Talks

Calculating the path integral over all causal sets will take a lot of computing power, and requires a way to suppress non-manifold like causal sets. To work towards these goals we can start by taking the path integral over a restricted class of causal sets, the 2d orders. Using these have found a phase transition and been able to study the Hartle-Hawking wave function in causal sets. In this talk I will present these recent results (arXiv:1410.8775 and arXiv:1706.06432), and some preliminary data exploring how the behavior of the 2d orders is influenced by coupling them to an Ising model.

Real-world quantum systems description - Pure state vs Mixed states - Purification of Mixed States; Generalized measurement - Mixtures of "ideal measurement" - Ideal measurement of a composite system - POVMs.

Infinite Dimensional Systems -  Dirac's approach vs von Neumann's approach; Operational Postulates for open (real-world) quantum systems: probabilistic mixtures of pure states vs Partial description of composite system (partial trace, reduced state) - Operational postulate 1. 

After a small review on divergent series and Borel resummation I will discuss a geometric approach based on Picard-Lefschetz theory to study the interplay between perturbative and non-perturbative effects in the QM path integral.

Such approach can be used to characterize when the perturbative series gives the full answer and when the inclusion of non-trivial saddles--instantons--is mandatory. I will then show how a simple deformation of the original perturbation theory allows to recover the full non perturbative answer from the perturbative coefficients alone, without the need of including instanton corrections. I will illustrate this technique in examples which are known to contain non-perturbative effects, such as the (supersymmetric) double-well potential, the pure anharmonic oscillator, and the perturbative expansion around a false vacuum.

The hydrodynamic approximation is an extremely powerful tool to describe the behavior of many-body systems such as gases. At the Euler scale (that is, when variations of densities and currents occur only on large space-time scales), the approximation is based on the idea of local thermodynamic equilibrium: locally, within fluid cells, the system is in a Galilean or relativistic boost of a Gibbs equilibrium state. This is expected to arise in conventional gases thanks to ergodicity and Gibbs thermalization, which in the quantum case is embodied by the eigenstate thermalization hypothesis. However, integrable systems are well known not to thermalize in the standard fashion. The presence of infinitely-many conservation laws preclude Gibbs thermalization, and instead generalized Gibbs ensembles emerge. In this talk I will introduce the associated theory of generalized hydrodynamics (GHD), which applies the hydrodynamic ideas to systems with infinitely-many conservation laws. It describes the dynamics from inhomogeneous states and in inhomogeneous force fields, and is valid both for quantum systems such as experimentally realized one-dimensional interacting Bose gases and quantum Heisenberg chains, and classical ones such as soliton gases and classical field theory. I will give an overview of what GHD is, how its main equations are derived, its relation to quantum and classical integrable systems, and some geometry that lies at its core. I will then explain how it reproduces the effects seen in the famous quantum Newton cradle experiment, and how it leads to exact results in transport problems such as Drude weights and non-equilibrium currents.

This is based on various collaborations with Alvise Bastianello, Olalla Castro Alvaredo, Jean-Sébastien Caux, Jérôme Dubail, Robert Konik, Herbert Spohn, Gerard Watts and my student Takato Yoshimura, and strongly inspired by previous collaborations with Denis Bernard, M. Joe Bhaseen, Andrew Lucas and Koenraad Schalm.

The study of super-Eddington accretion is essential to our understanding of the growth of super-massive black holes in the early universe, the accretion of tidally disrupted stars, and the nature of ultraluminous X-ray sources.  Unfortunately, this mode of accretion is particularly difficult to model because of the multidimensionality of the flow, the importance magnetohydrodynamic turbulence, and the dominant dynamical role played by radiation forces.  However, recent increases in computing power and advances in algorithms are facilitating major improvements in our ability to model radiation in numerical simulations of astrophysical plasmas.  I will briefly describe our new radiation transfer modules and discuss our efforts to model super-Eddington accretion flows around stellar mass and supermassive black holes.  I will focus on applications to ultraluminous X-ray sources, which must be radiating well above their Eddington luminosity unless they harbour intermediate mass black holes. I will argue that most of these sources can be (and likely are) "normal" ~10 solar mass black holes accreting and radiating with luminosities well above their Eddington "limit”.

Composite Quantum Systems - Examples and basic mathematical properties; Entanglement - Schmidt decomposition/Schmidt number; Infinite dimensional Hilbert space and unbounded operators - Dirac's approach vs von Neumann's approach.