40,498 research outputs found
About the Dedekind psi function in Pauli graphs
We study the commutation structure within the Pauli groups built on all
decompositions of a given Hilbert space dimension , containing a square,
into its factors. The simplest illustrative examples are the quartit ()
and two-qubit () systems. It is shown how the sum of divisor function
and the Dedekind psi function enter
into the theory for counting the number of maximal commuting sets of the qudit
system. In the case of a multiple qudit system (with and a prime),
the arithmetical functions and count the
cardinality of the symplectic polar space that endows the
commutation structure and its punctured counterpart, respectively. Symmetry
properties of the Pauli graphs attached to these structures are investigated in
detail and several illustrative examples are provided.Comment: Proceedings of Quantum Optics V, Cozumel to appear in Revista
Mexicana de Fisic
Quantum States Arising from the Pauli Groups, Symmetries and Paradoxes
We investigate multiple qubit Pauli groups and the quantum states/rays
arising from their maximal bases. Remarkably, the real rays are carried by a
Barnes-Wall lattice (). We focus on the smallest subsets of rays
allowing a state proof of the Bell-Kochen-Specker theorem (BKS). BKS theorem
rules out realistic non-contextual theories by resorting to impossible
assignments of rays among a selected set of maximal orthogonal bases. We
investigate the geometrical structure of small BKS-proofs involving
rays and -dimensional bases of -qubits. Specifically, we look at the
classes of parity proofs 18-9 with two qubits (A. Cabello, 1996), 36-11 with
three qubits (M. Kernaghan & A. Peres, 1995) and related classes. One finds
characteristic signatures of the distances among the bases, that carry various
symmetries in their graphs.Comment: The XXIXth International Colloquium on Group-Theoretical Methods in
Physics, China (2012
The Fast Multipole Method and Point Dipole Moment Polarizable Force Fields
We present an implementation of the fast multipole method for computing
coulombic electrostatic and polarization forces from polarizable force-fields
based on induced point dipole moments. We demonstrate the expected
scaling of that approach by performing single energy point calculations on
hexamer protein subunits of the mature HIV-1 capsid. We also show the long time
energy conservation in molecular dynamics at the nanosecond scale by performing
simulations of a protein complex embedded in a coarse-grained solvent using a
standard integrator and a multiple time step integrator. Our tests show the
applicability of FMM combined with state-of-the-art chemical models in
molecular dynamical systems.Comment: 11 pages, 8 figures, accepted by J. Chem. Phy
Spin and chiral stiffness of the XY spin glass in two dimensions
We analyze the zero-temperature behavior of the XY Edwards-Anderson spin
glass model on a square lattice. A newly developed algorithm combining exact
ground-state computations for Ising variables embedded into the planar spins
with a specially tailored evolutionary method, resulting in the genetic
embedded matching (GEM) approach, allows for the computation of numerically
exact ground states for relatively large systems. This enables a thorough
re-investigation of the long-standing questions of (i) extensive degeneracy of
the ground state and (ii) a possible decoupling of spin and chiral degrees of
freedom in such systems. The new algorithm together with appropriate choices
for the considered sets of boundary conditions and finite-size scaling
techniques allows for a consistent determination of the spin and chiral
stiffness scaling exponents.Comment: 6 pages, 2 figures, proceedings of the HFM2006 conference, to appear
in a special issue of J. Phys.: Condens. Matte
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