Harmonic analysis on Cayley Trees II: the Bose Einstein condensation

We investigate the Bose-Einstein Condensation on non homogeneous non amenable networks for the model describing arrays of Josephson junctions on perturbed Cayley Trees. The resulting topological model has also a mathematical interest in itself. The present paper is then the application to the Bose-Einstein Condensation phenomena, of the harmonic analysis aspects arising from additive and density zero perturbations, previously investigated by the author in a separate work. Concerning the appearance of the Bose-Einstein Condensation, the results are surprisingly in accordance with the previous ones, despite the lack of amenability. We indeed first show the following fact. Even when the critical density is finite (which is implied in all the models under consideration, thanks to the appearance of the hidden spectrum), if the adjacency operator of the graph is recurrent, it is impossible to exhibit temperature locally normal states (i.e. states for which the local particle density is finite) describing the condensation at all. The same occurs in the transient cases for which it is impossible to exhibit locally normal states describing the Bose--Einstein Condensation at mean particle density strictly greater than the critical density . In addition, for the transient cases, in order to construct locally normal temperature states through infinite volume limits of finite volume Gibbs states, a careful choice of the the sequence of the finite volume chemical potential should be done. For all such states, the condensate is essentially allocated on the base--point supporting the perturbation. This leads that the particle density always coincide with the critical one. It is shown that all such temperature states are Kubo-Martin-Schwinger states for a natural dynamics. The construction of such a dynamics, which is a very delicate issue, is also done.Comment: 28 pages, 6 figures, 1 tabl

Design and characterization of 90 GHz feedhorn-coupled TES polarimeter pixels in the SPTpol camera

The SPTpol camera is a two-color, polarization-sensitive bolometer receiver, and was installed on the 10 meter South Pole Telescope in January 2012. SPTpol is designed to study the faint polarization signals in the Cosmic Microwave Background, with two primary scientific goals. One is to constrain the tensor-to-scalar ratio of perturbations in the primordial plasma, and thus constrain the space of permissible inflationary models. The other is to measure the weak lensing effect of large-scale structure on CMB polarization, which can be used to constrain the sum of neutrino masses as well as other growth-related parameters. The SPTpol focal plane consists of seven 84-element monolithic arrays of 150 GHz pixels (588 total) and 180 individual 90 GHz single-pixel modules. In this paper we present the design and characterization of the 90 GHz modules

Versatile engineering of multimode squeezed states by optimizing the pump spectral profile in spontaneous parametric down-conversion

We study the quantum correlations induced by spontaneous parametric down-conversion (SPDC) of a frequency comb. We derive a theoretical method to find the output state corresponding to a pump with an arbitrary spectral profile. After applying it to the relevant example of a spectrally chirped pump, we run an optimization algorithm to numerically find the pump profiles maximizing some target functions. These include the number of independently squeezed modes and the variances of nullifiers defining cluster states used in many continuous-variable quantum information protocols. To assess the advantages of pump-shaping in real experiments we take into account the physical limitations of the pulse shaper.Comment: Updated title, improved presentation and figures, added references, corrected typos. Closer to the version accepted for publicatio

Constructing living buildings: a review of relevant technologies for a novel application of biohybrid robotics

Biohybrid robotics takes an engineering approach to the expansion and exploitation of biological behaviours for application to automated tasks. Here, we identify the construction of living buildings and infrastructure as a high-potential application domain for biohybrid robotics, and review technological advances relevant to its future development. Construction, civil infrastructure maintenance and building occupancy in the last decades have comprised a major portion of economic production, energy consumption and carbon emissions. Integrating biological organisms into automated construction tasks and permanent building components therefore has high potential for impact. Live materials can provide several advantages over standard synthetic construction materials, including self-repair of damage, increase rather than degradation of structural performance over time, resilience to corrosive environments, support of biodiversity, and mitigation of urban heat islands. Here, we review relevant technologies, which are currently disparate. They span robotics, self-organizing systems, artificial life, construction automation, structural engineering, architecture, bioengineering, biomaterials, and molecular and cellular biology. In these disciplines, developments relevant to biohybrid construction and living buildings are in the early stages, and typically are not exchanged between disciplines. We, therefore, consider this review useful to the future development of biohybrid engineering for this highly interdisciplinary application.publishe