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The definition of a consistent evolution equation for statistical hybrid quantum-classical systems is still an open problem. In this paper we analyze the case of Ehrenfest dynamics on systems defined by a probability density and identify the relations of the non-linearity of the dynamics with the obstructions to define a consistent dynamics for the first quantum moment of the distribution. This first quantum moment represents the physical states as a family of classically-parametrized density matrices $\hat \rho(\xi)$, for $\xi$ a classical point; and it is the most common representation of hybrid systems in the literature. Due to this obstruction, we consider higher order quantum moments, and argue that only a finite number of them are physically measurable. Because of this, we propose an effective solution for the hybrid dynamics problem based on approximating the distribution by those moments and representing the states by them., Comment: 21 pages. Minor correction in the list of affiliations

We generalize the Hamiltonian picture of General Relativity coupled to classical matter, known as geometrodynamics, to the case where such matter is described by a Quantum Field Theory in Curved Spacetime, but gravity is still described by a classical metric tensor field over a spatial hypersurface and its associated momentum. Thus, in our approach there is no non-dynamic background structure, apart from the manifold of events, and the gravitational and quantum degrees of freedom have their dynamics inextricably coupled. Given the Hamiltonian natureof the framework, we work with the generators of hypersurface deformations over the manifold of quantum states. The construction relies heavily on the differential geometry of a fibration of the set of quantum states over the set of gravitational variables. An important feature of this work is the use of Gaussian measures over the space of matter fields and of Hida distributions to define a common superspace to all possible Hilbert spaces with different measures, to properly characterize the Schrodinger wave functional picture of QFT in curved spacetime. This allows us to relate states within different Hilbert spaces in the case of vacuum states or measures that depend on the gravitational degrees of freedom, as the ones associated to Ashtekar's complex structure. This is achieved through the inclusion of a quantum Hermitian connection for the fibration, which will have profound physical implications. The most remarkable physical features of the construction are norm conservation of the quantum state (even if the total dynamics are non-unitary), the clear identification of the hybrid conserved quantities and the description of a dynamical backreaction of quantum matter on geometry and vice versa, which shall modify the physical properties the gravitational field would have in the absence of backreaction.

Based on Koopman formalism for classical statistical mechanics, we propose a formalism to define hybrid quantum-classical dynamical systems by defining (outer) automorphisms of the C*-algebra of hybrid operators and realizing them as linear transformations on the space of hybrid states. These hybrid states are represented as density matrices on the Hilbert space obtained from the hybrid C*-algebra by the GNS formalism. We also classify all possible dynamical systems which are unitary and obtain the possible hybrid Hamiltonian operators., Comment: 21 pages. Final version

This letter is about confinement in QCD. At the moment we have pictures of confinement to complete our understanding of the physics of strongly interacting particles, interaction which asks for confinement. As it is said in [1] : " In principle it should be possible to derive the confinement hypothesis from the QCD Lagrangian. At this time, no rigorous derivation exists, so it is not absolutely clear that the confinement hypothesis is a bone fide prediction of QCD". In this letter we show that a sufficient (of course not necessary) condition for confinement is that topological structure of vacuum in Nature does not correspond to the $\theta$-vacuum. Therefore, if different vacua with nontrivial winding number cannot be connected by tunneling, we obtain confinement as a consequence. Moreover, we show that an axion-like mechanism would suffice to describe a confined QCD phase., Comment: 13 pages

Molecular or condensed matter systems are often well approximated by hybrid quantum-classical models: the electrons retain their quantum character, whereas the ions are considered to be classical particles. We discuss various alternative approaches for the computation of equilibrium (canonical) ensemble averages for observables of these hybrid quantum-classical systems through the use of molecular dynamics (MD), i.e. by performing dynamics in the presence of a thermostat and computing time averages over the trajectories. Often, in classical or ab initio MD, the temperature of the electrons is ignored and they are assumed to remain at the instantaneous ground state given by each ionic configuration during the evolution. Here, however, we discuss the general case that considers both classical and quantum subsystems at finite temperature canonical equilibrium. Inspired by a recent formal derivation for the canonical ensemble for quantum classical hybrids, we discuss previous approaches found in the literature, and provide some new formulas., Comment: This is the version of the article before peer review or editing, as submitted by an author to New Journal of Physics. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at https://doi.org/10.1088/1367-2630/abf9b3

Waveguide arrays offer enormous potential to design circuit elements essential to fabricate optical devices capable to processing information codified by light. In this work we study the existence and stability of localized beams in one dimensional photonic lattices composed by a Kerr type waveguide array. We analyzed the case where discrete translation symmetry is broken in as much as one of the waveguides lacks a nonlinear response. Specifically, we determined the space of parameters where a coherent and robust mobility across the lattice is achieved. Moreover, we calculate the reflection and transmission coefficients when localized beams interact directly with the impurity, finding that it behaves as a variable filter depending of system parameters. Our results would shed light on develop solutions to keep unaltered information during its transmission within future optical devices., Comment: 7 pages, 4 figs

In this work we generalize and combine Gibbs and von Neumann approaches to build, for the first time, a rigorous definition of entropy for hybrid quantum-classical systems. The resulting function coincides with the two cases above when the suitable limits are considered. Then, we apply the MaxEnt principle for this hybrid entropy function and obtain the natural candidate for the Hybrid Canonical Ensemble (HCE). We prove that the suitable classical and quantum limits of the HCE coincide with the usual classical and quantum canonical ensembles since the whole scheme admits both limits, thus showing that the MaxEnt principle is applicable and consistent for hybrid systems., Comment: 7 pages. Final preprint corresponding to the published version of the manuscript

