28,757 research outputs found

### Quantum cryptography as a retrodiction problem

We propose a quantum key distribution protocol based on a quantum
retrodiction protocol, known as the Mean King problem. The protocol uses a two
way quantum channel. We show security against coherent attacks in a
transmission error free scenario, even if Eve is allowed to attack both
transmissions. This establishes a connection between retrodiction and key
distribution.Comment: 5 pages, 1 figur

### Quark-Gluon-Plasma Formation at SPS Energies?

By colliding ultrarelativistic ions, one achieves presently energy densities
close to the critical value, concerning the formation of a quark-gluon-plasma.
This indicates the importance of fluctuations and the necessity to go beyond
the investigation of average events. Therefore, we introduce a percolation
approach to model the final stage ($\tau > 1$ fm/c) of ion-ion collisions, the
initial stage being treated by well-established methods, based on strings and
Pomerons. The percolation approach amounts to finding high density domains, and
treating them as quark-matter droplets. In this way, we have a {\bf realistic,
microscopic, and Monte--Carlo based model which allows for the formation of
quark matter.} We find that even at SPS energies large quark-matter droplets
are formed -- at a low rate though. In other words: large quark-matter droplets
are formed due to geometrical fluctuation, but not in the average event.Comment: 7 Pages, HD-TVP-94-6 (1 uuencoded figure

### Propagation and spectral properties of quantum walks in electric fields

We study one-dimensional quantum walks in a homogeneous electric field. The
field is given by a phase which depends linearly on position and is applied
after each step. The long time propagation properties of this system, such as
revivals, ballistic expansion and Anderson localization, depend very
sensitively on the value of the electric field $\Phi$, e.g., on whether
$\Phi/(2\pi)$ is rational or irrational. We relate these properties to the
continued fraction expansion of the field. When the field is given only with
finite accuracy, the beginning of the expansion allows analogous conclusions
about the behavior on finite time scales.Comment: 7 pages, 4 figure

### The topological classification of one-dimensional symmetric quantum walks

We give a topological classification of quantum walks on an infinite 1D
lattice, which obey one of the discrete symmetry groups of the tenfold way,
have a gap around some eigenvalues at symmetry protected points, and satisfy a
mild locality condition. No translation invariance is assumed. The
classification is parameterized by three indices, taking values in a group,
which is either trivial, the group of integers, or the group of integers modulo
2, depending on the type of symmetry. The classification is complete in the
sense that two walks have the same indices if and only if they can be connected
by a norm continuous path along which all the mentioned properties remain
valid. Of the three indices, two are related to the asymptotic behaviour far to
the right and far to the left, respectively. These are also stable under
compact perturbations. The third index is sensitive to those compact
perturbations which cannot be contracted to a trivial one. The results apply to
the Hamiltonian case as well. In this case all compact perturbations can be
contracted, so the third index is not defined. Our classification extends the
one known in the translation invariant case, where the asymptotic right and
left indices add up to zero, and the third one vanishes, leaving effectively
only one independent index. When two translationally invariant bulks with
distinct indices are joined, the left and right asymptotic indices of the
joined walk are thereby fixed, and there must be eigenvalues at $1$ or $-1$
(bulk-boundary correspondence). Their location is governed by the third index.
We also discuss how the theory applies to finite lattices, with suitable
homogeneity assumptions.Comment: 36 pages, 7 figure

### Quantum Walks with Non-Orthogonal Position States

Quantum walks have by now been realized in a large variety of different
physical settings. In some of these, particularly with trapped ions, the walk
is implemented in phase space, where the corresponding position states are not
orthogonal. We develop a general description of such a quantum walk and show
how to map it into a standard one with orthogonal states, thereby making
available all the tools developed for the latter. This enables a variety of
experiments, which can be implemented with smaller step sizes and more steps.
Tuning the non-orthogonality allows for an easy preparation of extended states
such as momentum eigenstates, which travel at a well-defined speed with low
dispersion. We introduce a method to adjust their velocity by momentum shifts,
which allows to investigate intriguing effects such as the analog of Bloch
oscillations.Comment: 5 pages, 4 figure

### Summary: Remote sensing soil moisture research

During the 1969 and 1970 growing seasons research was conducted to investigate the relationship between remote sensing imagery and soil moisture. The research was accomplished under two completely different conditions: (1) cultivated cropland in east central South Dakota, and (2) rangeland in western South Dakota. Aerial and ground truth data are being studied and correlated in order to evaluate the moisture supply and water use. Results show that remote sensing is a feasible method for monitoring soil moisture

### Equilibrium states and invariant measures for random dynamical systems

Random dynamical systems with countably many maps which admit countable
Markov partitions on complete metric spaces such that the resulting Markov
systems are uniformly continuous and contractive are considered. A
non-degeneracy and a consistency conditions for such systems, which admit some
proper Markov partitions of connected spaces, are introduced, and further
sufficient conditions for them are provided. It is shown that every uniformly
continuous Markov system associated with a continuous random dynamical system
is consistent if it has a dominating Markov chain. A necessary and sufficient
condition for the existence of an invariant Borel probability measure for such
a non-degenerate system with a dominating Markov chain and a finite (16) is
given. The condition is also sufficient if the non-degeneracy is weakened with
the consistency condition. A further sufficient condition for the existence of
an invariant measure for such a consistent system which involves only the
properties of the dominating Markov chain is provided. In particular, it
implies that every such a consistent system with a finite Markov partition and
a finite (16) has an invariant Borel probability measure. A bijective map
between these measures and equilibrium states associated with such a system is
established in the non-degenerate case. Some properties of the map and the
measures are given.Comment: The article is published in DCDS-A, but without the 3rd paragraph on
page 4 (the complete removal of the paragraph became the condition for the
publication in the DCDS-A after the reviewer ran out of the citation
suggestions collected in the paragraph

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