431 research outputs found
Tensorial characterization and quantum estimation of weakly entangled qubits
In the case of two qubits, standard entanglement monotones like the linear
entropy fail to provide an efficient quantum estimation in the regime of weak
entanglement. In this paper, a more efficient entanglement estimation, by means
of a novel class of entanglement monotones, is proposed. Following an approach
based on the geometric formulation of quantum mechanics, these entanglement
monotones are defined by inner products on invariant tensor fields on bipartite
qubit orbits of the group SU(2)xSU(2).Comment: 23 pages, 3 figure
Classical tensors from quantum states
The embedding of a manifold M into a Hilbert-space H induces, via the
pull-back, a tensor field on M out of the Hermitian tensor on H. We propose a
general procedure to compute these tensors in particular for manifolds
admitting a Lie-group structure.Comment: 20 pages, submitted to Int. J. Geom. Meth. Modern Physic
Classical Tensors and Quantum Entanglement II: Mixed States
Invariant operator-valued tensor fields on Lie groups are considered. These
define classical tensor fields on Lie groups by evaluating them on a quantum
state. This particular construction, applied on the local unitary group
U(n)xU(n), may establish a method for the identification of entanglement
monotone candidates by deriving invariant functions from tensors being by
construction invariant under local unitary transformations. In particular, for
n=2, we recover the purity and a concurrence related function (Wootters 1998)
as a sum of inner products of symmetric and anti-symmetric parts of the
considered tensor fields. Moreover, we identify a distinguished entanglement
monotone candidate by using a non-linear realization of the Lie algebra of
SU(2)xSU(2). The functional dependence between the latter quantity and the
concurrence is illustrated for a subclass of mixed states parametrized by two
variables.Comment: 23 pages, 4 figure
Classical Tensors and Quantum Entanglement I: Pure States
The geometrical description of a Hilbert space asociated with a quantum
system considers a Hermitian tensor to describe the scalar inner product of
vectors which are now described by vector fields. The real part of this tensor
represents a flat Riemannian metric tensor while the imaginary part represents
a symplectic two-form. The immersion of classical manifolds in the complex
projective space associated with the Hilbert space allows to pull-back tensor
fields related to previous ones, via the immersion map. This makes available,
on these selected manifolds of states, methods of usual Riemannian and
symplectic geometry. Here we consider these pulled-back tensor fields when the
immersed submanifold contains separable states or entangled states. Geometrical
tensors are shown to encode some properties of these states. These results are
not unrelated with criteria already available in the literature. We explicitly
deal with some of these relations.Comment: 16 pages, 1 figure, to appear in Int. J. Geom. Meth. Mod. Phy
Geometrical Description of Quantum Mechanics - Transformations and Dynamics
In this paper we review a proposed geometrical formulation of quantum
mechanics. We argue that this geometrization makes available mathematical
methods from classical mechanics to the quantum frame work. We apply this
formulation to the study of separability and entanglement for states of
composite quantum systems.Comment: 22 pages, to be published in Physica Script
Direct simulation of ion beam induced stressing and amorphization of silicon
Using molecular dynamics (MD) simulation, we investigate the mechanical
response of silicon to high dose ion-irradiation. We employ a realistic and
efficient model to directly simulate ion beam induced amorphization. Structural
properties of the amorphized sample are compared with experimental data and
results of other simulation studies. We find the behavior of the irradiated
material is related to the rate at which it can relax. Depending upon the
ability to deform, we observe either the generation of a high compressive
stress and subsequent expansion of the material, or generation of tensile
stress and densification. We note that statistical material properties, such as
radial distribution functions are not sufficient to differentiate between
different densities of amorphous samples. For any reasonable deformation rate,
we observe an expansion of the target upon amorphization in agreement with
experimental observations. This is in contrast to simulations of quenching
which usually result in denser structures relative to crystalline Si. We
conclude that although there is substantial agreement between experimental
measurements and most simulation results, the amorphous structures being
investigated may have fundamental differences; the difference in density can be
attributed to local defects within the amorphous network. Finally we show that
annealing simulations of our amorphized samples can lead to a reduction of high
energy local defects without a large scale rearrangement of the amorphous
network. This supports the proposal that defects in amorphous silicon are
analogous to those in crystalline silicon.Comment: 13 pages, 12 figure
Boolean Dynamics with Random Couplings
This paper reviews a class of generic dissipative dynamical systems called
N-K models. In these models, the dynamics of N elements, defined as Boolean
variables, develop step by step, clocked by a discrete time variable. Each of
the N Boolean elements at a given time is given a value which depends upon K
elements in the previous time step.
We review the work of many authors on the behavior of the models, looking
particularly at the structure and lengths of their cycles, the sizes of their
basins of attraction, and the flow of information through the systems. In the
limit of infinite N, there is a phase transition between a chaotic and an
ordered phase, with a critical phase in between.
We argue that the behavior of this system depends significantly on the
topology of the network connections. If the elements are placed upon a lattice
with dimension d, the system shows correlations related to the standard
percolation or directed percolation phase transition on such a lattice. On the
other hand, a very different behavior is seen in the Kauffman net in which all
spins are equally likely to be coupled to a given spin. In this situation,
coupling loops are mostly suppressed, and the behavior of the system is much
more like that of a mean field theory.
We also describe possible applications of the models to, for example, genetic
networks, cell differentiation, evolution, democracy in social systems and
neural networks.Comment: 69 pages, 16 figures, Submitted to Springer Applied Mathematical
Sciences Serie
Cast aluminium single crystals cross the threshold from bulk to size-dependent stochastic plasticity
Metals are known to exhibit mechanical behaviour at the nanoscale different to bulk samples. This transition typically initiates at the micrometre scale, yet existing techniques to produce micrometre-sized samples often introduce artefacts that can influence deformation mechanisms. Here, we demonstrate the casting of micrometre-scale aluminium single-crystal wires by infiltration of a salt mould. Samples have millimetre lengths, smooth surfaces, a range of crystallographic orientations, and a diameter D as small as 6 μm. The wires deform in bursts, at a stress that increases with decreasing D. Bursts greater than 200 nm account for roughly 50% of wire deformation and have exponentially distributed intensities. Dislocation dynamics simulations show that single-arm sources that produce large displacement bursts halted by stochastic cross-slip and lock formation explain microcast wire behaviour. This microcasting technique may be extended to several other metals or alloys and offers the possibility of exploring mechanical behaviour spanning the micrometre scale
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