1,960,526 research outputs found
Quantitative behavior of unipotent flows and an effective avoidance principle
We give an effective bound on how much time orbits of a unipotent group
on an arithmetic quotient can stay near homogeneous subvarieties of
corresponding to -subgroups of . In particular, we
show that if such a -orbit is moderately near a proper homogeneous
subvariety of for a long time it is very near a different
homogeneous subvariety. Our work builds upon the linearization method of Dani
and Margulis.
Our motivation in developing these bounds is in order to prove quantitative
density statements about unipotent orbits, which we plan to pursue in a
subsequent paper. New qualitative implications of our effective bounds are also
given.Comment: 52 page
The variational principle and effective action for a spherical dust shell
The variational principle for a spherical configuration consisting of a thin
spherical dust shell in gravitational field is constructed. The principle is
consistent with the boundary-value problem of the corresponding Euler-Lagrange
equations, and leads to ``natural boundary conditions''. These conditions and
the field equations following from the variational principle are used for
performing of the reduction of this system. The equations of motion for the
shell follow from the obtained reduced action. The transformation of the
variational formula for the reduced action leads to two natural variants of the
effective action. One of them describes the shell from a stationary interior
observer's point of view, another from the exterior one. The conditions of
isometry of the exterior and interior faces of the shell lead to the momentum
and Hamiltonian constraints.Comment: 16 pages, LaTe
Generalized Uncertainty Principle as a Consequence of the Effective Field Theory
We will demonstrate that the generalized uncertainty principle exists because
of the derivative expansion in the effective field theories. This is because,
in the framework of the effective field theories, the minimum measurable length
scale has to be integrated away to obtain the low energy effective action. We
will analyze the deformation of a massive free scalar field theory by the
generalized uncertainty principle, and demonstrate that the minimum measurable
length scale corresponds to a second more massive scale in the theory, which
has been integrated away. We will also analyze CFT operators dual to this
deformed scalar field theory, and observe that scaling of the new CFT operators
indicates that they are dual to this more massive scale in the theory. We will
use holographic renormalization to explicitly calculate the renormalized
boundary action with counterterms for this scalar field theory deformed by the
generalized uncertainty principle and show that the generalized uncertainty
principle contributes to the matter conformal anomaly.Comment: 15 pages, no figures, Accepted for Publication in Physics Letters
First-principle Wannier functions and effective lattice fermion models for narrow-band compounds
We propose a systematic procedure for constructing effective lattice fermion
models for narrow-band compounds on the basis of first-principles electronic
structure calculations. The method is illustrated for the series of
transition-metal (TM) oxides: SrVO, YTiO, VO, and
YMoO. It consists of three parts, starting from LDA. (i)
construction of the kinetic energy Hamiltonian using downfolding method. (ii)
solution of an inverse problem and construction of the Wannier functions (WFs)
for the given kinetic energy Hamiltonian. (iii) calculation of screened Coulomb
interactions in the basis of \textit{auxiliary} WFs, for which the
kinetic-energy term is set to be zero. The last step is necessary in order to
avoid the double counting of the kinetic-energy term, which is included
explicitly into the model. The screened Coulomb interactions are calculated in
a hybrid scheme. First, we evaluate the screening caused by the change of
occupation numbers and the relaxation of the LMTO basis functions, using the
conventional constraint-LDA approach, where all matrix elements of
hybridization involving the TM orbitals are set to be zero. Then, we switch
on the hybridization and evaluate the screening associated with the change of
this hybridization in RPA. The second channel of screening is very important,
and results in a relatively small value of the effective Coulomb interaction
for isolated bands. We discuss details of this screening and consider
its band-filling dependence, frequency dependence, influence of the lattice
distortion, proximity of other bands, and the dimensionality of the model
Hamiltonian.Comment: 35 pages, 25 figure
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