500 research outputs found
Growth function for an -valued dynamics
This article answers the question of V.M. Buchstaber about the growth
function of a particular -valued group. This question is closely related to
discrete integrable systems. In this paper, we will find a formula for the
growth function in the case when is prime. In addition, we will prove a
polynomial asymptotic estimate for the growth function in the general case.
Finally, we will pose new problems and hypotheses about growth functions
On the solutions of the local Zamolodchikov tetrahedron equation
We study the solutions of the local Zamolodhcikov tetrahedron equation in the
form of correspondences derived by matrices. We present all the
associated generators of 4-simplex maps satisfying the local tetrahedron
equation. Moreover, we demonstrate that, from some of our solutions, we can
recover the 4-simplex extensions of Kashaev--Korepanov--Sergeev and Hirota type
tetrahedron maps. Finally, we construct several novel 4-simplex maps.Comment: 15 pages, 1 figur
Dynamical localization, measurements and quantum computing
We study numerically the effects of measurements on dynamical localization in
the kicked rotator model simulated on a quantum computer. Contrary to the
previous studies, which showed that measurements induce a diffusive probability
spreading, our results demonstrate that localization can be preserved for
repeated single-qubit measurements. We detect a transition from a localized to
a delocalized phase, depending on the system parameters and on the choice of
the measured qubit.Comment: 4 pages, 4 figures, research at Quantware MIPS Center
http://www.quantware.ups-tlse.f
Fractal Spin Glass Properties of Low Energy Configurations in the Frenkel-Kontorova chain
We study numerically and analytically the classical one-dimensional
Frenkel-Kontorova chain in the regime of pinned phase characterized by phonon
gap. Our results show the existence of exponentially many static equilibrium
configurations which are exponentially close to the energy of the ground state.
The energies of these configurations form a fractal quasi-degenerate band
structure which is described on the basis of elementary excitations. Contrary
to the ground state, the configurations inside these bands are disordered.Comment: revtex, 9 pages, 9 figure
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