Colloquium

Cold atomic gases in optical lattices are emerging as excellent laboratories for testing models of strongly interacting particles in condensed matter physics. It is possible to tune the interactions, dimensionality, spin, statistics and a host of other variables in a completely disorder free environment. This has opened up unique possibilities of mapping out phase diagrams of quantum models and observing quantum phase transitions for the very first time. I will discuss some of the challenges in this field.

Besides their experimental relevance in condensed matter and quantum information science, quantum spin systems are an interesting playground to study decoherence and quantum entanglement. Random matrices are used since the 50' to model quantum chaotic dynamics and complex quantum systems. I introduce new random matrix models which lead to explicit solutions for some simple open or closed quantum spin systems. They allow to probe the various dynamical regimes of decoherence and the emergence of the classical phase space for the spin, in particular in the non-Markovian regimes where no master equations are available.

Ideas about information are pervasive, yet the fundamental nature and structure of information - if indeed it has one! - remains elusive. Work done from many different perspectives, including those of physics, biology, logic, computer science, statistics, and game and decision theory, has yielded insights into various aspects of information. Could there be a comprehensive, unified theory? We shall chart a particular path, focusing on the idea of *information flow*, and show how common mathematical structures arise in the description of information flow in computer science, logic and quantum information.

Correlations in quantum states are sometimes inaccessible if only restricted types of quantum measurements can be performed, an effect known as quantum data hiding. For example highly entangled states shared by two parties might appear uncorrelated if the parties can only measure locally their shares of the state and communicate classically with each other. In this talk I will first discuss how a better understanding of the peculiar type of correlations found in quantum data hiding states is useful in addressing two challenges of quantum information theory: the design of efficient algorithms for determining if a quantum state is entangled, and the establishment of area laws in gapped local Hamiltonians. Second, I will present new efficient ways of generating data hiding, e.g. employing random local quantum circuits, and will briefly discuss the relevance of this approach to the problem of proving quick equilibration of quantum systems unitarily interacting with a large environment.

It is usually assumed that the quantum wave-particle duality can have no counterpart in classical physics. We were driven into revisiting this question when we found that a droplet bouncing on a vibrated bath could couple to the surface wave it excites. It thus becomes a self-propelled "walker", a symbiotic object formed by the droplet and its associated wave. Through several experiments, we addressed one central question. How can a continuous and spatially extended wave have a common dynamics with a localized and discrete droplet? Surprisingly, quantum-like behaviors emerge; both a form of uncertainty and a form of quantization are observed. This is interesting because the probabilistic aspects of quantum mechanics are often said to be intrinsic and to have no possible relation with underlying unresolved dynamical phenomena. In our experiment we find probabilistic behaviors and they do have a relation with chaotic individual trajectories. These quantum like properties are related in our system to the non-locality of a walker that we called its "wave mediated path memory". The relation of this experiment with the pilot wave model proposed for quantum mechanics by de Broglie will be discussed.

Low-temperature phases of strongly-interacting quantum many-body systems can exhibit a range of exotic quantum phenomena, from superconductivity to fractionalized particles. One exciting prospect is that the ground or low-temperature thermal state of an engineered quantum system can function as a quantum computer. The output of the computation can be viewed as a response, or 'susceptibility', to an applied input (say in the form of a magnetic field). For this idea to be sensible, the usefulness of a ground or low-temperature thermal state for quantum computation cannot be critically dependent on the details of the system's Hamiltonian; if so, engineering such systems would be difficult or even impossible. A much more powerful result would be the existence of a robust ordered phase which is characterised by its ability to perform quantum computation. I'll discuss some recent results on the existence of such a quantum computational phase of matter. I'll outline some positive results on a phase of a toy model that allows for quantum computation, including a recent result that provides sufficient conditions for fault-tolerance. I'll also introduce a more realistic model of antiferromagnetic spins, and demonstrate the existence of a quantum computational phase in a two-dimensional system. Together, these results reveal that the characterisation of quantum computational matter has a rich and complex structure, with connections to renormalisation and recently-proposed concepts of 'symmetry-protected topological order'.

String theory, famously, has a great many ground states. So many, in fact, that some argue that we should seek information in the statistical properties of these vacua, or worse, argue that we should abandon string theory as a theory with predictive power. On the other hand, very few vacua are known that look like the observed world of particle physics. In this talk I will review this situation and show that there are realistic models at the tip of the distribution of vacua, where topological complexity is minimised.

The Large Hadron Collider (LHC) is now running (after a rocky start). This talk reviews why the start was rocky and how this constrains the physics program over the next few years. I will briefly survey how 'naturalness' arguments argue why something should be discovered, and why theoretical proposals fall into three main categories. If time permits I will close by telling you why I think the cosmological constant problem implies the LHC will strike paydirt and make quantum gravity an experimental science.

Cosmic inflation has given us a remarkably successful cosmological phenomenology. But the original goal of explaining why the cosmos is *likely* to take the form we observe has proven very difficult to realize. I review the status of "eternal inflation" with an eye on the roles various infinities have (both helpful and unhelpful) in our current understanding. I then discuss attempts to construct an alternative cosmological framework that is truly finite, using ideas about equilibrium and dark energy. I report some recent results that point to observable signatures.

Hubeny identified a scenario in which a charged particle falling toward a near-extreme Reissner-Nordstrom black hole can penetrate the black hole and drive it beyond the extremal limit, thereby giving rise to an apparent violation of cosmic censorship. A version of this scenario, relevant to a Kerr black hole and involving a particle with orbital and/or spin angular momentum, was recently examined by Jacobson and Sotiriou (following up on earlier work by Hod); here also the black hole is driven beyond the extremal limit. The Hubeny analysis was inconclusive, however, because in her scenario the particle crosses the horizon with a near-vanishing acceleration; the test-body acceleration is of the same order of magnitude as the acceleration produced by the particle's own electromagnetic self-force, which was not fully incorporated in the analysis. In this talk we report on our computation of the electromagnetic self-force acting on a charged particle falling radially toward a Reissner-Nordstrom black hole, and we reveal whether the self-force acts as a cosmic censor by preventing the particle from reaching the event horizon.

In my talk I raise the question of the fundamental limits to the size of thermal machines - refrigerators, heat pumps and work producing engines - and I will present the smallest possible ones. I will also discuss the issue of a possible complementarity between size and efficiency and show that even the smallest machines could be maximally efficient. Finally I will present a new point of view over what is work and what do thermal machines actually do.

Sage is a collection of mature open source software for mathematics, and new code, all unified into one powerful and easy-to-use package. The mission statement of the Sage project is: "Creating a viable free open source alternative to Magma, Maple, Mathematica and Matlab." More information is available at www.sagemath.org. I will use the Sage notebook (a web interface) to demonstrate the use of Sage for a variety of mathematical problems and comment on its design and future direction.