Quantum splines are curves in a Hilbert space or, equivalently, in the corresponding Hilbert projective space, which generalize the notion of Riemannian cubic splines to the quantum domain. In this paper, we present a generalization of this concept to general density matrices with a Hamiltonian approach and using a geometrical formulation of quantum mechanics. Our main goal is to formulate an optimal control problem for a nonlinear system on the dual of the Lie algebra of the unitary group which corresponds to the variational problem of quantum splines. The corresponding Hamiltonian equations and interpolation conditions are derived. The results are illustrated with some examples and the corresponding quantum splines are computed with the implementation of a suitable iterative algorithm, Comment: 20 pages, 2 figures

Debris disks can be seen as the left-overs of giant planet formation and the possible nurseries of rocky planets. While M-type stars out-number more massive stars we know very little about the time evolution of their circumstellar disks at ages older than $\sim 10$\,Myr. Sub-millimeter observations are best to provide first order estimates of the available mass reservoir and thus better constrain the evolution of such disks. Here, we present ALMA Cycle\,3 Band\,7 observations of the debris disk around the M2 star TWA\,7, which had been postulated to harbor two spatially separated dust belts, based on unresolved far-infrared and sub-millimeter data. We show that most of the emission at wavelengths longer than $\sim 300$\,$\mu$m is in fact arising from a contaminant source, most likely a sub-mm galaxy, located at about 6.6" East of TWA\,7 (in 2016). Fortunately, the high resolution of our ALMA data allows us to disentangle the contaminant emission from that of the disc and report a significant detection of the disk in the sub-millimeter for the first time with a flux density of 2.1$\pm$0.4 mJy at 870 $\mu$m. With this detection, we show that the SED can be reproduced with a single dust belt., Comment: 6 pages, accepted to MNRAS

In previous works, we introduced a geometric route to define our Ehrenfest Statistical Dynamics (ESD) and we proved that, for a simple toy-model, the resulting ESD does not preserve purity. We now take a step further: we investigate decoherence and pointer basis in the ESD model by considering some uncertainty in the degrees of freedom of a simple but realistic molecular model, consisting of two classical cores and one quantum electron. The Ehrenfest model is sometimes discarded as a valid approximation to non-adiabatic coupled quantum-classical dynamics because it does not describe the decoherence in the quantum subsystem. However, any rigorous statistical analysis of the Ehrenfest dynamics, such as the described ESD formalism, proves that decoherence exists. In this article, decoherence in ESD is studied by measuring the change in the quantum subsystem purity and by analysing the appearance of the pointer basis to which the system decoheres, which for our example is composed by the eigenstates of the electronic Hamiltonian., Comment: 21 pages, 9 figures. Accepted for publication in the Journal of Chemical Theory and Computation

A geometric description of the space of states of a finite-dimensional quantum system and of the Markovian evolution associated with the Kossakowski-Lindblad operator is presented. This geometric setting is based on two composition laws on the space of observables defined by a pair of contravariant tensor fields. The first one is a Poisson tensor field that encodes the commutator product and allows us to develop a Hamiltonian mechanics. The other tensor field is symmetric, encodes the Jordan product and provides the variances and covariances of measures associated with the observables. This tensorial formulation of quantum systems is able to describe, in a natural way, the Markovian dynamical evolution as a vector field on the space of states. Therefore, it is possible to consider dynamical effects on non-linear physical quantities, such as entropies, purity and concurrence. In particular, in this work the tensorial formulation is used to consider the dynamical evolution of the symmetric and skew-symmetric tensors and to read off the corresponding limits as giving rise to a contraction of the initial Jordan and Lie products., Comment: 31 pages, 2 figures. Minor corrections

In this paper we consider a manifold with a dynamical vector field and inquire about the possible tangent bundle structures which would turn the starting vector field into a second order one. The analysis is restricted to manifolds which are diffeomorphic with affine spaces. In particular, we consider the problem in connection with conformal vector fields of second order and apply the procedure to vector fields conformally related with the harmonic oscillator (f-oscillators) . We select one which covers the vector field describing the Kepler problem., Comment: 17 pages, 2 figures

We prove that $t$-dependent Schr\"odinger equations on finite-dimensional Hilbert spaces determined by $t$-dependent Hermitian Hamiltonian operators can be described through Lie systems admitting a Vessiot--Guldberg Lie algebra of K\"ahler vector fields. This result is extended to other related Schr\"odinger equations, e.g. projective ones, and their properties are studied through Poisson, presymplectic and K\"ahler structures. This leads to derive nonlinear superposition rules for them depending in a lower (or equal) number of solutions than standard linear ones. Special attention is paid to applications in $n$-qubit systems., Comment: 36 pages

We review the geometrical formulation of Quantum Mechanics to identify, according to Klein's programme, the corresponding group of transformations. For closed systems, it is the unitary group. For open quantum systems, the semigroup of Kraus maps contains, as a maximal subgroup, the general linear group. The same group emerges as the exponentiation of the $C^{*}$--algebra associated with the quantum system, when thought of as a Lie algebra. Thus, open quantum systems seem to identify the general linear group as associated with quantum mechanics and moreover suggest to extend the Klein programme also to groupoids. The usual unitary group emerges as a maximal compact subgroup of the general linear group., Comment: Amsart class, 24 pages, 4 figures

