3,507 research outputs found
Deitmar's versus Toen-Vaquie's schemes over F_1
We show the equivalence between Deitmar's and Toen-Vaquie's notions of
schemes over F_1 (the 'field with one element'), establishing a symmetry with
the classical case of schemes, seen either as spaces with a structure sheaf, or
functors of points. In proving so, we also conclude some new basic results on
commutative algebra of monoids.Comment: 13 pages. Shorter, final version. To appear in Math. Z. The final
publication is available at springerlink.co
A motivic version of the theorem of Fontaine and Wintenberger
We prove the equivalence between the categories of motives of rigid analytic
varieties over a perfectoid field of mixed characteristic and over the
associated (tilted) perfectoid field of equal characteristic. This
can be considered as a motivic generalization of a theorem of Fontaine and
Wintenberger, claiming that the Galois groups of and are
isomorphic. A main tool for constructing the equivalence is Scholze's theory of
perfectoid spaces.Comment: Stable version added. Accepted for publication. 46 page
The Monsky-Washnitzer and the overconvergent realizations
We construct the dagger realization functor for analytic motives over
non-archimedean fields of mixed characteristic, as well as the
Monsky-Washnitzer realization functor for algebraic motives over a discrete
field of positive characteristic. In particular, the motivic language on the
classic \'etale site provides a new direct definition of the overconvergent de
Rham cohomology and rigid cohomology and shows that their finite dimensionality
follows formally from the one of Betti cohomology for smooth projective complex
varieties.Comment: 31 pages. Minor changes, K\"unneth formula added. Published online in
International Mathematics Research Notices (2017
Rigid cohomology via the tilting equivalence
We define a de Rham cohomology theory for analytic varieties over a valued
field of equal characteristic with coefficients in a chosen
untilt of the perfection of by means of the motivic version of
Scholze's tilting equivalence. We show that this definition generalizes the
usual rigid cohomology in case the variety has good reduction. We also prove a
conjecture of Ayoub yielding an equivalence between rigid analytic motives with
good reduction and unipotent algebraic motives over the residue field, also in
mixed characteristic.Comment: Minor changes. Published. 25 page
Analytical mean-field approach to the phase-diagram of ultracold bosons in optical superlattices
We report a multiple-site mean-field analysis of the zero-temperature phase
diagram for ultracold bosons in realistic optical superlattices. The system of
interacting bosons is described by a Bose-Hubbard model whose site-dependent
parameters reflect the nontrivial periodicity of the optical superlattice. An
analytic approach is formulated based on the analysis of the stability of a
fixed-point of the map defined by the self-consistency condition inherent in
the mean-field approximation. The experimentally relevant case of the period-2
one-dimensional superlattice is briefly discussed. In particular, it is shown
that, for a special choice of the superlattice parameters, the half-filling
insulator domain features an unusual loophole shape that the single-site
mean-field approach fails to capture.Comment: 7 pages, 1 figur
Complex phase-ordering of the one-dimensional Heisenberg model with conserved order parameter
We study the phase-ordering kinetics of the one-dimensional Heisenberg model
with conserved order parameter, by means of scaling arguments and numerical
simulations. We find a rich dynamical pattern with a regime characterized by
two distinct growing lengths. Spins are found to be coplanar over regions of a
typical size , while inside these regions smooth rotations associated
to a smaller length are observed. Two different and coexisting
ordering mechanisms are associated to these lengths, leading to different
growth laws and violating dynamical
scaling.Comment: 14 pages, 8 figures. To appear on Phys. Rev. E (2009
Strong-coupling expansions for the topologically inhomogeneous Bose-Hubbard model
We consider a Bose-Hubbard model with an arbitrary hopping term and provide
the boundary of the insulating phase thereof in terms of third-order strong
coupling perturbative expansions for the ground state energy. In the general
case two previously unreported terms occur, arising from triangular loops and
hopping inhomogeneities, respectively. Quite interestingly the latter involves
the entire spectrum of the hopping matrix rather than its maximal eigenpair,
like the remaining perturbative terms. We also show that hopping
inhomogeneities produce a first order correction in the local density of
bosons. Our results apply to ultracold bosons trapped in confining potentials
with arbitrary topology, including the realistic case of optical superlattices
with uneven hopping amplitudes. Significant examples are provided. Furthermore,
our results can be extented to magnetically tuned transitions in Josephson
junction arrays.Comment: 5 pages, 2 figures,final versio
Fractional-filling Mott domains in two dimensional optical superlattices
Ultracold bosons in optical superlattices are expected to exhibit
fractional-filling insulating phases for sufficiently large repulsive
interactions. On strictly 1D systems, the exact mapping between hard-core
bosons and free spinless fermions shows that any periodic modulation in the
lattice parameters causes the presence of fractional-filling insulator domains.
Here, we focus on two recently proposed realistic 2D structures where such
mapping does not hold, i.e. the two-leg ladder and the trimerized kagome'
lattice. Based on a cell strong-coupling perturbation technique, we provide
quantitatively satisfactory phase diagrams for these structures, and give
estimates for the occurrence of the fractional-filling insulator domains in
terms of the inter-cell/intra-cell hopping amplitude ratio.Comment: 4 pages, 3 figure
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