Alternative Structures and Bihamiltonian Systems

In the study of bi-Hamiltonian systems (both classical and quantum) one starts with a given dynamics and looks for all alternative Hamiltonian descriptions it admits.In this paper we start with two compatible Hermitian structures (the quantum analog of two compatible classical Poisson brackets) and look for all the dynamical systems which turn out to be bi-Hamiltonian with respect to them.Comment: 18 page

X-ray and Sunyaev-Zel'dovich scaling relations in galaxy clusters

[Abridged] We present an analysis of the scaling relations between X-ray properties and Sunyaev-Zel'dovich (SZ) parameters for a sample of 24 X-ray luminous galaxy clusters observed with Chandra and with measured SZ effect. These objects are in the redshift range 0.14--0.82 and have X-ray bolometric luminosity L>10^45 erg/s. We perform a spatially resolved spectral analysis and recover the density, temperature and pressure profiles of the ICM, just relying on the spherical symmetry of the cluster and the hydrostatic equilibrium hypothesis. We observe that the correlations among X-ray quantities only are in agreement with previous results obtained for samples of high-z X-ray luminous galaxy clusters. On the relations involving SZ quantities, we obtain that they correlate with the gas temperature with a logarithmic slope significantly larger than the predicted value from the self-similar model. The measured scatter indicates, however, that the central Compton parameter y_0 is a proxy of the gas temperature at the same level of other X-ray quantities like luminosity. Our results on the X-ray and SZ scaling relations show a tension between the quantities more related to the global energy of the system (e.g. gas temperature, gravitating mass) and the indicators of the structure of the ICM (e.g. gas density profile, central Compton parameter y_0), showing the most significant deviations from the values of the slope predicted from the self-similar model in the L-T, L-M_{tot}, M_{gas}-T, y_0-T relations. When the slope is fixed to the self-similar value, these relations consistently show a negative evolution suggesting a scenario in which the ICM at higher redshift has lower both X-ray luminosity and pressure in the central regions than the expectations from self-similar model.Comment: MNRAS in press - Minor revision to match published versio

Magnetic Monopole in the Loop Representation

We quantize the electromagnetic field in the presence of a static magnetic monopole, within the loop-representation formalism. We find that the loop-dependent wave functional becomes multivalued, in the sense that it acquires a dependence on the surfaces bounded by the loop. This generalizes what occurs in quantum mechanics in multiply connected spaces. When Dirac's quantization condition holds, this surface-dependence disappears, together with the effect of the monopole on the electromagnetic field.Comment: reference and comment adde

Bose-Einstein condensation of positronium: modification of the s-wave scattering length below the critical temperature

The production of a Bose-Einstein condensate made of positronium may be feasible in the near future. Below the condensation temperature, the positronium collision process is modified by the presence of the condensate. This makes the theoretical description of the positronium kinetics at low temperature challenging. Based on the quasi-particle Bogoliubov theory, we describe the many-body particle-particle collision in a simple manner. We find that, in a good approximation, the full positronium-positronium interaction can be described by an effective scattering length. Our results are general and apply to different species of bosons. The correction to the bare scattering length is expressed in terms of a single dimensionless parameter that completely characterizes the condensate

Reconstructing mass profiles of simulated galaxy clusters by combining Sunyaev-Zeldovich and X-ray images

We present a method to recover mass profiles of galaxy clusters by combining data on thermal Sunyaev-Zeldovich (tSZ) and X-ray imaging, thereby avoiding to use any information on X-ray spectroscopy. This method, which represents a development of the geometrical deprojection technique presented in Ameglio et al. (2007), implements the solution of the hydrostatic equilibrium equation. In order to quantify the efficiency of our mass reconstructions, we apply our technique to a set of hydrodynamical simulations of galaxy clusters. We propose two versions of our method of mass reconstruction. Method 1 is completely model-independent, while Method 2 assumes instead the analytic mass profile proposed by Navarro et al. (1997) (NFW). We find that the main source of bias in recovering the mass profiles is due to deviations from hydrostatic equilibrium, which cause an underestimate of the mass of about 10 per cent at r_500 and up to 20 per cent at the virial radius. Method 1 provides a reconstructed mass which is biased low by about 10 per cent, with a 20 per cent scatter, with respect to the true mass profiles. Method 2 proves to be more stable, reducing the scatter to 10 per cent, but with a larger bias of 20 per cent, mainly induced by the deviations from equilibrium in the outskirts. To better understand the results of Method 2, we check how well it allows to recover the relation between mass and concentration parameter. When analyzing the 3D mass profiles we find that including in the fit the inner 5 per cent of the virial radius biases high the halo concentration. Also, at a fixed mass, hotter clusters tend to have larger concentration. Our procedure recovers the concentration parameter essentially unbiased but with a scatter of about 50 per cent.Comment: 13 pages, 11 figures, submitted to MNRA

Ultrafast Magnetization Dynamics in Diluted Magnetic Semiconductors

We present a dynamical model that successfully explains the observed time evolution of the magnetization in diluted magnetic semiconductor quantum wells after weak laser excitation. Based on the pseudo-fermion formalism and a second order many-particle expansion of the exact p-d exchange interaction, our approach goes beyond the usual mean-field approximation. It includes both the sub-picosecond demagnetization dynamics and the slower relaxation processes which restore the initial ferromagnetic order in a nanosecond time scale. In agreement with experimental results, our numerical simulations show that, depending on the value of the initial lattice temperature, a subsequent enhancement of the total magnetization may be observed within a time scale of few hundreds of picoseconds.Comment: Submitted to PR

Alternative linear structures for classical and quantum systems

The possibility of deforming the (associative or Lie) product to obtain alternative descriptions for a given classical or quantum system has been considered in many papers. Here we discuss the possibility of obtaining some novel alternative descriptions by changing the linear structure instead. In particular we show how it is possible to construct alternative linear structures on the tangent bundle TQ of some classical configuration space Q that can be considered as "adapted" to the given dynamical system. This fact opens the possibility to use the Weyl scheme to quantize the system in different non equivalent ways, "evading", so to speak, the von Neumann uniqueness theorem.Comment: 32 pages, two figures, to be published in IJMP

Performance analysis of an interacting quantum dot thermoelectric system

We analyze the nanocaloritronic performance of an interacting quantum dot that is subject to an applied bias and an applied temperature gradient. It is now well known that, in the absence of phonon contribution, a weakly coupled non-interacting quantum dot can operate at thermoelectric efficiencies approaching the Carnot limit. However, it has also been recently pointed out that such peak efficiencies can only be achieved when operated in the reversible limit, with a vanishing current and hence a vanishing power output. In this paper, we point out three fundamental results affecting the thermoelectric performance due to the inclusion of Coulomb interactions: a) The reversible operating point carries zero efficiency, b) operation at finite power output is possible even at peak efficiencies approaching the Carnot value, and c) the evaluated trends of the the maximum efficiency deviate considerably from the conventional {\it{figure of merit}} $zT$ based result. Finally, we also analyze our system for thermoelectric operation at maximum power output.Comment: 10 pages, 6 figures, Resubmission- to be published in Phys. Rev.