Geometric Phase and Modulo Relations for Probability Amplitudes as Functions on Complex Parameter Spaces

We investigate general differential relations connecting the respective behavior s of the phase and modulo of probability amplitudes of the form \amp{\psi_f}{\psi}, where $\ket{\psi_f}$ is a fixed state in Hilbert space and $\ket{\psi}$ is a section of a holomorphic line bundle over some complex parameter space. Amplitude functions on such bundles, while not strictly holomorphic, nevertheless satisfy generalized Cauchy-Riemann conditions involving the U(1) Berry-Simon connection on the parameter space. These conditions entail invertible relations between the gradients of the phase and modulo, therefore allowing for the reconstruction of the phase from the modulo (or vice-versa) and other conditions on the behavior of either polar component of the amplitude. As a special case, we consider amplitude functions valued on the space of pure states, the ray space ${\cal R} = {\mathbb C}P^n$, where transition probabilities have a geometric interpretation in terms of geodesic distances as measured with the Fubini-Study metric. In conjunction with the generalized Cauchy-Riemann conditions, this geodesic interpretation leads to additional relations, in particular a novel connection between the modulus of the amplitude and the phase gradient, somewhat reminiscent of the WKB formula. Finally, a connection with geometric phases is established.Comment: 11 pages, 1 figure, revtex

Mode-Wise Entanglement of Gaussian States

We address the decomposition of a multi-mode pure Gaussian state with respect to a bi-partite division of the modes. For any such division the state can always be expressed as a product state involving entangled two-mode squeezed states and single mode local states at each side. The character of entanglement of the state can therefore be understood modewise; that is, a given mode on one side is entangled with only one corresponding mode of the other, and therefore the total bi-partite entanglement is the sum of the modewise entanglement. This decomposition is generally not applicable to all mixed Gaussian states. However, the result can be extended to a special family of "isotropic" states, characterized by a phase space covariance matrix with a completely degenerate symplectic spectrum.Comment: 4 pages, RevTex4. Replaced with revised version with reference added to a previous related paper. Minor typographical errors correcte

Analysis of ``Gauge Modes'' in Linearized Relativity

By writing the complete set of $3 + 1$ (ADM) equations for linearized waves, we are able to demonstrate the properties of the initial data and of the evolution of a wave problem set by Alcubierre and Schutz. We show that the gauge modes and constraint error modes arise in a straightforward way in the analysis, and are of a form which will be controlled in any well specified convergent computational discretization of the differential equations.Comment: 11pages LaTe

Gaussian quantum marginal problem

The quantum marginal problem asks what local spectra are consistent with a given spectrum of a joint state of a composite quantum system. This setting, also referred to as the question of the compatibility of local spectra, has several applications in quantum information theory. Here, we introduce the analogue of this statement for Gaussian states for any number of modes, and solve it in generality, for pure and mixed states, both concerning necessary and sufficient conditions. Formally, our result can be viewed as an analogue of the Sing-Thompson Theorem (respectively Horn's Lemma), characterizing the relationship between main diagonal elements and singular values of a complex matrix: We find necessary and sufficient conditions for vectors (d1, ..., dn) and (c1, ..., cn) to be the symplectic eigenvalues and symplectic main diagonal elements of a strictly positive real matrix, respectively. More physically speaking, this result determines what local temperatures or entropies are consistent with a pure or mixed Gaussian state of several modes. We find that this result implies a solution to the problem of sharing of entanglement in pure Gaussian states and allows for estimating the global entropy of non-Gaussian states based on local measurements. Implications to the actual preparation of multi-mode continuous-variable entangled states are discussed. We compare the findings with the marginal problem for qubits, the solution of which for pure states has a strikingly similar and in fact simple form.Comment: 18 pages, 1 figure, material added, references updated, except from figure identical with version to appear in Commun. Math. Phy

An ABS control logic based on wheel force measurement

The paper presents an anti-lock braking system (ABS) control logic based on the measurement of the longitudinal forces at the hub bearings. The availability of force information allows to design a logic that does not rely on the estimation of the tyre-road friction coefficient, since it continuously tries to exploit the maximum longitudinal tyre force. The logic is designed by means of computer simulation and then tested on a specific hardware in the loop test bench: the experimental results confirm that measured wheel force can lead to a significant improvement of the ABS performances in terms of stopping distance also in the presence of road with variable friction coefficien

A virtual laboratory to support chemical reaction engineering courses using real-life problems and industrial software

