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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)