2,507 research outputs found
Unified entropic measures of quantum correlations induced by local measurements
We introduce quantum correlations measures based on the minimal change in
unified entropies induced by local rank-one projective measurements, divided by
a factor that depends on the generalized purity of the system in the case of
non-additive entropies. In this way, we overcome the issue of the artificial
increasing of the value of quantum correlations measures based on non-additive
entropies when an uncorrelated ancilla is appended to the system without
changing the computability of our entropic correlations measures with respect
to the previous ones. Moreover, we recover as limiting cases the quantum
correlations measures based on von Neumann and R\'enyi entropies (i.e.,
additive entropies), for which the adjustment factor becomes trivial. In
addition, we distinguish between total and semiquantum correlations and obtain
some relations between them. Finally, we obtain analytical expressions of the
entropic correlations measures for typical quantum bipartite systems.Comment: 10 pages, 1 figur
On a classical spectral optimization problem in linear elasticity
We consider a classical shape optimization problem for the eigenvalues of
elliptic operators with homogeneous boundary conditions on domains in the
-dimensional Euclidean space. We survey recent results concerning the
analytic dependence of the elementary symmetric functions of the eigenvalues
upon domain perturbation and the role of balls as critical points of such
functions subject to volume constraint. Our discussion concerns Dirichlet and
buckling-type problems for polyharmonic operators, the Neumann and the
intermediate problems for the biharmonic operator, the Lam\'{e} and the
Reissner-Mindlin systems.Comment: To appear in the proceedings of the workshop `New Trends in Shape
Optimization', Friedrich-Alexander Universit\"{a}t Erlangen-Nuremberg, 23-27
September 201
Hyperhomocysteinemia in L-dopa treated patients with Parkinson's disease: potential implications in cognitive dysfunction and dementia?
Abstract: Background: Hyperhomocysteinemia has been associated with cognitive dysfunction and dementia. The incidence
of dementia in Parkinson’s Disease (PD) patients is higher than in the general population and plasma Homocysteine
concentrations are increased in L-dopa treated PD patients.
Objective: We evaluated the possible correlations between L-Dopa related hyperhomocysteinemia and cognitive dysfunction
in PD.
Methods: A Medline literature search was performed to identify all published studies on Homocysteine and cognitive dysfunction
and dementia during the course of PD from 1966 to 31/03/2010.
Results: Sixteen studies were found for review; ten studies focused on homocysteine and cognitive dysfunction in PD patients,
five on homocysteine and PD dementia and two on homocysteine and markers of neurodegeneration in PD. The design
of the study was retrospective in 14 studies, while 2 had a prospective design, with a variable follow-up period (from
24-weeks to 2 years). In most of the studies plasma homocysteine levels significantly correlated with cognitive functions,
dementia and markers of neurodegeneration in PD patients. However, some studies did not confirm these findings. Several
factors may concur to explain these partially conflicting results, including the retrospective design of the studies, their
small sample size, their high percentage of excluded patients, and the use of a wide range of neuropsychological tasks in
assessment of cognitive dysfunctions across the available studies.
Conclusions: Available data seem to indicate a potential role of L-dopa related hyperhomocysteinemia on cognitive impairment
and dementia during the course of PD
A family of generalized quantum entropies: definition and properties
We present a quantum version of the generalized -entropies,
introduced by Salicr\'u \textit{et al.} for the study of classical probability
distributions. We establish their basic properties, and show that already known
quantum entropies such as von Neumann, and quantum versions of R\'enyi,
Tsallis, and unified entropies, constitute particular classes of the present
general quantum Salicr\'u form. We exhibit that majorization plays a key role
in explaining most of their common features. We give a characterization of the
quantum -entropies under the action of quantum operations, and study
their properties for composite systems. We apply these generalized entropies to
the problem of detection of quantum entanglement, and introduce a discussion on
possible generalized conditional entropies as well.Comment: 26 pages, 1 figure. Close to published versio
Tuning the potential drop at graphene/protic ionic liquid interface by molecular structure engineering
Ionic liquids (ILs) have been extensively employed in many applications involving interfaces with carbon-based electrodes, such as energy storage devices (batteries or supercapacitors) or electrocatalytic devices, where the way each ion of the IL interacts with the electrode has a strong impact on the overall performance of the device. For instance, the amount of potential difference between the electrode and the bulk of the IL is highly sensitive to the IL composition and it is directly related to the device capacitance. The selection of the most suited pair of ions often proceeds by time-consuming and costly trial-and-error approaches. It is necessary to understand the atomistic features of the interface to determine the effect of each ion on the potential drop. By classical molecular dynamics simulations, we show that it is possible to quickly infer the interface potential arising at the carbon electrode by carefully inspecting the molecular structure of the IL. The ion orientation at the interface is, in fact, determined by the distribution of charges within the molecules. Depending on where charges are located, ions can either lie flat or perpendicular to the interface to minimize the surface energy. The interface potential is found to be mainly determined by ion-ion interactions dictating the interface energy minimization process, whereas ion-electrode interactions are found to enforce higher ordering and charge layers stacking but not to induce selective adsorption of an ion over the other
On an interior Calder\'{o}n operator and a related Steklov eigenproblem for Maxwell's equations
We discuss a Steklov-type problem for Maxwell's equations which is related to
an interior Calder\'{o}n operator and an appropriate Dirichlet-to-Neumann type
map. The corresponding Neumann-to-Dirichlet map turns out to be compact and
this provides a Fourier basis of Steklov eigenfunctions for the associated
energy spaces. With an approach similar to that developed by Auchmuty for the
Laplace operator, we provide natural spectral representations for the
appropriate trace spaces, for the Calder\'{o}n operator itself and for the
solutions of the corresponding boundary value problems subject to electric or
magnetic boundary conditions on a cavity.Comment: Submitted for publication to Siam Journal on Mathematical Analysis on
21 March 2019, revised on 12 May 2020, accepted for publication on 16 July
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