343 research outputs found
Frenkel-Kontorova model with cold trapped ions
We study analytically and numerically the properties of one-dimensional chain
of cold ions placed in a periodic potential of optical lattice and global
harmonic potential of a trap. In close similarity with the Frenkel-Kontorova
model, a transition from sliding to pinned phase takes place with the increase
of the optical lattice potential for the density of ions incommensurate with
the lattice period. Quantum fluctuations lead to a quantum phase transition and
melting of pinned instanton glass phase at large values of dimensional Planck
constant. The obtained results are also relevant for a Wigner crystal placed in
a periodic potential.Comment: RevTeX, 5 pages, 11 figures, research at
http://www.quantware.ups-tlse.f
Quantum synchronization
Using the methods of quantum trajectories we study numerically the phenomenon
of quantum synchronization in a quantum dissipative system with periodic
driving. Our results show that at small values of Planck constant the
classical devil's staircase remains robust with respect to quantum fluctuations
while at large values synchronization plateaus are destroyed. Quantum
synchronization in our model has close similarities with Shapiro steps in
Josephson junctions and it can be also realized in experiments with cold atoms.Comment: 5 pages, 5 figs, 1 fig added, research at
http://www.quantware.ups-tlse.f
Anderson transition for Google matrix eigenstates
We introduce a number of random matrix models describing the Google matrix G
of directed networks. The properties of their spectra and eigenstates are
analyzed by numerical matrix diagonalization. We show that for certain models
it is possible to have an algebraic decay of PageRank vector with the exponent
similar to real directed networks. At the same time the spectrum has no
spectral gap and a broad distribution of eigenvalues in the complex plain. The
eigenstates of G are characterized by the Anderson transition from localized to
delocalized states and a mobility edge curve in the complex plane of
eigenvalues.Comment: 9 pages, 12 figs, revte
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