34,334 research outputs found
Quantum Singularities in Spacetimes with Spherical and Cylindrical Topological Defects
Exact solutions of Einstein equations with null Riemman-Christoffel curvature
tensor everywhere, except on a hypersurface, are studied using quantum
particles obeying the Klein-Gordon equation. We consider the particular cases
when the curvature is represented by a Dirac delta function with support either
on a sphere or on a cylinder (spherical and cylindrical shells). In particular,
we analyze the necessity of extra boundary conditions on the shells.Comment: 7 page,1 fig., Revtex, J. Math. Phys, in pres
Point interactions in acoustics: one dimensional models
A one dimensional system made up of a compressible fluid and several
mechanical oscillators, coupled to the acoustic field in the fluid, is analyzed
for different settings of the oscillators array. The dynamical models are
formulated in terms of singular perturbations of the decoupled dynamics of the
acoustic field and the mechanical oscillators. Detailed spectral properties of
the generators of the dynamics are given for each model we consider. In the
case of a periodic array of mechanical oscillators it is shown that the energy
spectrum presents a band structure.Comment: revised version, 30 pages, 2 figure
The benefits of parenting: Government financial support for families with children since 1975
This commentary describes the changes to the structure of child-contingent support through the tax and benefit system since 1975. It also presents new results, which were produced to quantify explicitly the amount of government support for families with children, using representative samples of families from over the past three decades. With these data, it is possible to examine whether child-contingent support has become more or less progressive, or more or less slanted towards large families, lone-parents families or families with young children
Distribution of the very first PopIII stars and their relation to bright z~6 quasars
We discuss the link between dark matter halos hosting the first PopIII stars
and the rare, massive, halos that are generally considered to host bright
quasars at high redshift z~6. The main question that we intend to answer is
whether the super-massive black holes powering these QSOs grew out from the
seeds planted by the first intermediate massive black holes created in the
universe. This question involves a dynamical range of 10^13 in mass and we
address it by combining N-body simulations of structure formation to identify
the most massive halos at z~6 with a Monte Carlo method based on linear theory
to obtain the location and formation times of the first light halos within the
whole simulation box. We show that the descendants of the first ~10^6 Msun
virialized halos do not, on average, end up in the most massive halos at z~6,
but rather live in a large variety of environments. The oldest PopIII
progenitors of the most massive halos at z~6, form instead from density peaks
that are on average one and a half standard deviations more common than the
first PopIII star formed in the volume occupied by one bright high-z QSO. The
intermediate mass black hole seeds planted by the very first PopIII stars at
z>40 can easily grow to masses m_BH>10^9.5 Msun by z=6 assuming Eddington
accretion with radiative efficiency \epsilon~0.1. Quenching of the black hole
accretion is therefore crucial to avoid an overabundance of supermassive black
holes at lower redshift. This can be obtained if the mass accretion is limited
to a fraction \eta~6*10^{-3} of the total baryon mass of the halo hosting the
black hole. The resulting high end slope of the black hole mass function at z=6
is \alpha ~ -3.7, a value within the 1\sigma error bar for the bright end slope
of the observed quasar luminosity function at z=6.Comment: 30 pages, 9 figures, ApJ accepte
Path-Integral Formulation of Pseudo-Hermitian Quantum Mechanics and the Role of the Metric Operator
We provide a careful analysis of the generating functional in the path
integral formulation of pseudo-Hermitian and in particular PT-symmetric quantum
mechanics and show how the metric operator enters the expression for the
generating functional.Comment: Published version, 4 page
Strong-coupling asymptotic expansion for Schr\"odinger operators with a singular interaction supported by a curve in
We investigate a class of generalized Schr\"{o}dinger operators in
with a singular interaction supported by a smooth curve
. We find a strong-coupling asymptotic expansion of the discrete
spectrum in case when is a loop or an infinite bent curve which is
asymptotically straight. It is given in terms of an auxiliary one-dimensional
Schr\"{o}dinger operator with a potential determined by the curvature of
. In the same way we obtain an asymptotics of spectral bands for a
periodic curve. In particular, the spectrum is shown to have open gaps in this
case if is not a straight line and the singular interaction is strong
enough.Comment: LaTeX 2e, 30 pages; minor improvements, to appear in Rev. Math. Phy
A new proof of the analyticity of the electronic density of molecules
We give a new, short proof of the regularity away from the nuclei of the
electronic density of a molecule obtained in [1,2]. The new argument is based
on the regularity properties of the Coulomb interactions underlined in [3,4]
and on well-known elliptic technics. [1] S. Fournais, M. Hoffmann-Ostenhof, T.
Hoffmann-Ostenhof, T. Oe stergaard Soerensen: The electron density is smooth
away from the nuclei. Comm. Math. Phys. 228, no. 3 (2002), 401-415. [2] S.
Fournais, M. Hoffmann-Ostenhof, T. Hoffmann-Ostenhof, T. Oestergaard Soerensen:
Analyticity of the density of electronic wave functions. Ark. Mat. 42, no. 1
(2004), 87-106. [3] W. Hunziker: Distortion analyticity and molecular
resonances curves. Ann. Inst. H. Poincar\'e, s. A, t. 45, no 4, 339-358 (1986).
[4] M. Klein, A. Martinez, R. Seiler, X.P. Wang: On the Born-Oppenheimer
expansion for polyatomic molecules. Comm. Math. Phys. 143, no. 3, 607-639
(1992). The paper is published in Letters in Mathematical Physics 93, number 1,
pp. 73-83, 2010. The original publication is available at "
www.springerlink.com "
Long-Time Dynamics of Variable Coefficient mKdV Solitary Waves
We study the Korteweg-de Vries-type equation dt u=-dx(dx^2 u+f(u)-B(t,x)u),
where B is a small and bounded, slowly varying function and f is a
nonlinearity. Many variable coefficient KdV-type equations can be rescaled into
this equation. We study the long time behaviour of solutions with initial
conditions close to a stable, B=0 solitary wave. We prove that for long time
intervals, such solutions have the form of the solitary wave, whose centre and
scale evolve according to a certain dynamical law involving the function
B(t,x), plus an H^1-small fluctuation.Comment: 19 page
Multiparticle Schrodinger operators with point interactions in the plane
We study a system of N bosons in the plane interacting with delta function
potentials. After a coupling constant renormalization we show that the
Hamiltonian defines a self-adjoint operator and obtain a lower bound for the
energy. The same results hold if one includes a regular inter-particle
potential.Comment: 17 pages, Late
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