512 research outputs found
Phylogenetic Revision of Eryphanis Boisduval, with a Description of a New Species from Ecuador (Lepidoptera, Nymphalidae)
This study provides a species-level phylogeny for the Neotropical brassoline genus Eryphanis Boisduval based on 43 morphological characters. A revised generic definition is given. Three subspecies are elevated to species status and a new species is described; E. bubocula (Butler, 1872), status revised; E. lycomedon (C. Felder and R. Felder, 1862), status revised; E. opimus (Staudinger, 1887), status revised; and E. greeneyi Penz and DeVries, new species. Diagnoses, annotated redescriptions, and illustrations of habitus and genitalia are provided for the nine Eryphanis species
Unique continuation for the magnetic Schrödinger equation
The uniqueâcontinuation property from sets of positive measure is here proven for the manyâbody magnetic Schrödinger equation. This property guarantees that if a solution of the Schrödinger equation vanishes on a set of positive measure, then it is identically zero. We explicitly consider potentials written as sums of either oneâbody or twoâbody functions, typical for Hamiltonians in manyâbody quantum mechanics. As a special case, we are able to treat atomic and molecular Hamiltonians. The uniqueâcontinuation property plays an important role in densityâfunctional theories, which underpins its relevance in quantum chemistry
A new approach to quantum backflow
We derive some rigorous results concerning the backflow operator introduced
by Bracken and Melloy. We show that it is linear bounded, self adjoint, and not
compact. Thus the question is underlined whether the backflow constant is an
eigenvalue of the backflow operator. From the position representation of the
backflow operator we obtain a more efficient method to determine the backflow
constant. Finally, detailed position probability flow properties of a numerical
approximation to the (perhaps improper) wave function of maximal backflow are
displayed.Comment: 12 pages, 8 figure
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 structure of the density-potential mapping. Part I: Standard density-functional theory
The Hohenberg-Kohn theorem of density-functional theory (DFT) is broadly considered the conceptual basis for a full characterization of an electronic system in its ground state by just the one-body particle density. Part I of this review aims at clarifying the status of the Hohenberg-Kohn theorem within DFT and Part II at different extensions of the theory that include magnetic fields. We collect evidence that the Hohenberg-Kohn theorem does not so much form the basis of DFT, but is rather the consequence of a more comprehensive mathematical framework. Such results are especially useful when it comes to the construction of generalized DFTs
Force balance approach for advanced approximations in density functional theories
We propose a systematic and constructive way to determine the exchange-correlation potentials of density-functional theories including vector potentials. The approach does not rely on energy or action functionals. Instead, it is based on equations of motion of current quantities (force balance equations) and is feasible both in the ground-state and the time-dependent settings. This avoids, besides differentiability and causality issues, the optimized-effective-potential procedure of orbital-dependent functionals. We provide straightforward exchange-type approximations for different density functional theories that for a homogeneous system and no external vector potential reduce to the exchange-only local-density and Slater Xα approximations
Polaritonic Hofstadter butterfly and cavity control of the quantized Hall conductance
In a previous work [Rokaj et al., Phys. Rev. Lett. 123, 047202 (2019)] a translationally invariant framework called quantum-electrodynamical Bloch (QED-Bloch) theory was introduced for the description of periodic materials in homogeneous magnetic fields and strongly coupled to the quantized photon field in the optical limit. For such systems, we show that QED-Bloch theory predicts the existence of fractal polaritonic spectra as a function of the cavity coupling strength. In addition, for the energy spectrum as a function of the relative magnetic flux we find that a terahertz cavity can modify the standard Hofstadter butterfly. In the limit of no quantized photon field, QED-Bloch theory captures the well-known fractal spectrum of the Hofstadter butterfly and can be used for the description of two-dimensional materials in strong magnetic fields, which are of great experimental interest. As a further application, we consider Landau levels under cavity confinement and show that the cavity alters the quantized Hall conductance and that the Hall plateaus are modified as Ïxy=e2Îœ/h(1+η2) by the light-matter coupling η. Most of the aforementioned phenomena should be experimentally accessible, and corresponding implications are discussed
Phylogenetic analysis and review of Panacea and Batesia butterflies (Nymphalidae)
Phylogenetic analysis of 53 morphological characte rs for five species of Panacea and Batesia hypochlora supports the separation of the two genera and showed that the monotypic genus Batesia is basal to Panacea. Male genitalia were Ilniform within Panacea and characters inir)f)llative for phylogeny reconstruction were restricted to wing coloration. Illustrations of adults and genitalia, a brief diagnosis, and distributions are provided le)r each species
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