4,925 research outputs found
Global in Time Solutions to Kolmogorov-Feller Pseudodifferential Equations with Small Parameter
The goal in this paper is to demonstrate a new method for constructing
global-in-time approximate (asymptotic) solutions of (pseudodifferential)
parabolic equations with a small parameter. We show that, in the leading term,
such a solution can be constructed by using characteristics, more precisely, by
using solutions of the corresponding Hamiltonian system and without using any
integral representation. For completeness, we also briefly describe the
well-known scheme developed by V.P.Maslov for constructing global-in-time
solutions.Comment: 27 page
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Beam instabilities in Very Large Hadron Collider
The Very Large Hadron Collider (VLHC) is a supercon-ducting proton-proton collider with approximately 100 TeV cm and approximately 10{sup 34} s{sup -1}cm{sup -2} luminosity [1]. Currently, beam dynamics in this future accelerator is the subject of intensive studies within the framework of the US-wide VLHC R&D program. This presentation sum-marizes recent developments in the field. Besides general discussion on relevant VLHC parameters, we consider various beam instabilities and ways to avoid them. Finally, we outline possibilities for theoretical and experimental R&D
Radio-frequency Bloch-transistor electrometer
A quantum-limited electrometer based on charge modulation of the Josephson
supercurrent in the Bloch transistor inserted into a superconducting ring is
proposed. As this ring is inductive coupled to a high-Q resonance tank circuit,
the variations of the charge on the transistor island (input signal) are
converted into variations of amplitude and phase of radio-frequency
oscillations in the tank. These variations are amplified and then detected. The
output noise, the back-action fluctuations and their cross-correlation are
computed. It is shown that our device enables measurements of the charge with a
sensitivity which is determined by the energy resolution of its amplifier, that
can be reduced down to the standard quantum limit of \hbar/2. On the basis of
this setup a "back-action-evading" scheme of the charge measurements is
proposed.Comment: 5 pages incl. 2 figure
Four-body Efimov effect
We study three same spin state fermions of mass M interacting with a
distinguishable particle of mass m in the unitary limit where the interaction
has a zero range and an infinite s-wave scattering length. We predict an
interval of mass ratio 13.384 < M/m < 13.607 where there exists a purely
four-body Efimov effect, leading to the occurrence of weakly bound tetramers
without Efimov trimers.Comment: 4 pages, 2 figure
Picard group of hypersurfaces in toric 3-folds
We show that the usual sufficient criterion for a generic hypersurface in a
smooth projective manifold to have the same Picard number as the ambient
variety can be generalized to hypersurfaces in complete simplicial toric
varieties. This sufficient condition is always satisfied by generic K3 surfaces
embedded in Fano toric 3-folds.Comment: 14 pages. v2: some typos corrected. v3: Slightly changed title. Final
version to appear in Int. J. Math., incorporates many (mainly expository)
changes suggested by the refere
The Hodge--Poincar\'e polynomial of the moduli spaces of stable vector bundles over an algebraic curve
Let X be a nonsingular complex projective variety that is acted on by a
reductive group and such that . We
give formulae for the Hodge--Poincar\'e series of the quotient .
We use these computations to obtain the corresponding formulae for the
Hodge--Poincar\'e polynomial of the moduli space of properly stable vector
bundles when the rank and the degree are not coprime. We compute explicitly the
case in which the rank equals 2 and the degree is even.Comment: Final published version. arXiv admin note: text overlap with
arXiv:math/0305346, arXiv:math/0305347 by other author
Parity nonconservation effects in the photodesintegration of polarized deuterons
P-odd correlations in the deuteron photodesintegration are considered. The
-meson exchange is not operative in the case of unpolarized deuterons. For
polarized deuterons a P-odd correlation due to the -meson exchange is
about . Short-distance P-odd contributions exceed essentially
than the contribution of the -meson exchange.Comment: 12 pages, Latex, 3 figure
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