A major goal of the Atacama Large Millimeter/submillimeter Array (ALMA) is to make accurate images with resolutions of tens of milliarcseconds, which at submillimeter (submm) wavelengths requires baselines up to ~15 km. To develop and test this capability, a Long Baseline Campaign (LBC) was carried out from September to late November 2014, culminating in end-to-end observations, calibrations, and imaging of selected Science Verification (SV) targets. This paper presents an overview of the campaign and its main results, including an investigation of the short-term coherence properties and systematic phase errors over the long baselines at the ALMA site, a summary of the SV targets and observations, and recommendations for science observing strategies at long baselines. Deep ALMA images of the quasar 3C138 at 97 and 241 GHz are also compared to VLA 43 GHz results, demonstrating an agreement at a level of a few percent. As a result of the extensive program of LBC testing, the highly successful SV imaging at long baselines achieved angular resolutions as fine as 19 mas at ~350 GHz. Observing with ALMA on baselines of up to 15 km is now possible, and opens up new parameter space for submm astronomy., Comment: 11 pages, 7 figures, 2 tables; accepted for publication in the Astrophysical Journal Letters; this version with small changes to affiliations

We present initial results of very high resolution Atacama Large Millimeter/submillimeter Array (ALMA) observations of the $z$=3.042 gravitationally lensed galaxy HATLAS J090311.6+003906 (SDP.81). These observations were carried out using a very extended configuration as part of Science Verification for the 2014 ALMA Long Baseline Campaign, with baselines of up to 15 km. We present continuum imaging at 151, 236 and 290 GHz, at unprecedented angular resolutions as fine as 23 milliarcseconds (mas), corresponding to an un-magnified spatial scale of ~180 pc at z=3.042. The ALMA images clearly show two main gravitational arc components of an Einstein ring, with emission tracing a radius of ~1.5". We also present imaging of CO(10-9), CO(8-7), CO(5-4) and H2O line emission. The CO emission, at an angular resolution of ~170 mas, is found to broadly trace the gravitational arc structures but with differing morphologies between the CO transitions and compared to the dust continuum. Our detection of H2O line emission, using only the shortest baselines, provides the most resolved detection to date of thermal H2O emission in an extragalactic source. The ALMA continuum and spectral line fluxes are consistent with previous Plateau de Bure Interferometer and Submillimeter Array observations despite the impressive increase in angular resolution. Finally, we detect weak unresolved continuum emission from a position that is spatially coincident with the center of the lens, with a spectral index that is consistent with emission from the core of the foreground lensing galaxy., Comment: 9 pages, 5 figures and 3 tables, accepted for publication in the Astrophysical Journal Letters

We present Atacama Large Millimeter/submillimeter Array (ALMA) 1.3 mm continuum images of the asteroid 3 Juno obtained with an angular resolution of 0.042 arcseconds (60 km at 1.97 AU). The data were obtained over a single 4.4 hr interval, which covers 60% of the 7.2 hr rotation period, approximately centered on local transit. A sequence of ten consecutive images reveals continuous changes in the asteroid's profile and apparent shape, in good agreement with the sky projection of the three-dimensional model of the Database of Asteroid Models from Inversion Techniques. We measure a geometric mean diameter of 259pm4 km, in good agreement with past estimates from a variety of techniques and wavelengths. Due to the viewing angle and inclination of the rotational pole, the southern hemisphere dominates all of the images. The median peak brightness temperature is 215pm13 K, while the median over the whole surface is 197pm15 K. With the unprecedented resolution of ALMA, we find that the brightness temperature varies across the surface with higher values correlated to the subsolar point and afternoon areas, and lower values beyond the evening terminator. The dominance of the subsolar point is accentuated in the final four images, suggesting a reduction in the thermal inertia of the regolith at the corresponding longitudes, which are possibly correlated to the location of the putative large impact crater. These results demonstrate ALMA's potential to resolve thermal emission from the surface of main belt asteroids, and to measure accurately their position, geometric shape, rotational period, and soil characteristics., Comment: 8 pages, 3 figures, 2 tables, accepted for publication in the Astrophysical Journal Letters

We present Atacama Large Millimeter/submillimeter Array (ALMA) observations from the 2014 Long Baseline Campaign in dust continuum and spectral line emission from the HL Tau region. The continuum images at wavelengths of 2.9, 1.3, and 0.87 mm have unprecedented angular resolutions of 0.075 arcseconds (10 AU) to 0.025 arcseconds (3.5 AU), revealing an astonishing level of detail in the circumstellar disk surrounding the young solar analogue HL Tau, with a pattern of bright and dark rings observed at all wavelengths. By fitting ellipses to the most distinct rings, we measure precise values for the disk inclination (46.72pm0.05 degrees) and position angle (+138.02pm0.07 degrees). We obtain a high-fidelity image of the 1.0 mm spectral index ($\alpha$), which ranges from $\alpha\sim2.0$ in the optically-thick central peak and two brightest rings, increasing to 2.3-3.0 in the dark rings. The dark rings are not devoid of emission, we estimate a grain emissivity index of 0.8 for the innermost dark ring and lower for subsequent dark rings, consistent with some degree of grain growth and evolution. Additional clues that the rings arise from planet formation include an increase in their central offsets with radius and the presence of numerous orbital resonances. At a resolution of 35 AU, we resolve the molecular component of the disk in HCO+ (1-0) which exhibits a pattern over LSR velocities from 2-12 km/s consistent with Keplerian motion around a ~1.3 solar mass star, although complicated by absorption at low blue-shifted velocities. We also serendipitously detect and resolve the nearby protostars XZ Tau (A/B) and LkHa358 at 2.9 mm., Comment: 11 pages, 5 figures, 2 tables, accepted for publication in the Astrophysical Journal Letters

