16,039 research outputs found
Kinetic energy functional for Fermi vapors in spherical harmonic confinement
Two equations are constructed which reflect, for fermions moving
independently in a spherical harmonic potential, a differential virial theorem
and a relation between the turning points of kinetic energy and particle
densities. These equations are used to derive a differential equation for the
particle density and a non-local kinetic energy functional.Comment: 8 pages, 2 figure
The Ubiquitous Throat
We attempt to quantify the widely-held belief that large hierarchies induced
by strongly-warped geometries are common in the string theory landscape. To
this end, we focus on the arguably best-understood subset of vacua -- type IIB
Calabi-Yau orientifolds with non-perturbative Kaehler stabilization and a
SUSY-breaking uplift (the KKLT setup). Within this framework, vacua with a
realistically small cosmological constant are expected to come from Calabi-Yaus
with a large number of 3-cycles. For appropriate choices of flux numbers, many
of these 3-cycles can, in general, shrink to produce near-conifold geometries.
Thus, a simple statistical analysis in the spirit of Denef and Douglas allows
us to estimate the expected number and length of Klebanov-Strassler throats in
the given set of vacua. We find that throats capable of explaining the
electroweak hierarchy are expected to be present in a large fraction of the
landscape vacua while shorter throats are essentially unavoidable in a
statistical sense.Comment: References added, typos fixed. LaTex, 17 pages, 1 figur
Brief review related to the foundations of time-dependent density functional theory
The electron density n(\rb,t), which is the central tool of time-dependent
density functional theory, is presently considered to be derivable from a
one-body time-dependent potential V(\rb,t), via one-electron wave functions
satisfying a time- dependent Schr\"{o}dinger equation. This is here related via
a generalized equation of motion to a Dirac density matrix now involving .
Linear response theory is then surveyed, with a special emphasis on the
question of causality with respect to the density dependence of the potential.
Extraction of V(\rb,t) for solvable models is also proposed
Collective excitation frequencies of Bosons in a parabolic potential with interparticle harmonic interactions
The fact that the ground-state first-order density matrix for Bosons in a
parabolic potential with interparticle harmonic interactions is known in exact
form is here exploited to study collective excitations in the weak-coupling
regime. Oscillations about the ground-state density are treated analytically by
a linearized equation of motion which includes a kinetic energy contribution.
We show that the dipole mode has the frequency of the bare trap, in accord with
the Kohn theorem, and derive explicit expressions for the frequencies of the
higher-multipole modes in terms of a frequency renormalized by the
interactions.Comment: 6 pages, no figures, accepted for publication on Physics Letters
Integral equation for inhomogeneous condensed bosons generalizing the Gross-Pitaevskii differential equation
We give here the derivation of a Gross-Pitaevskii--type equation for
inhomogeneous condensed bosons. Instead of the original Gross-Pitaevskii
differential equation, we obtain an integral equation that implies less
restrictive assumptions than are made in the very recent study of Pieri and
Strinati [Phys. Rev. Lett. 91 (2003) 030401]. In particular, the Thomas-Fermi
approximation and the restriction to small spatial variations of the order
parameter invoked in their study are avoided.Comment: Phys. Rev. A (accepted
Vortex macroscopic superpositions in ultracold bosons in a double-well potential
We study macroscopic superpositions in the orbital rather than the spatial
degrees of freedom, in a three-dimensional double-well system. We show that the
ensuing dynamics of interacting excited ultracold bosons, which in general
requires at least eight single-particle modes and Fock
vectors, is described by a surprisingly small set of many-body states. An
initial state with half the atoms in each well, and purposely excited in one of
them, gives rise to the tunneling of axisymmetric and transverse vortex
structures. We show that transverse vortices tunnel orders of magnitude faster
than axisymmetric ones and are therefore more experimentally accessible. The
tunneling process generates macroscopic superpositions only distinguishable by
their orbital properties and within experimentally realistic times.Comment: 9 pages, 6 figure
The Small Observed Baryon Asymmetry from a Large Lepton Asymmetry
Primordial Big-Bang Nucleosynthesis (BBN) tightly constrains the existence of
any additional relativistic degrees of freedom at that epoch. However a large
asymmetry in electron neutrino number shifts the chemical equilibrium between
the neutron and proton at neutron freeze-out and allows such additional
particle species. Moreover, the BBN itself may also prefer such an asymmetry to
reconcile predicted element abundances and observations. However, such a large
asymmetry appears to be in conflict with the observed small baryon asymmetry if
they are in sphaleron mediated equilibrium. In this paper we point out the
surprising fact that in the Standard Model, if the asymmetries in the electron
number and the muon number are equal (and opposite) and of the size required to
reconcile BBN theory with observations, a baryon asymmetry of the Universe of
the correct magnitude and sign is automatically generated within a factor of
two. This small remaining discrepancy is naturally remedied in the
supersymmetric Standard Model.Comment: 14 page
Volume change of bulk metals and metal clusters due to spin-polarization
The stabilized jellium model (SJM) provides us a method to calculate the
volume changes of different simple metals as a function of the spin
polarization, , of the delocalized valence electrons. Our calculations
show that for bulk metals, the equilibrium Wigner-Seitz (WS) radius, , is always a n increasing function of the polarization i.e., the
volume of a bulk metal always increases as increases, and the rate of
increasing is higher for higher electron density metals. Using the SJM along
with the local spin density approximation, we have also calculated the
equilibrium WS radius, , of spherical jellium clusters, at
which the pressure on the cluster with given numbers of total electrons, ,
and their spin configuration vanishes. Our calculations f or Cs, Na,
and Al clusters show that as a function of behaves
differently depending on whether corresponds to a closed-shell or an
open-shell cluster. For a closed-shell cluster, it is an increasing function of
over the whole range , whereas in open-shell clusters
it has a decreasing behavior over the range , where
is a polarization that the cluster has a configuration consistent
with Hund's first rule. The resu lts show that for all neutral clusters with
ground state spin configuration, , the inequality always holds (self-compression) but, at some
polarization , the inequality changes the direction
(self-expansion). However, the inequality
always holds and the equality is achieved in the limit .Comment: 7 pages, RevTex, 10 figure
Particle density and non-local kinetic energy density functional for two-dimensional harmonically confined Fermi vapors
We evaluate analytically some ground state properties of two-dimensional
harmonically confined Fermi vapors with isotropy and for an arbitrary number of
closed shells. We first derive a differential form of the virial theorem and an
expression for the kinetic energy density in terms of the fermion particle
density and its low-order derivatives. These results allow an explicit
differential equation to be obtained for the particle density. The equation is
third-order, linear and homogeneous. We also obtain a relation between the
turning points of kinetic energy and particle densities, and an expression of
the non-local kinetic energy density functional.Comment: 7 pages, 2 figure
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