace formulae, we discuss a
coordinate-independent and canonically invariant formulation recently proposed
by A Sugita (2000, 2001). We give explicit formulae for its ingredients and
test them numerically for periodic orbits in several Hamiltonian systems with
mixed dynamics. We demonstrate how the Maslov indices and their ingredients can
be useful in the classification of periodic orbits in complicated bifurcation
scenarios, for instance in a novel sequence of seven orbits born out of a
tangent bifurcation in the H\'enon-Heiles system.Comment: LaTeX, 13 figures, 3 tables, submitted to J. Phys.
Clinical implications of novel activating EGFR mutations in malignant peritoneal mesothelioma
<p>Abstract</p> <p>Background</p> <p>There is a paucity of information about the molecular perturbations involved in MPM tumor formation. We previously reported that EGFR-TK mutations in MPM were predictive of achieving optimal surgical cytoreduction, but the status of EGFR pathway activation potential of these mutations was not known. Here we present the mutant EGFR activating potential and the matured survival data of the EGFR mutant(mut+) relative to wild type EGFR(mut-) mesothelioma.</p> <p>Methods</p> <p>Twenty-nine patients were evaluated and their tumors were probed for mutations in the catalytic TK-domain. Twenty-five patients were treated with cytoreductive surgery and complete clinical data was available for comparison of the mut+ and mut- groups. A COS-7 cell expression model was used to determine mutation activating profiles and response to erlotinib.</p> <p>Results</p> <p>Functional mutations were found in 31%(9/29) of patients; 7 of these mutations were novel and another was the L858R mutation. All missense mutations were found to be activating mutations and responsive to erlotinib. Of the 25 patients managed surgically, there were 7 mut+ and 18 mut-. Two of 7 (29%) mut+ developed progressive disease and died with a median follow-up time of 22 months; while 13/18 (72%) mut- developed progressive disease and 10/18 (56%) died with median TTP of 12 months and median survival of 14 months.</p> <p>Conclusions</p> <p>The novel EGFR mutations identified are activating mutations responsive to erlotinib. The mut+ subset have a 'relative' improved outcome. Erlotinib may have a role in MPM and exploration for mutations in a larger patient cohort is warranted.</p
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