Schr\"odinger suggested that thermodynamical functions cannot be based on the gratuitous allegation that quantum-mechanical levels (typically the orthogonal eigenstates of the Hamiltonian operator) are the only allowed states for a quantum system [E. Schr\"odinger, Statistical Thermodynamics (Courier Dover, Mineola, 1967)]. Different authors have interpreted this statement by introducing density distributions on the space of quantum pure states with weights obtained as functions of the expectation value of the Hamiltonian of the system. In this work we focus on one of the best known of these distributions, and we prove that, when considered in composite quantum systems, it defines partition functions that do not factorize as products of partition functions of the noninteracting subsystems, even in the thermodynamical regime. This implies that it is not possible to define extensive thermodynamical magnitudes such as the free energy, the internal energy or the thermodynamic entropy by using these models. Therefore, we conclude that this distribution inspired by Schr\"odinger's idea can not be used to construct an appropriate quantum equilibrium thermodynamics., Comment: 32 pages, revtex 4.1 preprint style, 5 figures. Published version with several changes with respect to v2 in text and references

In this paper we develop a picture of Quantum Mechanics based on the description of physical observables in terms of expectation value functions, generalizing thus the so called Ehrenfest theorems for quantum dynamics. Our basic technical ingredient is the set of tools which has been developed in the last years for the geometrical formulation of Quantum Mechanics. In the new picture, we analyze the problem of the dynamical equations, the uncertainty relations and interference and illustrate the construction with the simple case of a two-level system., Comment: Amsart, 17 pages. This paper is based on some lectures delivered by one of us (G. M.) at the international conference "Mathematical Structures in Quantum Systems and applications (MSQS2012)'' which took place at Benasque (Spain), July 8-14, 2012

In spite of the relevance of the proposal introduced in the recent work A. Abedi, N. T. Maitra and E. K. U. Gross, J. Chem. Phys. 137, 22A530, 2012, there is an important ingredient which is missing. Namely, the proof that the norms of the electronic and nuclear wavefunctions which are the solutions to the nonlinear equations of motion are preserved by the evolution. To prove the conservation of these norms is precisely the objective of this Comment., Comment: 2 pages, published version

Relevant algebraic structures for the description of Quantum Mechanics in the Heisenberg picture are replaced by tensorfields on the space of states. This replacement introduces a differential geometric point of view which allows for a covariant formulation of quantum mechanics under the full diffeomorphism group., Comment: 8 pages

We present a new sample of mid L to mid T dwarfs with effective temperatures of 1100 to 1700K selected from the UKIDSS Large Area Survey and confirmed with infrared spectra from X-Shooter/VLT. This effective temperature range is especially sensitive to the formation history of Galactic brown dwarfs and allows us to constrain the form of the sub-stellar birth rate, with sensitivity to differentiate between a flat (stellar like) birth rate, and an exponentially declining form. We present the discovery of 63 new L and T dwarfs from the UKIDSS LAS DR7, including the identification of 12 likely unresolved binaries, which form the first complete sub-set from our program, covering 495 sq degrees of sky, complete to J=18.1. We compare our results for this sub-sample with simulations of differing birth rates for objects of mass 0.10-0.03Msol and ages 1-10Gyrs. We find that the more extreme birth rates (e.g. a halo type form) can likely be excluded as the true form of the birth rate. In addition we find that although there is substantial scatter we find a preference for a mass function, with a power-law index, alpha in the range -1 < alpha < 0 that is consistent (within the errors) with the studies of late T dwarfs., Comment: 19 pages, 14 figures. Accepted for publication in MNRAS

At non-zero temperature and when a system has low-lying excited electronic states, the ground-state Born--Oppenheimer approximation breaks down and the low-lying electronic states are involved in any chemical process. In this work, we use a temperature-dependent effective potential for the nuclei which can accomodate the influence of an arbitrary number of electronic states in a simple way, while at the same time producing the correct Boltzmann equibrium distribution for the electronic part. With the help of this effective potential, we show that thermally-activated low-lying electronic states can have a significant effect in molecular properties for which electronic excitations are oftentimes ignored. We study the thermal expansion of the Manganese dimer, Mn$_2$, where we find that the average bond length experiences a change larger than the present experimental accuracy upon the inclusion of the excited states into the picture. We also show that, when these states are taken into account, reaction rate constants are modified. In particular, we study the opening of the ozone molecule, O$_3$, and show that in this case the rate is modified as much as a 20% with respect to the ground-state Born--Oppenheimer prediction., Comment: 9 pages, 6 figures

We discuss the evolution of purity in mixed quantum/classical approaches to electronic nonadiabatic dynamics in the context of the Ehrenfest model. As it is impossible to exactly determine initial conditions for a realistic system, we choose to work in the statistical Ehrenfest formalism that we introduced in Ref. 1. From it, we develop a new framework to determine exactly the change in the purity of the quantum subsystem along the evolution of a statistical Ehrenfest system. In a simple case, we verify how and to which extent Ehrenfest statistical dynamics makes a system with more than one classical trajectory and an initial quantum pure state become a quantum mixed one. We prove this numerically showing how the evolution of purity depends on time, on the dimension of the quantum state space $D$, and on the number of classical trajectories $N$ of the initial distribution. The results in this work open new perspectives for studying decoherence with Ehrenfest dynamics., Comment: Revtex 4-1, 14 pages, 2 figures. Final published version

