155 research outputs found
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Cover title"1789"--handwritten on cover. -- Series statement handwritten on coverIncludes bibliographical reference
Global fixed point proof of time-dependent density-functional theory
We reformulate and generalize the uniqueness and existence proofs of
time-dependent density-functional theory. The central idea is to restate the
fundamental one-to-one correspondence between densities and potentials as a
global fixed point question for potentials on a given time-interval. We show
that the unique fixed point, i.e. the unique potential generating a given
density, is reached as the limiting point of an iterative procedure. The
one-to-one correspondence between densities and potentials is a straightforward
result provided that the response function of the divergence of the internal
forces is bounded. The existence, i.e. the v-representability of a density, can
be proven as well provided that the operator norms of the response functions of
the members of the iterative sequence of potentials have an upper bound. The
densities under consideration have second time-derivatives that are required to
satisfy a condition slightly weaker than being square-integrable. This approach
avoids the usual restrictions of Taylor-expandability in time of the uniqueness
theorem by Runge and Gross [Phys.Rev.Lett.52, 997 (1984)] and of the existence
theorem by van Leeuwen [Phys.Rev.Lett. 82, 3863 (1999)]. Owing to its
generality, the proof not only answers basic questions in density-functional
theory but also has potential implications in other fields of physics.Comment: 4 pages, 1 figur
The (C-H) bond dissociation energy in the methyl group of toluene
A, kinetic study of the pyrolysis of toluene by a flow technique has been made, and assuming Szwarc\u27s mechanism, two activation energies (78.3 and 84 kcal/mole depending on the temperature range used) have been derived for the dissociation of the (C-H) bond in the methyl group of toluene. The lower value agrees quite well with Szwarc\u27s, and the higher value turns out to be approximately the average of 77.5 and 89.9. The results of this research suggest 84 kcal/mole as the upper limit for the activation energy
Optical microsphere resonators: optimal coupling to high-Q whispering gallery modes
A general model is presented for coupling of high- whispering-gallery
modes in optical microsphere resonators with coupler devices possessing
discrete and continuous spectrum of propagating modes. By contrast to
conventional high-Q optical cavities, in microspheres independence of high
intrinsic quality-factor and controllable parameters of coupling via evanescent
field offer variety of regimes earlier available in RF devices. The theory is
applied to the earlier-reported data on different types of couplers to
microsphere resonators and complemented by experimental demonstration of
enhanced coupling efficiency (about 80%) and variable loading regimes with
Q>10^8 fused silica microspheres.Comment: 14 pages, 4 figure
Inventory of survey questions about the interests of the American public
Statement of responsibility on t.p. reads: Ithiel de Sola Pool, Gilbert E. Scharfenberger, David M. Griffel, Allan R. Kessler"#1997"--handwritten on coverPrepared for the Markle Foundatio
Density-potential mappings in quantum dynamics
In a recent letter [Europhys. Lett. 95, 13001 (2011)] the question of whether
the density of a time-dependent quantum system determines its external
potential was reformulated as a fixed point problem. This idea was used to
generalize the existence and uniqueness theorems underlying time-dependent
density functional theory. In this work we extend this proof to allow for more
general norms and provide a numerical implementation of the fixed-point
iteration scheme. We focus on the one-dimensional case as it allows for a more
in-depth analysis using singular Sturm-Liouville theory and at the same time
provides an easy visualization of the numerical applications in space and time.
We give an explicit relation between the boundary conditions on the density and
the convergence properties of the fixed-point procedure via the spectral
properties of the associated Sturm-Liouville operator. We show precisely under
which conditions discrete and continuous spectra arise and give explicit
examples. These conditions are then used to show that in the most physically
relevant cases the fixed point procedure converges. This is further
demonstrated with an example.Comment: 20 pages, 8 figures, 3 table
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