Search results for "Theorem"
showing 10 items of 1250 documents
Individual Estimates of the Virial Factor in 10 Quasars: Implications on the Kinematics of the Broad Line Region
2020
Assuming a gravitational origin for the Fe III$\lambda\lambda$2039-2113 redshift and using microlensing based estimates of the size of the region emitting this feature, we obtain individual measurements of the virial factor, $f$, in 10 quasars. The average values for the Balmer lines, $\langle f_{H\beta}\rangle={\bf 0.43\pm 0.20}$ and $\langle f_{H\alpha}\rangle={\bf 0.50\pm 0.24}$, are in good agreement with the results of previous studies for objects with lines of comparable widths. In the case of Mg II, consistent results, $f_{Mg II} \sim {\bf 0.44}$, can be also obtained accepting a reasonable scaling for the size of the emitting region. The modeling of the cumulative histograms of indi…
Measuring Supermassive Black Hole Masses: Correlation between the Redshifts of the Fe III UV Lines and the Widths of Broad Emission Lines
2019
We test the recently proposed (Mediavilla et al. 2018) black hole mass scaling relationship based on the redshift {with respect to the quasar's rest frame} of the Fe III$\lambda\lambda$2039-2113 line blend. To this end, we fit this feature in the spectra of a well suited sample of quasars, observed with X-shooter at the Very Large Telescope (VLT), whose masses have been independently estimated using the virial theorem. For the quasars of this sample we consistently confirm the redshift of the Fe III$\lambda\lambda$2039-2113 blend and find that it correlates with the squared widths of H$\beta$, H$\alpha$ and Mg II, which are commonly used as a measure of $M_{BH}/R$ to determine masses from t…
Classical Geometric Phases: Foucault and Euler
2020
In the last chapter we saw how a quantum system can give rise to a Berry phase, by studying the adiabatic round trip of its quantum state on a certain parameter space. Rather than considering what happens to states in Hilbert space, we now turn to classical mechanics, where we are concerned instead with the evolution of the system in configuration space. As a first example, we are interested in the geometric phase of an oscillator that is constrained to a plane that is transported over some surface which moves along a certain path in three-dimensional space. Contrary to determining the Berry phase, there is no adiabatic approximation of the motion along the curve involved. The Foucault phas…
Information encoding of a qubit into a multilevel environment
2010
I consider the interaction of a small quantum system (a qubit) with a structured environment consisting of many levels. The qubit will experience a decoherence process, which implies that part of its initial information will be encoded into correlations between system and environment. I investigate how this information is distributed on a given subset of levels as a function of its size, using the mutual information between both entities, in the spirit of the partial-information plots studied by Zurek and co-workers. In this case we can observe some differences, which arise from the fact that I am partitioning just one quantum system and not a collection of them. However, some similar featu…
Poincaré sphere analysis of a ferroelectric liquid crystal optical modulator: application to optimize the contrast ratio
2008
The Poincare sphere representation is used to analyze the polarization transformation achieved with a ferroelectric liquid crystal (FLC) optical modulator. This device acts as a switchable wave-plate, in which the orientation of the principal axes rotates under the action of an applied bipolar voltage. In the standard operational mode for intensity switching, the rotation angle of the principal axes is �θ = π/4 and the phase shift is φ = π (half-wave-plate). However, for wavelengths different from the design one, the FLC deviates from the half-wave-plate performance and the optical contrast is diminished. We use the Poincare sphere representation to perform a theoretical analysis of the int…
Advanced models for nonlocal magneto-electro-elastic multilayered plates based on Reissner mixed variational theorem
2019
In the present work, nonlocal layer-wise models for the analysis of magneto-electro-elastic multilayered plates are formulated. An Eringen non-local continuum behaviour is assumed for the layers material; in particular, as usual in plate theories, partial in-plane nonlocality is assumed whereas local constitutive behaviour is considered in the thickness direction. The proposed plate theories are obtained via the Reissner Mixed Variational Theorem, assuming the generalized displacements and generalized out-of-plane stresses as primary variables, and expressing them as through-the-thickness expansions of suitably selected functions, considering the expansion order as a free parameter. In the …
Driven harmonic oscillators in the adiabatic Magnus approximation
1993
The time evolution of driven harmonic oscillators is determined by applying the Magnus expansion in the basis set of instantaneous eigenstates of the total Hamiltonian. It is shown that the first-order approximation already provides transition probabilities close to the exact values even in the intermediate regime.
Nonequilibrated oscillations of coherence in coupled nonlinear wave systems
2006
International audience; We show that a conservative system of a pair of coupled incoherent nonlinear waves exhibits huge oscillations of coherence, which are characterized by a recurrent transfer of noise fluctuations between the coupled waves. This sustained oscillatory behavior is in contradiction with the expected irreversible evolution towards equilibrium. As a consequence, the process of coherence transfer is characterized by a reduction of nonequilibrium entropy, which violates the H theorem of entropy growth inherent to the kinetic theory.
Adiabatic approximation for quantum dissipative systems: formulation, topology and superadiabatic tracking
2010
A generalized adiabatic approximation is formulated for a two-state dissipative Hamiltonian which is valid beyond weak dissipation regimes. The history of the adiabatic passage is described by superadiabatic bases as in the nondissipative regime. The topology of the eigenvalue surfaces shows that the population transfer requires, in general, a strong coupling with respect to the dissipation rate. We present, furthermore, an extension of the Davis-Dykhne-Pechukas formula to the dissipative regime using the formalism of Stokes lines. Processes of population transfer by an external frequency-chirped pulse-shaped field are given as examples.
The virial theorem and the dark matter problem in hybrid metric-Palatini gravity
2012
Hybrid metric-Palatini gravity is a recently proposed theory, consisting of the superposition of the metric Einstein-Hilbert Lagrangian with an f(R) term constructed a la Palatini. The theory predicts the existence of a long-range scalar field, which passes the Solar System observational constraints, even if the scalar field is very light, and modifies the cosmological and galactic dynamics. Thus, the theory opens new possibilities to approach, in the same theoretical framework, the problems of both dark energy and dark matter. In this work, we consider the generalized virial theorem in the scalar-tensor representation of the hybrid metric-Palatini gravity. More specifically, taking into ac…