Scientific Series

The standard approach to quantum nonlocality (Bell's Theorem) relies on the assumption of the existence of "free will". I will explain how to get rid of this mysterious assumption in favor of the independence of sources. From this new point of view, Bell's Theorem becomes a statement about Bayesian networks. Besides allowing a more intuitive formulation of the standard result, our formalism also provides new network topologies giving rise to new kinds of nonlocality. Some of these relate to results by Steudel and Ay on the statistical inference of causal relations. Witnessing quantum nonlocality in new network topologies is a challenge which I will pose as an open problem.

We study the general class of gravitational field theories constructed on the basis of scale invariance (and therefore absence of any mass parameters) and invariance under transverse diffeomorphisms (TDiff), which are the 4-volume conserving coordinate transformations. We show that these theories are equivalent to a specific type of scalar-tensor theories of gravity (invariant under all diffeomorphisms) with a number of properties, making them phenomenologically interesting. In particular, they lead to the evolution of the universe supported by present observations: inflation in the past, followed by the radiation and matter dominated stages and accelerated expansion at present. All mass scales in this type of theories come from one and the same source. The massless particle spectrum of these theories contains the graviton and a new particle -- dilaton, which has only derivative couplings and thus escapes the fifth force constraints.

We relate the discrete classical phase space of loop gravity to the continuous phase space of general relativity. Our construction shows that the flux variables do not label a unique geometry, but rather a class of gauge-equivalent geometries. We resolve the tension between the loop gravity geometrical interpretation in terms of singular geometry, and the spin foam interpretation in terms of piecewise-flat geometry, showing that both geometries belong to the same equivalence class. We also establish a clear relationship between Regge geometries and the piecewise-flat spin foam geometries. All of this is based on arXiv:1110.4833.

We present a quantization method based on theEhrenfest theorem embedded in an extended algebraic structure capableof consistently describing hybrid quantum-classical systems, where thestandard quantum and classical mechanics are two limiting cases. TheWigner phase space formulation and the Schordinger equation are foundto be two alternative representations of the quantum case while theKoopman-von Neumann equation is the corresponding classicalcounterpart. Moreover, the developed quantization procedure isgeneralized to describe open systems, quantum/classical field theoriesand relativistic mechanics where new dynamical equations appear,shedding new light on important practical problems such asunderstanding of the quantum/classical transition and modeling ofmesoscopic systems.

Related references: arXiv:1105.4014, arXiv:1112.3679, arXiv:1107.5139

We evaluate the partition function of three dimensional general relativity with a negative cosmological constant, including all known perturbative and non-perturbative contributions to the sum over geometries.

In this talk, I am going to test the concordance cosmology in three different cosmic scales. (1) On the super-horizon scale, “Copi etal. (2009)” have been arguing that the lack of large angular correlations of the CMB temperature field provides strong evidence against the standard, statistically isotropic, LCDM cosmology. I am going to argue that the “ad-hoc” discrepancy is due to the sub-optimal estimator of the low-l multipoles, and a posteriori statistics, which exaggerates the statistical significance. (2) LCDM model also predict the existence of primordial gravitational wave, for which B-mode polarization will be a powerful tool to distinguish different models of the early Universe; (3) On Galactic scales, “Watkins et al. (2008)” shows that the very large bulk flow prefers a very large density fluctuation, which seems to contradict to the LCDM model. We provide a physical explanation for this big bulk flow, based on the assumption that CMB frame does not coincide with matter rest frame, resulting in the tilted Universe. We show that the ‘tilted Universe’ could well explain the bulk flow phenomena and more importantly, the constraints for this tilted Universe can lead to the constraint on the number of e-folds of inflation; (4) In addition, cosmic Mach Number from peculiar velocity catalog may provide a powerful test of the growth of the structure.

I will introduce models of dynamical electroweak symmetry breaking and their present and future impact on LHC physics. I will start by reviewing what LHC has seen and not seen and the main challenges of models of dynamical electroweak symmetry breaking. To overcome some of these problems we need a better understanding of strong dynamics. I will therefore review the state-of-the-art of the phase diagram of strongly coupled theories as function of the number of flavors, colors and matter representation. I will then show how these models can also lead to natural dark matter candidates able to provide a simple resolution to current experimental observations. If times allows, I will introduce new successful models of inflation in which the inflaton emerges as a composite state from a natural four-dimensional strongly coupled theory coupled to gravity.

Categorical quantum mechanics (CQM) uses symmetric monoidal categories to formalize quantum theory, in order to extract the key structures that yield protocols such as teleportation in an abstract way. This formalism admits a purely graphical calculus, but the causal structure of these diagrams, and the formalism in general, is unclear. We begin by considering the signaling abilities of probabilistic devices with inputs and outputs and we show how a non-signaling device can become a perfect signaling device under time-reversal. This conflicts with the causal structure of relativity, and suggests that an `asymmetry' is needed when formalizing causality in CQM. We then show how a fixed causal structure within CQM corresponds to topological connectedness in the graphical language, and that correlations, either classical or quantum, force terminality of the tensor unit. We also show that well-definedness of a global state forces the monoidal product to be only partially defined, which in turn results in a covariance theorem. These structural results lead to a mathematical entity which we call a `causal category'.

I will first present a theorem based on the Decoupling Theorem of [1] which gives sufficient and necessary conditions for a quantum channel (CPTPM) being such that it yields the same output for almost all possible inputs. This theorem allows us to reproduce and generalize results oft [2,3], in which cornerstones of statistical physics are derived from first principles of quantum mechanics, in a very natural and easy way. Specifically, we express them in a way which allows to apply results about random 2-qubit interactions [4]. Furthermore, we apply this theorem to provide a criterion for whether different initial states of some subspace of a quantum mechanical system in contact with an environment have at some given time already evolved to the same state or not. As it turns out, this question can be answered by examining a simple entropic inequality evaluated for just one particular state [5]. Applying this criterion to realistic Hamiltonians with local interactions may lead to improved bounds on the thermalization times of quantum mechanical systems.