4,444 research outputs found
Effects of non-local initial conditions in the Quantum Walk on the line
We report an enhancement of the decay rate of the survival probability when
non-local initial conditions in position space are considered in the Quantum
Walk on the line. It is shown how this interference effect can be understood
analytically by using previously derived results. Within a restricted position
subspace, the enhanced decay is correlated with a maximum asymptotic
entanglement level while the normal decay rate corresponds to initial relative
phases associated to a minimum entanglement level.Comment: 5 pages, 1 figure, Elsevier style, to appear in Physica
Anomalous diffusion in the resonant quantum kicked rotor
We study the resonances of the quantum kicked rotor subjected to an
excitation that follows a deterministic time-dependent prescription. For the
primary resonances we find an analytical relation between the long-time
behavior of the standard deviation and the external kick strength. For the
secondary resonances we obtain essentially the same result numerically.
Selecting the time sequence of the kick allows to obtain a variety of
asymptotic wave-function spreadings: super-ballistic, ballistic, sub-ballistic,
diffusive, sub-diffusive and localized.Comment: 5 pages, 3 figures To appear in Physica A
Quantum games via search algorithms
We build new quantum games, similar to the spin flip game, where as a novelty
the players perform measurements on a quantum system associated to a continuous
time search algorithm. The measurements collapse the wave function into one of
the two possible states. These games are characterized by a continuous space of
strategies and the selection of a particular strategy is determined by the
moments when the players measure.Comment: 4 pages, 3 figure
Quantum walk on the line: entanglement and non-local initial conditions
The conditional shift in the evolution operator of a quantum walk generates
entanglement between the coin and position degrees of freedom. This
entanglement can be quantified by the von Neumann entropy of the reduced
density operator (entropy of entanglement). In the long time limit, it
converges to a well defined value which depends on the initial state. Exact
expressions for the asymptotic (long-time) entanglement are obtained for (i)
localized initial conditions and (ii) initial conditions in the position
subspace spanned by the +1 and -1 position eigenstates.Comment: A few mistakes where corrected. One of them leads to a factor of 2 in
eq. (49), the other results remain unchanged. In this version, several
figures where replaced by color version
Driving quantum walk spreading with the coin operator
We generalize the discrete quantum walk on the line using a time dependent
unitary coin operator. We find an analytical relation between the long-time
behaviors of the standard deviation and the coin operator. Selecting the coin
time sequence allows to obtain a variety of predetermined asymptotic
wave-function spreadings: ballistic, sub-ballistic, diffusive, sub-diffusive
and localized.Comment: 6 pages, 3 figures, appendix added. to appear in PR
Driving the resonant quantum kicked rotor via extended initial conditions
We study the resonances of the quantum kicked rotor subjected to an extended
initial distribution. For the primary resonances we obtain the dispersion
relation for the map of this system. We find an analytical dependence of the
statistical moments on the shape of the initial distribution. For the secondary
resonances we obtain numerically a similar dependence. This allows us to devise
an extended initial condition which produces an average angular momentum
pointing in a preset direction which increases with time with a preset ratio.Comment: 6 pages, 5 figures, send to EPJ
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