Scientific Series

The TeV energy range is a privileged part of the EM spectrum for astrophysical observations, allowing a view of some of the most energetic processes in the Universe, in objects as diverse as supernova remnants and black-hole driven Active Galactic Nuclei. Driven by new instruments, TeV gamma-rays astrophysics has made enormous strides in recent years with the discovery of many new sources, including new classes of sources such as galactic micro-quasars. This talk will give an overview of the state of TeV gamma-ray astrophysics, including the air Cherenkov technique used by ground-based TeV gamma ray detectors, the new instruments in operation or coming on line soon, and some of the results already obtained.

We will postulate a novel notion of probability; this will involve introducing an extra axiom of probability that seems natural from a Bayesian perspective. We will then provide an analogue of Gleason's theorem for these probabilities. We will also discuss why this approach may be useful for generalizations of quantum theory such as quantum gravity theories; this will involve discussing an analogy between Bayesian approaches and relational approaches.

Asymptotic statements like the almost-equi-partition law, the theorm of Shannon Mc -Millan-Breiman, the theorem of Sanov have all natural quantum analogs. They all talk about the thermodynamik limit of quantum spin systems. I will try to summarize these results and sketch the main ideas of proof.

I look at the information-processing involved in a quantum computation, in terms of the difference between the Boolean logic underlying a classical computation and the non-Boolean logic represented by the projective geometry of Hilbert space, in which the subspace structure of Hilbert space replaces the set-theoretic structure of classical logic. I show that the original Deutsch XOR algorithm, Simon's algorithm, and Shor's algorithm all involve a similar geometric formulation. In terms of this picture, I consider the question of where the speedup relative to classical algorithms comes from.

In this talk I will expose different results concerning the properties of quantum many-body systems: on the one hand, I will introduce the concept of fine-grained entanglement loss together with its relation with majorization relations along parameter flows and Renormalization Group flows. The machinery of Conformal Field Theory will allow us to derive very general analytical properties, and some examples -like the XY quantum spin chain- will also be considered. On the other hand, I will describe results concerning the classical simulability of quantum many-body systems by means of Matrix Product States. In particular, I will present an approximated classical simulation of a quantum algorithm by adiabatic evolution solving hard instances of an NP-Complete problem up to 100 qubits.

It is shown that inflationary cosmology may be used to test the statistical predictions of quantum theory at very short distances. Hidden-variables theories, such as the pilot-wave theory of de Broglie and Bohm, allow the existence of vacuum states with non-standard field fluctuations (“quantum non-equilibrium”). It is shown that such non-equilibrium vacua lead to statistical anomalies, such as a breaking of scale invariance for the primordial power spectrum. The results depend only weakly on the details of the de Broglie-Bohm dynamics. Recent observations of the cosmic microwave background are used to set limits on violations of quantum theory in the early universe.

The problem of associating beables (hidden variables) to QFT, in the spirit of what Bohm did for nonrelativistic QM, is not trivial. In 1984, John Bell suggested a way of solving the problem, according to which the beables are the positions of fermions, in a discretized version of QFT, and obey a stochastic evolution that simulates all predictions of QFT. In the continuum limit, it will be shown that the Bell model becomes deterministic and that it is related to the choice of the charge density as a beable. Moreover, the charge superselection rule is a consequence of the Bell model. The non-relativistic limit and the derivation of Bohm's first quantized interpretation in this limit are also studied. I will also consider whether the Bell model can be applied to bosons.