Fast Quantum Maps
We develop number theoretic tools that allow to perform computations relevant for the quantum mechanics over finite fields of arbitrary, odd size, with the same speedup that is enjoyed by the Fast Fourier Transform.
math-ph↗
arXiv subjects
G. G. Athanasiu
Publications and source records attributed to G. G. Athanasiu.
K-system generator of pseudorandom numbers on Galois field
We analyze the structure of the periodic trajectories of the K-system generator of pseudorandom numbers on rational sublattice which coincides with the Galois field. The period of the trajectories increases as a function of lattice size and the dimension of the K-matrix. We emphasize the connection of this approach with the one which is based on primitive matrices over Galois fields.
physics.comp-ph↗
Holomorphic Quantization on the Torus and Finite Quantum Mechanics
We construct explicitly the quantization of classical linear maps of $SL(2, R)$ on toroidal phase space, of arbitrary modulus, using the holomorphic (chiral) version of the metaplectic representation. We show that Finite Quantum Mechanics (FQM) on tori of arbitrary integer discretization, is a consistent restriction of the holomorphic quantization of $SL(2, Z)$ to the subgroup $SL(2, Z)/Γ_l$, $Γ_l$ being the principal congruent subgroup mod l, on a finite dimensional Hilbert space. The generators of the ``rotation group'' mod l, $O_{l}(2)\subset SL(2,l)$, for arbitrary values of l are determined as well as their quantum mechanical eigenvalues and eigenstates.
hep-th↗
Period of K System Generator of Pseudorandom Numbers
We analyze the structure of the periodic trajectories of the matrix generator of pseudorandom numbers which has been proposed earlier. The structure of the periodic trajectories becomes more transparent when the rational sublattice coincides with the Galois field $GF[p]$. We are able to compute the period of the trajectories as a function of $p$ and the dimension of the matrix $d$.
hep-lat↗