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 figures

The International Design Study for the Neutrino Factory (the IDS-NF) was established by the community at the ninth "International Workshop on Neutrino Factories, super-beams, and beta- beams" which was held in Okayama in August 2007. The IDS-NF mandate is to deliver the Reference Design Report (RDR) for the facility on the timescale of 2012/13. In addition, the mandate for the study [3] requires an Interim Design Report to be delivered midway through the project as a step on the way to the RDR. This document, the IDR, has two functions: it marks the point in the IDS-NF at which the emphasis turns to the engineering studies required to deliver the RDR and it documents baseline concepts for the accelerator complex, the neutrino detectors, and the instrumentation systems. The IDS-NF is, in essence, a site-independent study. Example sites, CERN, FNAL, and RAL, have been identified to allow site-specific issues to be addressed in the cost analysis that will be presented in the RDR. The choice of example sites should not be interpreted as implying a preferred choice of site for the facility.

The Muon Ionization Cooling Experiment (MICE) is a strategic R&D project intended to demonstrate the only practical solution to providing high brilliance beams necessary for a neutrino factory or muon collider. MICE is under development at the Rutherford Appleton Laboratory (RAL) in the United Kingdom. It comprises a dedicated beamline to generate a range of input muon emittances and momenta, with time-of-flight and Cherenkov detectors to ensure a pure muon beam. The emittance of the incoming beam will be measured in the upstream magnetic spectrometer with a scintillating fiber tracker. A cooling cell will then follow, alternating energy loss in Liquid Hydrogen (LH2) absorbers to RF cavity acceleration. A second spectrometer, identical to the first, and a second muon identification system will measure the outgoing emittance. In the 2010 run at RAL the muon beamline and most detectors were fully commissioned and a first measurement of the emittance of the muon beam with particle physics (time-of-flight) detectors was performed. The analysis of these data was recently completed and is discussed in this paper. Future steps for MICE, where beam emittance and emittance reduction (cooling) are to be measured with greater accuracy, are also presented., Comment: Proceedings of the DPF-2011 Conference, Providence, RI, August 8-13, 2011

We present an updated version of the spectroscopic white dwarf-main sequence (WDMS) binary catalogue from the Sloan Digital Sky Survey (SDSS). 395 new systems are serendipitous discoveries from the spectroscopic SDSSI/II Legacy targets. As part of SEGUE, we have carried out a dedicated and efficient (64 per cent success rate) search for WDMS binaries with a strong contribution of the companion star, which were underrepresented by all previous surveys, identifying 251 additional systems. In total, our catalogue contains 2248 WDMS binaries, and includes, where available, magnitudes from the GALEX All Sky Survey in the ultraviolet and from the UKIRT Infrared Sky Survey (UKIDSS) in the near-infrared. We also provide radial velocities of the companion stars, measured from the SDSS spectroscopy using the NaI8183.27,8194.81 absorption doublet and/or the Halpha emission. Using an updated version of our spectral decomposition/fitting technique we determine/update the white dwarf effective temperatures, surface gravities and masses, as well as the spectral type of the companion stars for the entire catalogue. Comparing the distributions of white dwarf mass, temperature, and companion spectral type, we confirm that our SEGUE survey project has been successful in identifying WDMS binaries with cooler and more massive white dwarfs, as well as earlier spectral types than found previously. Finally, we have developed a publicly available interactive on-line data base for spectroscopic SDSS WDMS binaries containing all available stellar parameters, radial velocities and magnitudes which we briefly describe., Comment: 13 pages, 6 figures, 8 tables, accepted for publication in MNRAS

Quantum dynamics (i.e., the Schr\"odinger equation) and classical dynamics (i.e., Hamilton equations) can both be formulated in equal geometric terms: a Poisson bracket defined on a manifold. In this paper we first show that the hybrid quantum-classical dynamics prescribed by the Ehrenfest equations can also be formulated within this general framework, what has been used in the literature to construct propagation schemes for Ehrenfest dynamics. Then, the existence of a well defined Poisson bracket allows to arrive to a Liouville equation for a statistical ensemble of Ehrenfest systems. The study of a generic toy model shows that the evolution produced by Ehrenfest dynamics is ergodic and therefore the only constants of motion are functions of the Hamiltonian. The emergence of the canonical ensemble characterized by the Boltzmann distribution follows after an appropriate application of the principle of equal a priori probabilities to this case. Once we know the canonical distribution of a Ehrenfest system, it is straightforward to extend the formalism of Nos\'e (invented to do constant temperature Molecular Dynamics by a non-stochastic method) to our Ehrenfest formalism. This work also provides the basis for extending stochastic methods to Ehrenfest dynamics., Comment: 28 pages, 1 figure. Published version. arXiv admin note: substantial text overlap with arXiv:1010.1494

This paper analyzes the optimal control problem of cubic polynomials on compact Lie groups from a Hamiltonian point of view and its symmetries. The dynamics of the problem is described by a presymplectic formalism associated with the canonical symplectic form on the cotangent bundle of the semidirect product of the Lie group and its Lie algebra. Using these control geometric tools, the relation between the Hamiltonian approach developed here and the known variational one is analyzed. After making explicit the left trivialized system, we use the technique of Marsden-Weinstein reduction to remove the symmetries of the Hamiltonian system. In view of the reduced dynamics, we are able to guarantee, by means of the Lie-Cartan theorem, the existence of a considerable number of independent integrals of motion in involution., Comment: 20 pages. Final version which incorporates the Corrigendum recently published (J. Phys. A: Math. Theor. 46 189501, 2013)

