The Poincare-Birkhoff theorem in Quantum Mechanics

Quantum manifestations of the dynamics around resonant tori in perturbed Hamiltonian systems, dictated by the Poincar\'e--Birkhoff theorem, are shown to exist. They are embedded in the interactions involving states which differ in a number of quanta equal to the order of the classical resonance. Moreover, the associated classical phase space structures are mimicked in the quasiprobability density functions and their zeros.Comment: 5 pages, 3 figures, Full resolution figures available at http://www.df.uba.ar/users/wisniaki/publications.htm

ISO observations of M8, the Lagoon nebula

In this paper, IRAS, ISO, and molecular line observations of the M8 and M8E sources in the Lagoon Nebula are reported

Shocks and PDRs in an intermediate mass star forming globule: the case of IC1396N

The dark globule IC1396N is a typical example of a star formation process induced by radiation driven implosion due to the strong UV field from a nearby O6 star. The IRAS source embedded in the globule and its associated molecular outflow have been observed with the Long Wavelength Spectrometer (LWS) on ISO revealing an extremely rich spectrum including: CO rotational lines from J=14-13 up to J=28-27, rotational lines from ortho-H2O, OH lines involving the first four rotational levels of both ladders, atomic (OI 63μm, OI 145μm) and ionic (CII 157μm, OIII 52μm, OIII 88μm) lines. A complex picture arises, where an externally illuminated PDR coexists with strong C-shocks within IC1396N and whose origin is not clear

Multifractal eigenstates of quantum chaos and the Thue-Morse sequence

We analyze certain eigenstates of the quantum baker's map and demonstrate, using the Walsh-Hadamard transform, the emergence of the ubiquitous Thue-Morse sequence, a simple sequence that is at the border between quasi-periodicity and chaos, and hence is a good paradigm for quantum chaotic states. We show a family of states that are also simply related to Thue-Morse sequence, and are strongly scarred by short periodic orbits and their homoclinic excursions. We give approximate expressions for these states and provide evidence that these and other generic states are multifractal.Comment: Substantially modified from the original, worth a second download. To appear in Phys. Rev. E as a Rapid Communicatio

Probing the quantum phase transition in the Dicke model through mechanical vibrations

This paper is concerned with quantum dynamics of a system coupled to a critical reservoir. In this context, we employ the Dicke model which is known to exhibit a super radiant quantum phase transition (QPT) and we allow one of the mirrors to move under a linear restoring force. The electromagnetic field couples to the movable mirror though radiation pressure just like in typical optomechanical setups. We show that, in the thermodynamical limit, the super-radiant phase induces a classical driving force on the mirror without causing decoherence.Comment: 6 pages, 3 figures, final versio

Quantum Process Tomography of the Quantum Fourier Transform

The results of quantum process tomography on a three-qubit nuclear magnetic resonance quantum information processor are presented, and shown to be consistent with a detailed model of the system-plus-apparatus used for the experiments. The quantum operation studied was the quantum Fourier transform, which is important in several quantum algorithms and poses a rigorous test for the precision of our recently-developed strongly modulating control fields. The results were analyzed in an attempt to decompose the implementation errors into coherent (overall systematic), incoherent (microscopically deterministic), and decoherent (microscopically random) components. This analysis yielded a superoperator consisting of a unitary part that was strongly correlated with the theoretically expected unitary superoperator of the quantum Fourier transform, an overall attenuation consistent with decoherence, and a residual portion that was not completely positive - although complete positivity is required for any quantum operation. By comparison with the results of computer simulations, the lack of complete positivity was shown to be largely a consequence of the incoherent errors during the quantum process tomography procedure. These simulations further showed that coherent, incoherent, and decoherent errors can often be identified by their distinctive effects on the spectrum of the overall superoperator. The gate fidelity of the experimentally determined superoperator was 0.64, while the correlation coefficient between experimentally determined superoperator and the simulated superoperator was 0.79; most of the discrepancies with the simulations could be explained by the cummulative effect of small errors in the single qubit gates.Comment: 26 pages, 17 figures, four tables; in press, Journal of Chemical Physic

Accuracy of Trace Formulas

Using quantum maps we study the accuracy of semiclassical trace formulas. The role of chaos in improving the semiclassical accuracy, in some systems, is demonstrated quantitatively. However, our study of the standard map cautions that this may not be most general. While studying a sawtooth map we demonstrate the rather remarkable fact that at the level of the time one trace even in the presence of fixed points on singularities the trace formula may be exact, and in any case has no logarithmic divergences observed for the quantum bakers map. As a byproduct we introduce fantastic periodic curves akin to curlicues.Comment: 20 pages, uuencoded and gzipped, 1 LaTex text file and 9 PS files for figure

Wigner Functions and Separability for Finite Systems

A discussion of discrete Wigner functions in phase space related to mutually unbiased bases is presented. This approach requires mathematical assumptions which limits it to systems with density matrices defined on complex Hilbert spaces of dimension p^n where p is a prime number. With this limitation it is possible to define a phase space and Wigner functions in close analogy to the continuous case. That is, we use a phase space that is a direct sum of n two-dimensional vector spaces each containing p^2 points. This is in contrast to the more usual choice of a two-dimensional phase space containing p^(2n) points. A useful aspect of this approach is that we can relate complete separability of density matrices and their Wigner functions in a natural way. We discuss this in detail for bipartite systems and present the generalization to arbitrary numbers of subsystems when p is odd. Special attention is required for two qubits (p=2) and our technique fails to establish the separability property for more than two qubits.Comment: Some misprints have been corrected and a proof of the separability of the A matrices has been adde

Proper Motion of Water Masers Associated with IRAS 21391+5802: Bipolar Outflow and an AU-Scale Dusty Circumstellar Shell

We present VLBA observations of water maser emission associated with the star-forming region IRAS 21391+5802, which is embedded in a bright rimmed cometary globule in IC1396. The angular resolution of the maps is about 0.8 mas, corresponding to a spatial resolution of about 0.6 AU, at an estimated distance of 750 pc. Proper motions are derived for 10 maser features identified consistently over three epochs, which were separated by intervals of about one month. The masers appear in four groups, which are aligned linearly on the sky, roughly along a northeast-southwest direction, with a total separation of about 520 AU (about 0.7 arcseconds). The 3-D velocities of the masers have a maximum value of about 42 km/s (about 9 AU/yr). The average error on the derived proper motions is about 4 km/s. The overall pattern of proper motions is indicative of a bipolar outflow. Proper motions of the masers in a central cluster, with a projected extent of about 20 AU, show systematic deviations from a radial outflow. However, we find no evidence of Keplerian rotation, as has been claimed elsewhere. A nearly circular loop of masers lies near the middle of the cluster. The radius of this loop is 1 AU and the line-of-sight velocities of the masers in the loop are within 2 km/s of the systemic velocity of the region. These masers presumably exist at the radial distance where significant dust condensation occurs in the outflow emanating from the star.Comment: 15 pages, 4 figures. Accepted for publication in the Astrophysical Journal. Version 2.12.00: Astrometric coordinates of maser revise

Phase space contraction and quantum operations

We give a criterion to differentiate between dissipative and diffusive quantum operations. It is based on the classical idea that dissipative processes contract volumes in phase space. We define a quantity that can be regarded as ``quantum phase space contraction rate'' and which is related to a fundamental property of quantum channels: non-unitality. We relate it to other properties of the channel and also show a simple example of dissipative noise composed with a chaotic map. The emergence of attaractor-like structures is displayed.Comment: 8 pages, 6 figures. Changes added according to refferee sugestions. (To appear in PRA