Fundamental limitations in the purifications of tensor networks

We show a fundamental limitation in the description of quantum many-body mixed states with tensor networks in purification form. Namely, we show that there exist mixed states which can be represented as a translationally invariant (TI) matrix product density operator valid for all system sizes, but for which there does not exist a TI purification valid for all system sizes. The proof is based on an undecidable problem and on the uniqueness of canonical forms of matrix product states. The result also holds for classical states.

The Sound of the Digital Global City

Madrid has been the center of Spanish musical scene and industry since the 80s, when “la movida” becomes the metaphor for the new colorful, young and cosmopolitan country established with the arrival of democracy. The city, in this way, is basically a place. But this sense of place started to crash with the arrival of digital music. In the new paradigm, intermediaries were supposed to disappear and music was something contained in networks and computers. The question now is how to integrate digital music, a nonphysical, individual experience, with the way in which the city of Madrid is lived through in musical terms. With the advent of digital music, concerts became the primary source of income for musicians. The centrality of the gig can be understood as the confirmation that we are living in an economy of experience. This centrality also reorganized the way in which music is produced and consumed: now, records are produced in order to create the opportunity of a musical event (band promote their tour as presentation of their latest recordings) that can be promoted in social networks and media; concerts are the places where musicians construct their fans’ communities and are the places were records are sold, not a way to know the band but to demonstrate both the support for the band and the status of the listeners. To study the place of music in the process of metropolization in Madrid we need to understand music as a field of tension

Strength of the Iberian intraplate lithosphere: Cenozoic deformations and seismicity

Previous studies about the strength of the lithosphere in the center of Iberia fail to resolve the depth of earthquakes because of the rheological uncertainties. Therefore, new contributions are considered (the crustal structure from a density model) and several parameters (tectonic regime, mantle rheology, strain rate) are checked in this paper to properly examine the role of lithospheric strength in the intraplate seismicity and the Cenozoic evolution. The strength distribution with depth, the integrated strength, the effective elastic thickness and the seismogenic thickness have been calculated by a finite element modelling of the lithosphere across the Central System mountain range and the bordering Duero and Madrid sedimentary basins. Only a dry mantle under strike-slip/extension and a strain rate of 10-15 s-1, or under extension and 10-16 s-1, causes a strong lithosphere. The integrated strength and the elastic thickness are lower in the mountain chain than in the basins. This heterogeneity has been maintained since the Cenozoic and determine the mountain uplift and the biharmonic folding of the Iberian lithosphere during the Alpine deformations. The seismogenic thickness bounds the seismic activity in the upper–middle crust, and the decreasing crustal strength from the Duero Basin towards the Madrid Basin is related to a parallel increase in Plio–Quaternary deformations and seismicity. However, elasto–plastic modelling shows that current African–Eurasian convergence is resolved elastically or ductilely, which accounts for the low seismicity recorded in this region.