In this paper we study optimal control problems for nonholonomic systems defined on Lie algebroids by using quasi-velocities. We consider both kinematic, i.e. systems whose cost functional depends only on position and velocities, and dynamic optimal control problems, i.e. systems whose cost functional depends also on accelerations. The formulation of the problem directly at the level of Lie algebroids turns out to be the correct framework to explain in detail similar results appeared recently (Maruskin and Bloch, 2007). We also provide several examples to illustrate our construction., Comment: Revtex 4.1, 20 pages. To appear in Int. J. Geom. Meth. Modern Physics

We consider the geometrization of quantum mechanics. We then focus on the pull-back of the Fubini-Study metric tensor field from the projective Hibert space to the orbits of the local unitary groups. An inner product on these tensor fields allows us to obtain functions which are invariant under the considered local unitary groups. This procedure paves the way to an algorithmic approach to the identification of entanglement monotone candidates. Finally, a link between the Fubini-Study metric and a quantum version of the Fisher information metric is discussed., Comment: 24 pages, 3 figures

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 figures

Quantum dynamics (e.g., the Schr\"odinger equation) and classical dynamics (e.g., Hamilton equations) can both be formulated in equal geometric terms: a Poisson bracket defined on a manifold. The difference between both worlds is due to the presence of extra structure in the quantum case, that leads to the appearance of the probabilistic nature of the measurements and the indetermination and superposition principles. In this paper we first show that the quantum-classical dynamics prescribed by the Ehrenfest equations can also be formulated within this general framework, what has been used in the literature to construct propagation schemes for Ehrenfest dynamics. Then, the existence of a well defined Poisson bracket allows to arrive to a Liouville equation for a statistical ensemble of Ehrenfest systems. The study of a generic toy model shows that the evolution produced by Ehrenfest dynamics is ergodic and therefore the only constants of motion are functions of the Hamiltonian. The emergence of the canonical ensemble characterized by the Boltzmann's distribution follows after an appropriate application of the principle of equal a priori probabilities to this case. This work provides the basis for extending stochastic methods to Ehrenfest dynamics., Comment: LaTeX(RevTeX 4.1), 14 pages, 1 figure. Submitted for publication

We present the discovery of the first T dwarf + white dwarf binary system LSPM 1459+0857AB, confirmed through common proper motion and spectroscopy. The white dwarf is a high proper motion object from the LSPM catalogue that we confirm spectroscopically to be a relatively cool (Teff=5535+\-45K) and magnetic (B~2MG) hydrogen-rich white dwarf, with an age of at least 4.8Gyrs. The T dwarf is a recent discovery from the UKIRT Infrared Deep Sky Survey (ULAS 1459+0857), and has a spectral type of T4.5+\-0.5 and a distance in the range 43-69pc. With an age constraint (inferred from the white dwarf) of >4.8Gyrs we estimate Teff=1200-1500K and logg=5.4-5.5 for ULAS 1459+0857, making it a benchmark T dwarf with well constrained surface gravity. We also compare the T dwarf spectra with the latest LYON group atmospheric model predictions, which despite some shortcomings are in general agreement with the observed properties of ULAS 1459+0857. The separation of the binary components (16,500-26,500AU, or 365 arcseconds on the sky) is consistent with an evolved version of the more common brown dwarf + main-sequence binary systems now known, and although the system has a wide separation, it is shown to be statistically robust as a non spurious association. The observed colours of the T dwarf show that it is relatively bright in the z band compared to other T dwarfs of similar type, and further investigation is warranted to explore the possibility that this could be a more generic indicator of older T dwarfs. Future observations of this binary system will provide even stronger constraints on the T dwarf properties, and additional systems will combine to give a more comprehensively robust test of the model atmospheres in this temperature regime., Comment: 14 pages, 11 figures, MNRAS accepted

In recent years, analyses of eclipsing binary systems have unveiled differences between the observed fundamental properties of low-mass stars and those predicted by stellar structure models. Particularly, radius and effective temperatures computed from models are ~ 5-10% lower and ~ 3-5% higher than observed, respectively. These discrepancies have been attributed to different factors, notably to the high levels of magnetic activity present on these stars. In this paper, we test the effect of magnetic activity both on models and on the observational analysis of eclipsing binaries using a sample of such systems with accurate fundamental properties. Regarding stellar models, we have found that unrealistically high spot coverages need to be assumed to reproduce the observations. Tests considering metallicity effects and missing opacities on models indicate that these are not able to explain the radius discrepancies observed. With respect to the observations, we have tested the effect of several spot distributions on the light curve analysis. Our results show that spots cause systematic deviations on the stellar radii derived from light curve analysis when distributed mainly over the stellar poles. Assuming the existence of polar spots, overall agreement between models and observations is reached when ~ 35% spot coverage is considered on stellar models. Such spot coverage induces a systematic deviation in the radius determination from the light curve analysis of ~ 3% and is also compatible with the modulations observed on the light curves of these systems. Finally, we have found that the effect of activity or rotation on convective transport in partially radiative stars may also contribute to explain the differences seen in some of the systems with shorter orbital periods., Comment: 12 pages, 9 figures, accepted for publication in ApJ

