404 research outputs found
Nonlinear nanomechanical resonators for quantum optoelectromechanics
We present a scheme for tuning and controlling nano mechanical resonators by
subjecting them to electrostatic gradient fields, provided by nearby tip
electrodes. We show that this approach enables access to a novel regime of
optomechanics, where the intrinsic nonlinearity of the nanoresonator can be
explored. In this regime, one or several laser driven cavity modes coupled to
the nanoresonator and suitably adjusted gradient fields allow to control the
motional state of the nanoresonator at the single phonon level. Some
applications of this platform have been presented previously [New J. Phys. 14,
023042 (2012), Phys. Rev. Lett. 110, 120503 (2013)]. Here, we provide a
detailed description of the corresponding setup and its optomechanical coupling
mechanisms, together with an in-depth analysis of possible sources of damping
or decoherence and a discussion of the readout of the nanoresonator state.Comment: 15 pages, 6 figure
Finding All Solutions of Equations in Free Groups and Monoids with Involution
The aim of this paper is to present a PSPACE algorithm which yields a finite
graph of exponential size and which describes the set of all solutions of
equations in free groups as well as the set of all solutions of equations in
free monoids with involution in the presence of rational constraints. This
became possible due to the recently invented emph{recompression} technique of
the second author.
He successfully applied the recompression technique for pure word equations
without involution or rational constraints. In particular, his method could not
be used as a black box for free groups (even without rational constraints).
Actually, the presence of an involution (inverse elements) and rational
constraints complicates the situation and some additional analysis is
necessary. Still, the recompression technique is general enough to accommodate
both extensions. In the end, it simplifies proofs that solving word equations
is in PSPACE (Plandowski 1999) and the corresponding result for equations in
free groups with rational constraints (Diekert, Hagenah and Gutierrez 2001). As
a byproduct we obtain a direct proof that it is decidable in PSPACE whether or
not the solution set is finite.Comment: A preliminary version of this paper was presented as an invited talk
at CSR 2014 in Moscow, June 7 - 11, 201
Exciton-assisted optomechanics with suspended carbon nanotubes
We propose a framework for inducing strong optomechanical effects in a
suspended carbon nanotube based on deformation potential exciton-phonon
coupling. The excitons are confined using an inhomogeneous axial electric field
which generates optically active quantum dots with a level spacing in the
milli-electronvolt range and a characteristic size in the 10-nanometer range. A
transverse field induces a tunable parametric coupling between the quantum dot
and the flexural modes of the nanotube mediated by electron-phonon
interactions. We derive the corresponding excitonic deformation potentials and
show that this interaction enables efficient optical ground-state cooling of
the fundamental mode and could allow us to realise the strong and ultra-strong
coupling regimes of the Jaynes-Cummings and Rabi models.Comment: 25 pages, 2 figure
Iterative algorithm versus analytic solutions of the parametrically driven dissipative quantum harmonic oscillator
We consider the Brownian motion of a quantum mechanical particle in a
one-dimensional parabolic potential with periodically modulated curvature under
the influence of a thermal heat bath. Analytic expressions for the
time-dependent position and momentum variances are compared with results of an
iterative algorithm, the so-called quasiadiabatic propagator path integral
algorithm (QUAPI). We obtain good agreement over an extended range of
parameters for this spatially continuous quantum system. These findings
indicate the reliability of the algorithm also in cases for which analytic
results may not be available a priori.Comment: 15 pages including 11 figures, one reference added, minor typos
correcte
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Semantic memory redux: an experimental test of hierarchical category representation
Four experiments investigated the classic issue in semantic memory of whether people organize categorical information in hierarchies and use inference to retrieve information from them, as proposed by Collins & Quillian (1969). Past evidence has focused on RT to confirm sentences such as “All birds are animals” or “Canaries breathe.” However, confounding variables such as familiarity and associations between the terms have led to contradictory results. Our experiments avoided such problems by teaching subjects novel materials. Experiment 1 tested an implicit hierarchical structure in the features of a set of studied objects (e.g., all brown objects were large). Experiment 2 taught subjects nested categories of artificial bugs. In Experiment 3, subjects learned a tree structure of novel category hierarchies. In all three, the results differed from the predictions of the hierarchical inference model. In Experiment 4, subjects learned a hierarchy by means of paired associates of novel category names. Here we finally found the RT signature of hierarchical inference. We conclude that it is possible to store information in a hierarchy and retrieve it via inference, but it is difficult and avoided whenever possible. The results are more consistent with feature comparison models than hierarchical models of semantic memory
Free subgroups of one-relator relative presentations
Suppose that G is a nontrivial torsion-free group and w is a word over the
alphabet G\cup\{x_1^{\pm1},...,x_n^{\pm1}\}. It is proved that for n\ge2 the
group \~G= always contains a nonabelian free subgroup.
For n=1 the question about the existence of nonabelian free subgroups in \~G is
answered completely in the unimodular case (i.e., when the exponent sum of x_1
in w is one). Some generalisations of these results are discussed.Comment: V3: A small correction in the last phrase of the proof of Theorem 1.
4 page
The usability of description logics: understanding the cognitive difficulties presented by description logics
Description Logics have been extensively studied from the viewpoint of decidability and computational tractability. Less attention has been given to their usability and the cognitive difficulties they present, in particular for those who are not specialists in logic. This paper reports on a study into the difficulties associated with the most commonly used Description Logic features. Psychological theories are used to take account of these. Whilst most of the features presented no difficulty to participants, the comprehension of some was affected by commonly occurring misconceptions. The paper proposes explanations and remedies for some of these difficulties. In addition, the time to confirm stated inferences was found to depend both on the maximum complexity of the relations involved and the number of steps in the argument
Enhancing non-classicality in mechanical systems
We study the effects of post-selection measurements on both the non-classicality of the state of a mechanical oscillator and the entanglement between two mechanical systems that are part of a distributed optomechanical network. We address the cases of both Gaussian and non-Gaussian measurements, identifying in which cases simple photon counting and Geiger-like measurements are effective in distilling a strongly non-classical mechanical state and enhancing the purely mechanical entanglement between two elements of the network
Experimental Evidence for Quantum Structure in Cognition
We proof a theorem that shows that a collection of experimental data of
membership weights of items with respect to a pair of concepts and its
conjunction cannot be modeled within a classical measure theoretic weight
structure in case the experimental data contain the effect called
overextension. Since the effect of overextension, analogue to the well-known
guppy effect for concept combinations, is abundant in all experiments testing
weights of items with respect to pairs of concepts and their conjunctions, our
theorem constitutes a no-go theorem for classical measure structure for common
data of membership weights of items with respect to concepts and their
combinations. We put forward a simple geometric criterion that reveals the non
classicality of the membership weight structure and use experimentally measured
membership weights estimated by subjects in experiments to illustrate our
geometrical criterion. The violation of the classical weight structure is
similar to the violation of the well-known Bell inequalities studied in quantum
mechanics, and hence suggests that the quantum formalism and hence the modeling
by quantum membership weights can accomplish what classical membership weights
cannot do.Comment: 12 pages, 3 figure
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