98 research outputs found
Chaos in Andreev Billiards
A new type of classical billiard - the Andreev billiard - is investigated
using the tangent map technique. Andreev billiards consist of a normal region
surrounded by a superconducting region. In contrast with previously studied
billiards, Andreev billiards are integrable in zero magnetic field, {\it
regardless of their shape}. A magnetic field renders chaotic motion in a
generically shaped billiard, which is demonstrated for the Bunimovich stadium
by examination of both Poincar\'e sections and Lyapunov exponents. The issue of
the feasibility of certain experimental realizations is addressed.Comment: ReVTeX3.0, 4 pages, 3 figures appended as postscript file (uuencoded
with uufiles
Integrability and Ergodicity of Classical Billiards in a Magnetic Field
We consider classical billiards in plane, connected, but not necessarily
bounded domains. The charged billiard ball is immersed in a homogeneous,
stationary magnetic field perpendicular to the plane. The part of dynamics
which is not trivially integrable can be described by a "bouncing map". We
compute a general expression for the Jacobian matrix of this map, which allows
to determine stability and bifurcation values of specific periodic orbits. In
some cases, the bouncing map is a twist map and admits a generating function
which is useful to do perturbative calculations and to classify periodic
orbits. We prove that billiards in convex domains with sufficiently smooth
boundaries possess invariant tori corresponding to skipping trajectories.
Moreover, in strong field we construct adiabatic invariants over exponentially
large times. On the other hand, we present evidence that the billiard in a
square is ergodic for some large enough values of the magnetic field. A
numerical study reveals that the scattering on two circles is essentially
chaotic.Comment: Explanations added in Section 5, Section 6 enlarged, small errors
corrected; Large figures have been bitmapped; 40 pages LaTeX, 15 figures,
uuencoded tar.gz. file. To appear in J. Stat. Phys. 8
Prompt reactivity determination in a subcritical assembly through the response to a Dirac pulse
The full understanding of the kinetics of a subcritical assembly is a key issue for its online reactivity control. Point kinetics is not sufficient to determine the prompt reactivity of a subcritical assembly through the response to a dirac pulse, in particular in the cases of a large reflector, a small reactor, or a large subcriticality.Taking into account the distribution of intergeneration times, which appears as a robust characteristic of each type of reactor, helps to understand this behaviour.Eventually, a method is proposed for the determination of the prompt reactivity. It provides a decrease rate function depending on the prompt multiplication coefficient Keffp. Fitting a measured decrease rate with this function, calculated once for the reactor, gives the true value of keffp. The robustness of the method is tested. (Elsevier
Exact boundary conditions at finite distance for the time-dependent Schrodinger equation
Exact boundary conditions at finite distance for the solutions of the
time-dependent Schrodinger equation are derived. A numerical scheme based on
Crank-Nicholson method is proposed to illustrate its applicability in several
examples.Comment: Latex.tar.gz file, 20 pages, 9 figure
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