1,239 research outputs found
Distortions Of The Phase Space Behavior Of A Particle During one-third integral Resonance Extraction
Symplectic tracking using point magnets and a reference orbit made of circular arcs and straight lines
Symplectic tracking of beam particles using point magnets is achieved using a
reference orbit made of circular arcs and straight lines that join smoothly
with each other. For this choice of the reference orbit, results are given for
the transfer functions, transfer matrices, and the transit times of the magnets
and drift spaces. These results provide a symplectic integrator, and allow the
linear orbit parameters to be computed by multiplying transfer matrices. It is
shown that this integrator is a second-order integrator, and that the transfer
functions can be derived from a hamiltonian.Comment: 16 pages, PDF fil
A direct proof of Kim's identities
As a by-product of a finite-size Bethe Ansatz calculation in statistical
mechanics, Doochul Kim has established, by an indirect route, three
mathematical identities rather similar to the conjugate modulus relations
satisfied by the elliptic theta constants. However, they contain factors like
and , instead of . We show here that
there is a fourth relation that naturally completes the set, in much the same
way that there are four relations for the four elliptic theta functions. We
derive all of them directly by proving and using a specialization of
Weierstrass' factorization theorem in complex variable theory.Comment: Latex, 6 pages, accepted by J. Physics
Proof that the Hydrogen-antihydrogen Molecule is Unstable
In the framework of nonrelativistic quantum mechanics we derive a necessary
condition for four Coulomb charges ,
where all masses are assumed finite, to form the stable system. The obtained
stability condition is physical and is expressed through the required minimal
ratio of Jacobi masses. In particular this provides the rigorous proof that the
hydrogen-antihydrogen molecule is unstable. This is the first result of this
sort for four particles.Comment: Submitted to Phys.Rev.Let
Electromagnetic Oscillations in a Driven Nonlinear Resonator: A New Description of Complex Nonlinear Dynamics
Many intriguing properties of driven nonlinear resonators, including the
appearance of chaos, are very important for understanding the universal
features of nonlinear dynamical systems and can have great practical
significance. We consider a cylindrical cavity resonator driven by an
alternating voltage and filled with a nonlinear nondispersive medium. It is
assumed that the medium lacks a center of inversion and the dependence of the
electric displacement on the electric field can be approximated by an
exponential function. We show that the Maxwell equations are integrated exactly
in this case and the field components in the cavity are represented in terms of
implicit functions of special form. The driven electromagnetic oscillations in
the cavity are found to display very interesting temporal behavior and their
Fourier spectra contain singular continuous components. To the best of our
knowledge, this is the first demonstration of the existence of a singular
continuous (fractal) spectrum in an exactly integrable system.Comment: 5 pages, 3 figure
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