We present a second paper of fully characterization of a sample of stars whose low-depth transits were discovered by the OGLE-III campaign in order to select the most promising candidates for spectroscopic confirmation, following the same analysis done in Gallardo et al. (2005). We present new optical and near-IR photometry, deriving physical parameters like effective temperature (Teff), distance (d), the stellar radii (R*) and the companion radii (Rc). We selected eight M (2800 K \le Teff \le 3850 K) or K (3850 K \le Teff \le 5150 K) spectral type stellar objects as potential candidates to host exoplanets, even though, considering the radii of their companions, only stars OGLE-TR-61, OGLE-TR-74, OGLE-TR-123 and OGLE-TR-173 are the most promising M-type transit candidates to host planets. Confirmation of the planetary nature of any of these objects will yield another transiting extrasolar planet orbiting a M-type star, or even more interesting, the first extrasolar planets orbiting a late M-type dwarf of effective temperature about 2900 K., Comment: 6 pages, 2 figures, 2 tables, accepted for publication in Astronomy and Astrophysics

We identify 806 ultra-cool dwarfs from their SDSS riz photometry (of which 34 are newly discovered L dwarfs) and obtain proper motions through cross matching with UKIDSS and 2MASS. Proper motion and distance constraints show that nine of our ultra-cool dwarfs are members of widely separated binary systems; SDSS 0101 (K5V+M9.5V), SDSS 0207 (M1.5V+L3V), SDSS 0832 (K3III+L3.5V), SDSS 0858 (M4V+L0V), SDSS 0953 (M4V+M9.5V), SDSS 0956 (M2V+M9V), SDSS 1304 (M4.5V+L0V), SDSS 1631 (M5.5V+M8V), SDSS 1638 (M4V+L0V). One of these (SDSS 0832) is shown to be a companion to the bright K3 giant Eta Cancri. Such primaries can provide age and metallicity constraints for any companion objects, yielding excellent benchmark objects. Eta Cancri AB is the first wide ultra-cool dwarf + giant binary system identified. We present new observations and analysis that constrain the metallicity of Eta Cancri A to be near solar, and use recent evolutionary models to constrain the age of the giant to be 2.2-6.1 Gyr. If Eta Cancri B is a single object, we estimate its physical attributes to be; mass = 63-82 M_Jup, T_eff = 1800+/-150 K, log g = 5.3-5.5, [M/H] = 0.0+/-0.1. Its colours are non typical when compared to other ultra-cool dwarfs, and we also assess the possibility that Eta Cancri B is itself an unresolved binary, showing that the combined light of an L4 + T4 system could provide a reasonable explanation for its colours., Comment: 20 pages, 14 figures, accepted to MNRAS

The number of brown dwarfs (BDs) now identified tops 700. Yet our understanding of these cool objects is still lacking, and models are struggling to accurately reproduce observations. What is needed is a method of calibrating the models, BDs whose properties (e.g. age, mass, distance, metallicity) that can be independently determined can provide such calibration. The ability to calculate properties based on observables is set to be of vital importance if we are to be able to measure the properties of fainter, more distant populations of BDs that near-future surveys will reveal, for which ground based spectroscopic studies will become increasingly difficult. We present here the state of the current population of age benchmark brown dwarfs., Comment: 2 pages, 1 figure, to appear in the conference proceedings "New Technologies for Probing the Diversity of Brown Dwarfs and Exoplanets", Shanghai, 19-24 July, 2009

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. Phys

We present spectroscopic rotation velocities (v sin i) for 56 M dwarf stars using high resolution HET HRS red spectroscopy. In addition we have also determined photometric effective temperatures, masses and metallicities ([Fe/H]) for some stars observed here and in the literature where we could acquire accurate parallax measurements and relevant photometry. We have increased the number of known v sin is for mid M stars by around 80% and can confirm a weakly increasing rotation velocity with decreasing effective temperature. Our sample of v sin is peak at low velocities (~3 km/s). We find a change in the rotational velocity distribution between early M and late M stars, which is likely due to the changing field topology between partially and fully convective stars. There is also a possible further change in the rotational distribution towards the late M dwarfs where dust begins to play a role in the stellar atmospheres. We also link v sin i to age and show how it can be used to provide mid-M star age limits. When all literature velocities for M dwarfs are added to our sample there are 198 with v sin i less than or equal to 10 km/s and 124 in the mid-to-late M star regime (M3.0-M9.5) where measuring precision optical radial-velocities is difficult. In addition we also search the spectra for any significant Halpha emission or absorption. 43% were found to exhibit such emission and could represent young, active objects with high levels of radial-velocity noise. The tables presented here will aid any future M star planet search target selection to extract stars that will exhibit low radial-velocity jitter., Comment: 22 pages, 11 figures, 4 tables, Accepted for publication in ApJ

We present evolutionary models for young low mass stars and brown dwarfs taking into account episodic phases of accretion at early stages of the evolution, a scenario supported by recent large surveys of embedded protostars. An evolution including short episodes of vigorous accretion ($\mdot \ge 10^{-4} \msolyr$) followed by longer quiescent phases ($\mdot < 10^{-6} \msolyr$) can explain the observed luminosity spread in HR diagrams of star forming regions at ages of a few Myr, for objects ranging from a few Jupiter masses to a few tenths of a solar mass. The gravitational contraction of these accreting objects strongly departs from the standard Hayashi track at constant $\te$. The best agreement with the observed luminosity scatter is obtained if most of the accretion shock energy is radiated away. The obtained luminosity spread at 1 Myr in the HR diagram is equivalent to what can be misinterpreted as a $\sim$ 10 Myr age spread for non-accreting objects. We also predict a significant spread in radius at a given $\te$, as suggested by recent observations. These calculations bear important consequences on our understanding of star formation and early stages of evolution and on the determination of the IMF for young ($\le$ a few Myr) clusters. Our results also show that the concept of a stellar birthline for low-mass objects has no valid support., Comment: 8 pages, 5 figures, accepted for publication in APJ Letter