A virtual laboratory has been developed to support chemical reaction engineering courses. Real-life engineering challenges that are difficult to address in a university laboratory give the opportunity to illustrate basic concepts of chemical reaction engineering such as the relationship between temperature and reaction rate, space time and conversion, and inert concentration and selectivity. Six virtual experiments covering topics from petroleum refining, diesel combustion, nanoparticle growth, and hydrogen combustion form the basis of the virtual laboratory. The characteristics embedded in the experiments include the use of economic analysis to give closure to open-ended problems, the solution of engineering problems with high environmental relevance and finally, the ability to solve complex engineering problems related to state-of-the-art technologies, for example the synthesis of functionalized nanoparticles. Trial tests with senior students, with continual feedback and freedom in terms of the delivery date were used to evaluate and improve the experiments. Subsequently, a classroom test with 45 undergraduate students with a fixed deadline was performed. The challenges and opportunities to use virtual experiments supported by industrial software to teach real-life problems to undergraduate students have been critically assessed

Symplectic invariants, entropic measures and correlations of Gaussian states

We present a derivation of the Von Neumann entropy and mutual information of arbitrary two--mode Gaussian states, based on the explicit determination of the symplectic eigenvalues of a generic covariance matrix. The key role of the symplectic invariants in such a determination is pointed out. We show that the Von Neumann entropy depends on two symplectic invariants, while the purity (or the linear entropy) is determined by only one invariant, so that the two quantities provide two different hierarchies of mixed Gaussian states. A comparison between mutual information and entanglement of formation for symmetric states is considered, remarking the crucial role of the symplectic eigenvalues in qualifying and quantifying the correlations present in a generic state.Comment: 6 pages, no figures, revised version, sections and references added, to appear in J. Phys.

Recent models for adaptive personality differences: a review

In this paper we review recent models that provide adaptive explanations for animal personalities: individual differences in behaviour (or suites of correlated behaviours) that are consistent over time or contexts. We start by briefly discussing patterns of variation in behaviour that have been documented in natural populations. In the main part of the paper we discuss models for personality differences that (i) explain animal personalities as adaptive behavioural responses to differences in state, (ii) investigate how feedbacks between state and behaviour can stabilize initial differences among individuals and (iii) provide adaptive explanations for animal personalities that are not based on state differences. Throughout, we focus on two basic questions. First, what is the basic conceptual idea underlying the model? Second, what are the key assumptions and predictions of the model? We conclude by discussing empirical features of personalities that have not yet been addressed by formal modelling. While this paper is primarily intended to guide empiricists through current adaptive theory, thereby stimulating empirical tests of these models, we hope it also inspires theoreticians to address aspects of personalities that have received little attention up to now

Removal efficiency for emerging contaminants in a WWTP from Madrid (Spain) after secondary and tertiary treatment and environmental impact on the Manzanares River

The effluents from wastewater treatment plants (WWTPs) can be an important contamination source for receiving waters. In this work, a comprehensive study on the impact of a WWTP from Madrid on the aquatic environment has been performed, including a wide number of pharmaceuticals and pesticides, among them those included in the European Watch List. 24-h composite samples of influent (IWW) and effluent wastewater after secondary (EWW2) and after secondary + tertiary treatment (EWW3) were monitored along two campaigns. Average weekly concentrations in IWW and EWW2 and EWW3 allowed estimating the removal efficiency of the WWTP for pharmaceutical active substances (PhACs). In addition, the impact of EWW3 on the water quality of the Manzanares River was assessed, in terms of PhAC and pesticide concentrations, through analysis of the river water collected upstream and downstream of the discharge point. After a preliminary risk assessment, a detailed evaluation of the impact on the aquatic environment, including a toxicological study and screening of pharmaceutical metabolites, was made for the seven most relevant PhACs: sulfamethoxazole, azithromycin and clarithromycin (antibiotics), metoprolol (antihypertensive), diclofenac (anti-inflammatory/analgesic), irbesartan (antihypertensive), and the antidepressant venlafaxine. Among selected PhACs, irbesartan, clarithromycin and venlafaxine presented moderate or high risk in the river water downstream of the discharge. Albeit no acute toxicity was detected, more detailed studies should be carried out for these substances, including additional toxicological studies, to set up potential sublethal and chronic effects on aquatic organisms.This work was developed under the financial support of DRACE INFRAESTRUCTURAS S.A. as a part of the project Estudio de contaminantes emergentes en aguas residuales y superficiales de Madrid. The authors acknowledge the support of Jose Ramon Rodriguez from DRACE INFRAESTRUCTURAS S.A., for collection of wastewater and surface water samples, as well as the discussion and useful suggestions from Jesus Angel López, Pedro Miguel Catalinas and Maria Elvira Benito, from Sub-Direccion General de Aguas, Ayuntamiento de Madrid. The University Jaume I of Castellón, Spain (project UJI-B2018-55), the Ministry of Science, Innovation and University, Spain (Ref RTI2018-097417-B-I00) and Generalitat Valenciana, Spain (research group of excellence PROMETEO 2019/040) are also acknowledged. The authors are very grateful to the Serveis Centrals d'Instrumentació Científica (SCIC) of University Jaume I for the use of LC-MS/MS instrumentation