2,092 research outputs found
Quantum network architecture of tight-binding models with substitution sequences
We study a two-spin quantum Turing architecture, in which discrete local
rotations \alpha_m of the Turing head spin alternate with quantum controlled
NOT-operations. Substitution sequences are known to underlie aperiodic
structures. We show that parameter inputs \alpha_m described by such sequences
can lead here to a quantum dynamics, intermediate between the regular and the
chaotic variant. Exponential parameter sensitivity characterizing chaotic
quantum Turing machines turns out to be an adequate criterion for induced
quantum chaos in a quantum network.Comment: Accepted for publication in J. mod. Optics [Proc. Workshop
"Entanglement and Decoherence", Gargnano (Italy), Sept 1999], 3 figure
Local Versus Global Thermal States: Correlations and the Existence of Local Temperatures
We consider a quantum system consisting of a regular chain of elementary
subsystems with nearest neighbor interactions and assume that the total system
is in a canonical state with temperature . We analyze under what condition
the state factors into a product of canonical density matrices with respect to
groups of subsystems each, and when these groups have the same temperature
. While in classical mechanics the validity of this procedure only depends
on the size of the groups , in quantum mechanics the minimum group size
also depends on the temperature ! As examples, we apply our
analysis to a harmonic chain and different types of Ising spin chains. We
discuss various features that show up due to the characteristics of the models
considered. For the harmonic chain, which successfully describes thermal
properties of insulating solids, our approach gives a first quantitative
estimate of the minimal length scale on which temperature can exist: This
length scale is found to be constant for temperatures above the Debye
temperature and proportional to below.Comment: 12 pages, 5 figures, discussion of results extended, accepted for
publication in Phys. Rev.
Analysis of contagion maps on a class of networks that are spatially embedded in a torus
A spreading process on a network is influenced by the network's underlying
spatial structure, and it is insightful to study the extent to which a
spreading process follows such structure. We consider a threshold contagion on
a network whose nodes are embedded in a manifold and where the network has both
`geometric edges', which respect the geometry of the underlying manifold, and
`non-geometric edges' that are not constrained by that geometry. Building on
ideas from Taylor et al. \cite{Taylor2015}, we examine when a contagion
propagates as a wave along a network whose nodes are embedded in a torus and
when it jumps via long non-geometric edges to remote areas of the network. We
build a `contagion map' for a contagion spreading on such a `noisy geometric
network' to produce a point cloud; and we study the dimensionality, geometry,
and topology of this point cloud to examine qualitative properties of this
spreading process. We identify a region in parameter space in which the
contagion propagates predominantly via wavefront propagation. We consider
different probability distributions for constructing non-geometric edges ---
reflecting different decay rates with respect to the distance between nodes in
the underlying manifold --- and examine the effect of such choices on the
qualitative properties of the spreading dynamics. Our work generalizes the
analysis in Taylor et al. and consolidates contagion maps both as a tool for
investigating spreading behavior on spatial networks and as a technique for
manifold learning
Measurable Consequences of the Local Breakdown of the Concept of Temperature
Local temperature defined by a local canonical state of the respective
subsystem, does not always exist in quantum many body systems. Here, we give
some examples of how this breakdown of the temperature concept on small length
scales might be observed in experiments: Measurements of magnetic properties of
an anti-ferromagnetic spin-1 chain. We show that those magnetic properties are
in fact strictly local. As a consequence their measurement reveals whether the
local (reduced) state can be thermal. If it is, a temperature may be associated
to the measurement results, while this would lead to inconsistencies otherwise.Comment: some comments added, results remain unchange
Multipartite entanglement in fermionic systems via a geometric measure
We study multipartite entanglement in a system consisting of
indistinguishable fermions. Specifically, we have proposed a geometric
entanglement measure for N spin-1/2 fermions distributed over 2L modes (single
particle states). The measure is defined on the 2L qubit space isomorphic to
the Fock space for 2L single particle states. This entanglement measure is
defined for a given partition of 2L modes containing m >= 2 subsets. Thus this
measure applies to m <= 2L partite fermionic system where L is any finite
number, giving the number of sites. The Hilbert spaces associated with these
subsets may have different dimensions. Further, we have defined the local
quantum operations with respect to a given partition of modes. This definition
is generic and unifies different ways of dividing a fermionic system into
subsystems. We have shown, using a representative case, that the geometric
measure is invariant under local unitaries corresponding to a given partition.
We explicitly demonstrate the use of the measure to calculate multipartite
entanglement in some correlated electron systems. To the best of our knowledge,
there is no usable entanglement measure of m > 3 partite fermionic systems in
the literature, so that this is the first measure of multipartite entanglement
for fermionic systems going beyond the bipartite and tripartite cases.Comment: 25 pages, 8 figure
Phase space contraction and quantum operations
We give a criterion to differentiate between dissipative and diffusive
quantum operations. It is based on the classical idea that dissipative
processes contract volumes in phase space. We define a quantity that can be
regarded as ``quantum phase space contraction rate'' and which is related to a
fundamental property of quantum channels: non-unitality. We relate it to other
properties of the channel and also show a simple example of dissipative noise
composed with a chaotic map. The emergence of attaractor-like structures is
displayed.Comment: 8 pages, 6 figures. Changes added according to refferee sugestions.
(To appear in PRA
Water issues in Hawaii: public attitudes in 2004 and 2010
This report examines Hawai‘i residents' awareness of, attitudes about, and actions taken concerning water quality. "Water quality" is a measure of the suitability of water for a particular use, such as drinking, recreation, agricultural irrigation, or protection and maintenance of aquatic life
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