12,909 research outputs found
On Exotic Lagrangian Tori in CP^2
We construct an exotic monotone Lagrangian torus in CP^2 using techniques
motivated by mirror symmetry. We show that it bounds 10 families of Maslov
index 2 holomorphic discs, and it follows that this exotic torus is not
Hamiltonian isotopic to the known Clifford and Chekanov tori.Comment: 62 page
Infinitely many monotone Lagrangian tori in del Pezzo surfaces
We construct almost toric fibrations (ATFs) on all del Pezzo surfaces,
endowed with a monotone symplectic form. Except for and ,
we are able to get almost toric base diagrams (ATBDs) of triangular shape and
prove the existence of infinitely many symplectomorphism (in particular
Hamiltonian isotopy) classes of monotone Lagrangian tori in , for k=0,3,4,5,6,7,8. We name these tori
. Using the work of Karpov-Nogin, we are able to
classify all ATBDs of triangular shape. We are able to prove that
also have infinitely many
monotone Lagrangian tori up to symplectomorphism and we conjecture that the
same holds for . Finally, the
Lagrangian tori inside a del Pezzo surface
can be seen as monotone fibres of ATFs, such that, over its edge lies a fixed
anticanonical symplectic torus . We argue that
give rise to infinitely many exact Lagrangian
tori in , even after attaching the positive end of a
symplectization to the boundary of .Comment: 28 pages, 20 figure
Continuum families of non-displaceable Lagrangian tori in
We construct a family of Lagrangian tori
, , where , is the
monotone twist Lagrangian torus described by Chekanov-Schlenk. We show that for
and these tori are non-displaceable. Then by considering
, with and ,
we get several -dimensional families of non-displaceable
Lagrangian tori. We also show that there exists partial symplectic quasi-states
and linearly independent homogeneous
Calabi quasimorphims or which
are -superheavy and
-superheavy. We also prove a similar
result for , where
is a family of symplectic forms in
, for which is monotone.Comment: 17 pages, 1 Figur
Low-area Floer theory and non-displaceability
We introduce a new version of Floer theory of a non-monotone Lagrangian
submanifold which only uses least area holomorphic disks with boundary on it.
We use this theory to prove non-displaceability theorems about continuous
families of Lagrangian tori in the complex projective plane and other del Pezzo
surfaces.Comment: 32 pages, 9 figures; v2: major improvements, added a new result
concerning del Pezzos, corrected some mistakes; v3: explained transversality
for annuli, commented on higher dimensions; accepted versio
Computable Measures for the Entanglement of Indistinguishable Particles
We discuss particle entanglement in systems of indistinguishable bosons and
fermions, in finite Hilbert spaces, with focus on operational measures of
quantum correlations. We show how to use von Neumann entropy, Negativity and
entanglement witnesses in these cases, proving interesting relations. We obtain
analytic expressions to quantify quantum correlations in homogeneous
D-dimensional Hamiltonian models with certain symmetries.Comment: 9 page
Optimal estimation of quantum processes using incomplete information: variational quantum process tomography
We develop a quantum process tomography method, which variationally
reconstruct the map of a process, using noisy and incomplete information about
the dynamics. The new method encompasses the most common quantum process
tomography schemes. It is based on the variational quantum tomography method
(VQT) proposed by Maciel et al. in arXiv:1001.1793[quant-ph].Comment: 3 pages, one figure. Revised version, including numerical example
Resonant interaction between an ultrashort pulse train and a two-level system: frequency domain analysis
We investigate the problem of two-level atoms driven by an ultrashort pulse
train in the frequency domain. At low intensity regime, we obtain a
perturbative analytical solution that allows us to discuss the role of the mode
number of the frequency comb near or at resonance on the temporal evolution of
the atomic coherence. At high intensities, the effect of the number of modes is
analyzed in the steady-state regime through numerical calculations.Comment: 8 pages, 8 figure
Quantumness of correlations in indistinguishable particles
We discuss a general notion of quantum correlations in fermionic or bosonic
indistinguishable particles. Our approach is mainly based on the identification
of the algebra of single-particle observables, which allows us to devise an
activation protocol in which the \textit{quantumness of correlations} in the
system leads to a unavoidable creation of entanglement with the measurement
apparatus. Using the distillable entanglement, or the relative entropy of
entanglement, as entanglement measure, we show that our approach is equivalent
to the notion of minimal disturbance in a single-particle von Neumann
measurement, also leading to a geometrical approach for its quantification.Comment: 7 pages, 2 figure
Asymptotic behavior of Vianna's exotic Lagrangian tori in as
In this paper, we study various asymptotic behavior of the infinite family of
monotone Lagrangian tori in associated to Markov
triples described in \cite{Vi14}. We first prove that the Gromov
capacity of the complement is greater than
or equal to of the area of the complex line for all Markov triple
. We then prove that there is a representative of the family
whose loci completely miss a metric ball of nonzero size and in
particular the loci of the union of the family is not dense in .Comment: 24 pages, 7 figures;v2) typos corrected, English improved, More
references added;v3) 32 pages, 16 figures, the third author newly added,
previous main theorem improved, density question resolved and many more
results on relative ball packings adde
Entanglement of indistinguishable particles as a probe for quantum phase transitions in the extended Hubbard model
We investigate the quantum phase transitions of the extended Hubbard model at
half-filling with periodic boundary conditions employing the entanglement of
particles, as opposed to the more traditional entanglement of modes. Our
results show that the entanglement has either discontinuities or local minima
at the critical points. We associate the discontinuities to first order
transitions, and the minima to second order ones. Thus we show that the
entanglement of particles can be used to derive the phase diagram, except for
the subtle transitions between the phases SDW-BOW, and the superconductor
phases TS-SS.Comment: Improved text and dicussions. Added finite size scaling analysis. 9
pages, 8 figures. Accepted for publication in Phys. Rev.
- β¦