778 research outputs found
Quivers, curves, and the tropical vertex
Elements of the tropical vertex group are formal families of
symplectomorphisms of the 2-dimensional algebraic torus. Commutators in the
group are related to Euler characteristics of the moduli spaces of quiver
representations and the Gromov-Witten theory of toric surfaces. After a short
survey of the subject (based on lectures of Pandharipande at the 2009 Geometry
summer school in Lisbon), we prove new results about the rays and symmetries of
scattering diagrams of commutators (including previous conjectures by
Gross-Siebert and Kontsevich). Where possible, we present both the quiver and
Gromov-Witten perspectives.Comment: 43 page
Ground State Properties of Fermi Gases in the Strongly Interacting Regime
The ground state energies and pairing gaps in dilute superfluid Fermi gases
have now been calculated with the quantum Monte Carlo method without detailed
knowledge of their wave functions. However, such knowledge is essential to
predict other properties of these gases such as density matrices and pair
distribution functions. We present a new and simple method to optimize the wave
functions of quantum fluids using Green's function Monte Carlo method. It is
used to calculate the pair distribution functions and potential energies of
Fermi gases over the entire regime from atomic Bardeen-Cooper-Schrieffer
superfluid to molecular Bose-Einstein condensation, spanned as the interaction
strength is varied.Comment: 4 pages, 4 figure
Neutron Stars and the Cosmological Constant Problem
The gravitational aether theory is a modification of general relativity that
decouples vacuum energy from gravity, and thus can potentially address the
cosmological constant problem. The classical theory is distinguishable from
general relativity only in the presence of relativistic pressure (or
vorticity). Since the interior of neutron stars has high pressure and as their
mass and radius can be measured observationally, they are the perfect
laboratory for testing the validity of the aether theory. In this paper, we
solve the equations of stellar structure for the gravitational aether theory
and find the predicted mass-radius relation of non-rotating neutron stars using
two different realistic proposals for the equation of state of nuclear matter.
We find that the maximum neutron star mass predicted by the aether theory is
12% - 16% less than the maximum mass predicted by general relativity assuming
these two equations of state. We also show that the effect of aether is similar
to modifying the equation of state in general relativity. The effective
pressure of the neutron star given by the aether theory at a fiducial density
differs from the values given by the two nuclear equations of state to an
extent that can be constrained using future gravitational wave observations of
neutron stars in compact systems. This is a promising way to test the aether
theory if further progress is made in constraining the equation of state of
nuclear matter in densities above the nuclear saturation density.Comment: 8 pages, 6 figure
Holomorphic anomaly equations and the Igusa cusp form conjecture
Let be a K3 surface and let be an elliptic curve. We solve the
reduced Gromov-Witten theory of the Calabi-Yau threefold for all
curve classes which are primitive in the K3 factor. In particular, we deduce
the Igusa cusp form conjecture.
The proof relies on new results in the Gromov-Witten theory of elliptic
curves and K3 surfaces. We show the generating series of Gromov-Witten classes
of an elliptic curve are cycle-valued quasimodular forms and satisfy a
holomorphic anomaly equation. The quasimodularity generalizes a result by
Okounkov and Pandharipande, and the holomorphic anomaly equation proves a
conjecture of Milanov, Ruan and Shen. We further conjecture quasimodularity and
holomorphic anomaly equations for the cycle-valued Gromov-Witten theory of
every elliptic fibration with section. The conjecture generalizes the
holomorphic anomaly equations for ellliptic Calabi-Yau threefolds predicted by
Bershadsky, Cecotti, Ooguri, and Vafa. We show a modified conjecture holds
numerically for the reduced Gromov-Witten theory of K3 surfaces in primitive
classes.Comment: 68 page
Center-of-mass effects on the quasi-hole spectroscopic factors in the 16O(e,e'p) reaction
The spectroscopic factors for the low-lying quasi-hole states observed in the
16O(e,e'p)15N reaction are reinvestigated with a variational Monte Carlo
calculation for the structure of the initial and final nucleus. A computational
error in a previous report is rectified. It is shown that a proper treatment of
center-of-mass motion does not lead to a reduction of the spectroscopic factor
for -shell quasi-hole states, but rather to a 7% enhancement. This is in
agreement with analytical results obtained in the harmonic oscillator model.
The center-of-mass effect worsens the discrepancy between present theoretical
models and the experimentally observed single-particle strength. We discuss the
present status of this problem, including some other mechanisms that may be
relevant in this respect.Comment: 14 pages, no figures, uses Revtex, to be published in Phys. Rev. C 58
(1998
Kaon Energies in Dense Matter
We discuss the role of kaon-nucleon and nucleon-nucleon correlations in kaon
condensation in dense matter. Correlations raise the threshold density for kaon
condensation, possibly to densities higher than those encountered in stable
neutron stars.Comment: RevTeX, 11 pages, 2 PostScript figures; manuscript also available, in
PostScript form, at http://www.nordita.dk/locinfo/preprints.htm
Cold Bose gases with large scattering lengths
We calculate the energy and condensate fraction for a dense system of bosons
interacting through an attractive short range interaction with positive s-wave
scattering length . At high densities, , the energy per particle,
chemical potential, and square of the sound speed are independent of the
scattering length and proportional to , as in Fermi systems.Comment: 4 pages, 3 figure
Curve counting via stable pairs in the derived category
For a nonsingular projective 3-fold , we define integer invariants
virtually enumerating pairs where is an embedded curve and
is a divisor. A virtual class is constructed on the associated
moduli space by viewing a pair as an object in the derived category of . The
resulting invariants are conjecturally equivalent, after universal
transformations, to both the Gromov-Witten and DT theories of . For
Calabi-Yau 3-folds, the latter equivalence should be viewed as a wall-crossing
formula in the derived category.
Several calculations of the new invariants are carried out. In the Fano case,
the local contributions of nonsingular embedded curves are found. In the local
toric Calabi-Yau case, a completely new form of the topological vertex is
described.
The virtual enumeration of pairs is closely related to the geometry
underlying the BPS state counts of Gopakumar and Vafa. We prove that our
integrality predictions for Gromov-Witten invariants agree with the BPS
integrality. Conversely, the BPS geometry imposes strong conditions on the
enumeration of pairs.Comment: Corrected typos and duality error in Proposition 4.6. 47 page
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