9,910 research outputs found
Infinite Dimensional Pathwise Volterra Processes Driven by Gaussian Noise -- Probabilistic Properties and Applications
We investigate the probabilistic and analytic properties of Volterra
processes constructed as pathwise integrals of deterministic kernels with
respect to the H\"older continuous trajectories of Hilbert-valued Gaussian
processes. To this end, we extend the Volterra sewing lemma from
\cite{HarangTindel} to the two dimensional case, in order to construct two
dimensional operator-valued Volterra integrals of Young type. We prove that the
covariance operator associated to infinite dimensional Volterra processes can
be represented by such a two dimensional integral, which extends the current
notion of representation for such covariance operators. We then discuss a
series of applications of these results, including the construction of a rough
path associated to a Volterra process driven by Gaussian noise with possibly
irregular covariance structures, as well as a description of the irregular
covariance structure arising from Gaussian processes time-shifted along
irregular trajectories. Furthermore, we consider an infinite dimensional
fractional Ornstein-Uhlenbeck process driven by Gaussian noise, which can be
seen as an extension of the volatility model proposed by Rosenbaum et al. in
\cite{ElEuchRosenbaum}.Comment: 38 page
Representation by Integrating Reproducing Kernels
Based on direct integrals, a framework allowing to integrate a parametrised
family of reproducing kernels with respect to some measure on the parameter
space is developed. By pointwise integration, one obtains again a reproducing
kernel whose corresponding Hilbert space is given as the image of the direct
integral of the individual Hilbert spaces under the summation operator. This
generalises the well-known results for finite sums of reproducing kernels;
however, many more special cases are subsumed under this approach: so-called
Mercer kernels obtained through series expansions; kernels generated by
integral transforms; mixtures of positive definite functions; and in particular
scale-mixtures of radial basis functions. This opens new vistas into known
results, e.g. generalising the Kramer sampling theorem; it also offers
interesting connections between measurements and integral transforms, e.g.
allowing to apply the representer theorem in certain inverse problems, or
bounding the pointwise error in the image domain when observing the pre-image
under an integral transform
Control of electron spin and orbital resonance in quantum dots through spin-orbit interactions
Influence of resonant oscillating electromagnetic field on a single electron
in coupled lateral quantum dots in the presence of phonon-induced relaxation
and decoherence is investigated. Using symmetry arguments it is shown that spin
and orbital resonance can be efficiently controlled by spin-orbit interactions.
The control is possible due to the strong sensitivity of Rabi frequency to the
dot configuration (orientation of the dot and a static magnetic field) as a
result of the anisotropy of the spin-orbit interactions. The so called easy
passage configuration is shown to be particularly suitable for magnetic
manipulation of spin qubits, ensuring long spin relaxation time and protecting
the spin qubit from electric field disturbances accompanying on-chip
manipulations.Comment: 11 pages, 5 figures; v2: introduction and conclusions broadened,
moderate structure and content change
Spectrum of Low-Lying Excitations in a Supersymmetric Extended Hubbard Model
We continue the study of the -supersymmetric extension of the Hubbard
model in one dimension. We determine the excitation spectrum at zero
temperature even in the sectors where the ground states are
-descendants of Bethe states. The excitations include spinons, holons,
electrons, localons (local electrons pairs, moving coherently through the
lattice) and their bound states. The spectra are found to be very different for
repulsive and attractive on-site interaction. We also study the thermodynamics
of the model.Comment: 37 pages, uuencoded compressed postscript fil
Fuelling quasars with hot gas
We consider a model for quasar formation in which massive black holes are
formed and fuelled largely by the accretion of hot gas during the process of
galaxy formation. In standard hierarchical collapse models, objects about the
size of normal galaxies and larger form a dense hot atmosphere when they
collapse. We show that if such an atmosphere forms a nearly "maximal" cooling
flow, then a central black hole can accrete at close to its Eddington limit.
This leads to exponential growth of a seed black hole, resulting in a quasar in
some cases. In this model, the first quasars form soon after the first
collapses to produce hot gas. The hot gas is depleted as time progresses,
mostly by cooling, so that the accretion rate eventually falls below the
threshold for advection-dominated accretion, at which stage radiative
efficiency plummets and any quasar turns off. A simple implementation of this
model, incorporated into a semi-analytical model for galaxy formation,
over-produces quasars when compared with observed luminosity functions, but is
consistent with models of the X-ray Background which indicate that most
accretion is obscured. It produces few quasars at high redshift due to the lack
of time needed to grow massive black holes. Quasar fuelling by hot gas provides
a minimum level, sufficient to power most quasars at redshifts between one and
two, to which other sources of fuel can be added. The results are sensitive to
feedback effects, such as might be due to radio jets and other outflows.Comment: 12 pages, 6 figures, MN Latex style, accepted for publication in
MNRA
The role of cooling flows in galaxy formation
The present structure of galaxies is governed by the radiative dissipation of
the gravitational and supernova energy injected during formation. A crucial
aspect of this process is whether the gas cools as fast as it falls into the
gravitational potential well. If it does then rapid normal star formation is
assumed to ensue. If not, and the gas can still cool by the present time, then
the situation resembles that of a cooling flow, such as commonly found in
clusters of galaxies. The cooled matter is assumed to accumulate as very cold
clouds and/or low mass stars, i.e. as baryonic dark matter. In this paper we
investigate the likelihood of a cooling flow phase during the hierarchical
formation of galaxies. We concentrate on the behaviour of the gas, using a
highly simplified treatment of the evolution of the dark matter potential
within which the gas evolves. We assume that normal star formation is limited
by how much gas the associated supernovae can unbind and allow the gas profile
to flatten as a consequence of supernova energy injection. We find that cooling
flows are an important phase in the formation of most galaxies with total (dark
plus luminous) masses approxgt 10^12 Msun , creating about 20 per cent of the
total dark halo in a galaxy such as our own and a smaller but comparable
fraction of an elliptical galaxy of similar mass. The onset of a cooling flow
determines the upper mass limit for the formation of a visible spheroid from
gas, setting a characteristic mass scale for normal galaxies. We argue that
disk formation requires a cooling flow phase and that dissipation in the
cooling flow phase is the most important factor in the survival of normal
galaxies during subsequent hierarchical mergers.Comment: uuencoded compressed postscript. The preprint is also available at
http://www.ast.cam.ac.uk/preprint/PrePrint.htm
Existence of mesons after deconfinement
We investigate the possibility for a quark-antiquark pair to form a bound
state at temperatures higher than the critical one (), thus after
deconfinement. Our main goal is to find analytical criteria constraining the
existence of such mesons. Our formalism relies on a Schr\"{o}dinger equation
for which we study the physical consequences of both using the free energy and
the internal energy as potential term, assuming a widely accepted
temperature-dependent Yukawa form for the free energy and a recently proposed
nonperturbative form for the screening mass. We show that using the free energy
only allows for the 1S bottomonium to be bound above , with a dissociation
temperature around . The situation is very different with the
internal energy, where we show that no bound states at all can exist in the
deconfined phase. But, in this last case, quasi-bound states could be present
at higher temperatures because of a positive barrier appearing in the
potential.Comment: 14 pages, 3 figures; only the case T>T_c is discussed in v
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