7 research outputs found
Multiplicities of Periodic Orbit Lengths for Non-Arithmetic Models
Multiplicities of periodic orbit lengths for non-arithmetic Hecke triangle
groups are discussed. It is demonstrated both numerically and analytically that
at least for certain groups the mean multiplicity of periodic orbits with
exactly the same length increases exponentially with the length. The main
ingredient used is the construction of joint distribution of periodic orbits
when group matrices are transformed by field isomorphisms. The method can be
generalized to other groups for which traces of group matrices are integers of
an algebraic field of finite degree
Quantum baker maps with controlled-NOT coupling
The characteristic stretching and squeezing of chaotic motion is linearized
within the finite number of phase space domains which subdivide a classical
baker map. Tensor products of such maps are also chaotic, but a more
interesting generalized baker map arises if the stacking orders for the factor
maps are allowed to interact. These maps are readily quantized, in such a way
that the stacking interaction is entirely attributed to primary qubits in each
map, if each subsystem has power-of-two Hilbert space dimension. We here study
the particular example of two baker maps that interact via a controlled-not
interaction. Numerical evidence indicates that the control subspace becomes an
ideal Markovian environment for the target map in the limit of large Hilbert
space dimension.Comment: 8 page
Point perturbations of circle billiards
The spectral statistics of the circular billiard with a point-scatterer is
investigated. In the semiclassical limit, the spectrum is demonstrated to be
composed of two uncorrelated level sequences. The first corresponds to states
for which the scatterer is located in the classically forbidden region and its
energy levels are not affected by the scatterer in the semiclassical limit
while the second sequence contains the levels which are affected by the
point-scatterer. The nearest neighbor spacing distribution which results from
the superposition of these sequences is calculated analytically within some
approximation and good agreement with the distribution that was computed
numerically is found.Comment: 9 pages, 2 figure