In this review, we summarize our present knowledge of the behaviour of the mass-radius relationship from solar-type stars down to terrestrial planets, across the regime of substellar objects, brown dwarfs and giant planets. Particular attention is paid to the identification of the main physical properties or mechanisms responsible for this behaviour. Indeed, understanding the mechanical structure of an object provides valuable information about its internal structure, composition and heat content as well as its formation history. Although the general description of these properties is reasonably well mastered, disagreement between theory and observation in certain cases points to some missing physics in our present modelling of at least some of these objects. The mass-radius relationship in the overlaping domain between giant planets and low-mass brown dwarfs is shown to represent a powerful diagnostic to distinguish between these two different populations and shows once again that the present IAU distinction between these two populations at a given mass has no valid foundation., Comment: Cool Stars, Stellar Systems and the Sun 15, invited review

Spectroscopic and eclipsing binary systems offer the best means for determining accurate physical properties of stars, including their masses and radii. The data available for low-mass stars have yielded firm evidence that stellar structure models predict smaller radii and higher effective temperatures than observed, but the number of systems with detailed analyses is still small. In this paper we present a complete reanalysis of one of such eclipsing systems, CM Dra, composed of two dM4.5 stars. New and existing light curves as well as a radial velocity curve are modeled to measure the physical properties of both components. The masses and radii determined for the components of CM Dra are M1=0.2310+/-0.0009 Msun, M2=0.2141+/-0.0010 Msun, R1=0.2534+/-0.0019 Rsun, and R2=0.2396+/-0.0015 Rsun. With relative uncertainties well below the 1% level, these values constitute the most accurate properties to date for fully convective stars. This makes CM Dra a valuable benchmark for testing theoretical models. In comparing our measurements with theory, we confirm the discrepancies reported previously for other low-mass eclipsing binaries. These discrepancies seem likely to be due to the effects of magnetic activity. We find that the orbit of this system is slightly eccentric, and we have made use of eclipse timings spanning three decades to infer the apsidal motion and other related properties., Comment: 19 pages, 9 figures. Accepted for publication in ApJ

We briefly review the most relevant aspects of complete integrability for classical systems and identify those aspects which should be present in a definition of quantum integrability. We show that a naive extension of classical concepts to the quantum framework would not work because all infinite dimensional Hilbert spaces are unitarily isomorphic and, as a consequence, it would not be easy to define degrees of freedom. We argue that a geometrical formulation of quantum mechanics might provide a way out., Comment: 37 pages, AmsLatex, 1 figure

In this paper we present a survey of the use of differential geometric formalisms to describe Quantum Mechanics. We analyze Schr\"odinger framework from this perspective and provide a description of the Weyl-Wigner construction. Finally, after reviewing the basics of the geometric formulation of quantum mechanics, we apply the methods presented to the most interesting cases of finite dimensional Hilbert spaces: those of two, three and four level systems (one qubit, one qutrit and two qubit systems). As a more practical application, we discuss the advantages that the geometric formulation of quantum mechanics can provide us with in the study of situations as the functional independence of entanglement witnesses., Comment: AmsLaTeX, 37 pages, 8 figures. This paper is an expanded version of some lectures delivered by one of us (G. M.) at the ``Advanced Winter School on the Mathematical Foundation of Quantum Control and Quantum Information'' which took place at Castro Urdiales (Spain), February 11-15, 2008

The path integral approach to quantum mechanics requires a substantial generalisation to describe the dynamics of systems confined to bounded domains. Non-local boundary conditions can be introduced in Feynman's approach by means of boundary amplitude distributions and complex phases to describe the quantum dynamics in terms of the classical trajectories. The different prescriptions involve only trajectories reaching the boundary and correspond to different choices of boundary conditions of selfadjoint extensions of the Hamiltonian. One dimensional particle dynamics is analysed in detail., Comment: 8 pages

It has been observed \cite{break} that breakdown in an 805 MHz pill-box cavi ty occurs at much lower gradients as an external axial magnetic field is inc reased. This effect was not observed with on open iris cavity. It is propose d that this effect depends on the relative angles of the magnetic and maximu m electric fields: parallel in the pill-box case; at an angle in the open ir is case. If so, using an open iris structure with solenoid coils in the iris es should perform even better. A lattice, using this principle, is presented, for use in 6D cooling for a Muon Collider. Experimental layouts to test th is principle are proposed., Comment: 3 pages, 7 figures color; submitted to NUFAC07

Numerous investigations on the fundamental properties of low-mass stars using eclipsing binaries indicate a strong discrepancy between theory and observations that is still awaiting explanation. Current models seem to predict radii for stars less massive than the Sun that are some 10% smaller than observed, while their effective temperatures are some 5% larger. Here we discuss recent new observational data that are relevant to this issue and review the progress made in understanding the origin of the important differences with theoretical calculations. Notably, we provide evidence that stellar activity may be responsible for the mismatch between observations and theory through two different channels: inhibition of convection or effects of a significant starspot coverage. The activity hypothesis is put to a test with observational diagnostics and some of the consequences of the large starspot coverage are evaluated. We conclude that stellar activity likely plays a key role in defining the properties of active low-mass stars and that this should be properly taken into account when investigating young, active stars in clusters or star-forming regions., Comment: 7 pages, to appear in Memorie della Societa Astronomica Italiana, vol. 79, proceedings of the workshop "XXI century challenges for stellar evolution", eds S. Cassisi & M. Salaris