21,596 research outputs found
Factorization of the Non-Stationary Schrodinger Operator
We consider a factorization of the non-stationary Schrodinger operator based
on the parabolic Dirac operator introduced by Cerejeiras/ Kahler/ Sommen. Based
on the fundamental solution for the parabolic Dirac operators, we shall
construct appropriated Teodorescu and Cauchy-Bitsadze operators. Afterwards we
will describe how to solve the nonlinear Schrodinger equation using Banach
fixed point theorem.Comment: Accepted for publication in Advances in Applied Clifford Algebra
Signatures of the self-modulation instability of relativistic proton bunches in the AWAKE experiment
We investigate numerically the detection of the self-modulation instability
in a virtual detector located downstream from the plasma in the context of
AWAKE. We show that the density structures, appearing in the temporally
resolving virtual detector, map the transverse beam phase space distribution at
the plasma exit. As a result, the proton bunch radius that appears to grow
along the bunch in the detector results from the divergence increase along the
bunch, related with the spatial growth of the self-modulated wakefields. In
addition, asymmetric bunch structures in the detector are a result of
asymmetries of the bunch divergence, and do not necessarily reflect asymmetric
beam density distributions in the plasma.Comment: Accepted for publication in NIM-A for the proceedings of the 3rd
European Advanced Accelerator Workshop. 5 pages, 2 figure
Chaos in Periodically Perturbed Monopole + Quadrupole Like Potentials
The motion of a particle that suffers the influence of simple inner (outer)
periodic perturbations when it evolves around a center of attraction modeled by
an inverse square law plus a quadrupole-like term is studied. The equations of
motion are used to reduce the Melnikov method to the study of simple graphics.Comment: 12 pages, 6 Postscript figure
Phase diagram of random lattice gases in the annealed limit
An analysis of the random lattice gas in the annealed limit is presented. The
statistical mechanics of disordered lattice systems is briefly reviewed. For
the case of the lattice gas with an arbitrary uniform interaction potential and
random short-range interactions the annealed limit is discussed in detail. By
identifying and extracting an entropy of mixing term, a correct physical
expression for the pressure is explicitly given. As an application, the
one-dimensional lattice gas with uniform long-range interactions and random
short-range interactions satisfying a bimodal annealed probability distribution
is discussed. The model is exactly solved and is shown to present interesting
behavior in the presence of competition between interactions, such as the
presence of three phase transitions at constant temperature and the occurrence
of triple and quadruple points.Comment: Final version to be published in the Journal of Chemical Physic
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