25,471 research outputs found
Open shells in reduced-density-matrix-functional theory
Reduced-density-matrix-functional theory is applied to open-shell systems. We
introduce a spin-restricted formulation by appropriately expressing approximate
correlation-energy functionals in terms of spin-dependent occupation numbers
and spin-independent natural orbitals. We demonstrate that the additional
constraint of total-spin conservation is indispensable for the proper treatment
of open-shell systems. The formalism is applied to the first-row open-shell
atoms. The obtained ground-state energies are in very good agreement with the
exact values as well as other state of the art quantum chemistry calculationsComment: 4 pages, 2 figures, corrected typo
Enumerative aspects of the Gross-Siebert program
We present enumerative aspects of the Gross-Siebert program in this
introductory survey. After sketching the program's main themes and goals, we
review the basic definitions and results of logarithmic and tropical geometry.
We give examples and a proof for counting algebraic curves via tropical curves.
To illustrate an application of tropical geometry and the Gross-Siebert program
to mirror symmetry, we discuss the mirror symmetry of the projective plane.Comment: A version of these notes will appear as a chapter in an upcoming
Fields Institute volume. 81 page
Optimal control of time-dependent targets
In this work, we investigate how and to which extent a quantum system can be
driven along a prescribed path in Hilbert space by a suitably shaped laser
pulse. To calculate the optimal, i.e., the variationally best pulse, a properly
defined functional is maximized. This leads to a monotonically convergent
algorithm which is computationally not more expensive than the standard
optimal-control techniques to push a system, without specifying the path, from
a given initial to a given final state. The method is successfully applied to
drive the time-dependent density along a given trajectory in real space and to
control the time-dependent occupation numbers of a two-level system and of a
one-dimensional model for the hydrogen atom.Comment: less typo
Gauging the three-nucleon spectator equation
We derive relativistic three-dimensional integral equations describing the
interaction of the three-nucleon system with an external electromagnetic field.
Our equations are unitary, gauge invariant, and they conserve charge. This has
been achieved by applying the recently introduced gauging of equations method
to the three-nucleon spectator equations where spectator nucleons are always on
mass shell. As a result, the external photon is attached to all possible places
in the strong interaction model, so that current and charge conservation are
implemented in the theoretically correct fashion. Explicit expressions are
given for the three-nucleon bound state electromagnetic current, as well as the
transition currents for the scattering processes
\gamma He3 -> NNN, Nd -> \gamma Nd, and \gamma He3 -> Nd. As a result, a
unified covariant three-dimensional description of the NNN-\gamma NNN system is
achieved.Comment: 23 pages, REVTeX, epsf, 4 Postscript figure
Photoelectron spectra of anionic sodium clusters from time-dependent density-functional theory in real-time
We calculate the excitation energies of small neutral sodium clusters in the
framework of time-dependent density-functional theory. In the presented
calculations, we extract these energies from the power spectra of the dipole
and quadrupole signals that result from a real-time and real-space propagation.
For comparison with measured photoelectron spectra, we use the ionic
configurations of the corresponding single-charged anions. Our calculations
clearly improve on earlier results for photoelectron spectra obtained from
static Kohn-Sham eigenvalues
Some exact results on the matter star-product in the half-string formalism
We show that the D25 sliver wavefunction, just as the D-instanton sliver,
factorizes when expressed in terms of half-string coordinates. We also
calculate analytically the star-product of two zero-momentum eigenstates of
using the vertex in the oscillator basis, thereby showing that the
star-product in the matter sector can indeed be seen as multiplication of
matrices acting on the space of functionals of half strings. We then use the
above results to establish that the matrices , conjectured by
Rastelli, Sen and Zwiebach to be left and right projectors on the sliver, are
indeed so.Comment: 27 pages; footnote adde
Donaldson-Thomas invariants and wall-crossing formulas
Notes from the report at the Fields institute in Toronto. We introduce the
Donaldson-Thomas invariants and describe the wall-crossing formulas for
numerical Donaldson-Thomas invariants.Comment: 18 pages. To appear in the Fields Institute Monograph Serie
Classifying bases for 6D F-theory models
We classify six-dimensional F-theory compactifications in terms of simple
features of the divisor structure of the base surface of the elliptic
fibration. This structure controls the minimal spectrum of the theory. We
determine all irreducible configurations of divisors ("clusters") that are
required to carry nonabelian gauge group factors based on the intersections of
the divisors with one another and with the canonical class of the base. All 6D
F-theory models are built from combinations of these irreducible
configurations. Physically, this geometric structure characterizes the gauge
algebra and matter that can remain in a 6D theory after maximal Higgsing. These
results suggest that all 6D supergravity theories realized in F-theory have a
maximally Higgsed phase in which the gauge algebra is built out of summands of
the types su(3), so(8), f_4, e_6, e_8, e_7, (g_2 + su(2)), and su(2) + so(7) +
su(2), with minimal matter content charged only under the last three types of
summands, corresponding to the non-Higgsable cluster types identified through
F-theory geometry. Although we have identified all such geometric clusters, we
have not proven that there cannot be an obstruction to Higgsing to the minimal
gauge and matter configuration for any possible F-theory model. We also
identify bounds on the number of tensor fields allowed in a theory with any
fixed gauge algebra; we use this to bound the size of the gauge group (or
algebra) in a simple class of F-theory bases.Comment: 28 pages, 2 figures, 1 appendix. v2: added references, minor changes;
v3: two signs correcte
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