Topological resonances on quantum graphs
Françoise Truc, (Université de Grenoble, Institut Fourier)
We consider metric graphs which consist of a finite graph with some
to some vertices. To this graph is associated a Laplacian using the
Kirchoff conditions. We describe some asymptotic properties of the resonances close to
the real axis. This is a joint work with Y. Colin de Verdière.
Classification of randomized reference models for temporal network data
Taro Takaguchi (National Institute of Information and Communications Technology, Tokyo)
When we have a network data, randomization techniques give us insights into its structural characteristics. The networks resampled after randomizations work as a baseline for a comparison with the empirical network (like a null model for statistical hypothesis testing). This randomization framework has successfully unveiled notable features of complex “static” networks. When the focal data is “temporal” networks, researchers have also proposed different randomization techniques. However, the addition of temporality makes the number of possible combinations of randomization procedures diverge, and thus choosing and designing suitable randomization techniques are nontrivial problems. As a first step towards developing a unified framework of randomization, we propose a taxonomy of existing randomization techniques, based on their methodological nature and their effects on network structure. We hope this work be a starting point for the development of the principled approach for the characterization of general time-varying network data based on randomizations.
This work is the result of a collaboration project with Laetitia Gauvin (ISI), Marton Karsai (ENS Lyon), Mikko Kivela (Aalto), Mathieu Genois (GESIS), Eugenio Valdano (Universitat Rovira i Virgili), and Christian Vestergaard (Institut Pasteur).
Complex Langevin simulations and the QCD phase diagram
Benjamin Jaeger (ETH, Zürich)
The sign problem in particle physics appears in QCD as soon as a non-zero chemical potential is studied. This prevents direct Lattice simulations to determine the phase structure of the strong force. Complex Langevin methods have been successfully used for various models or approximations of QCD, however, in some scenarios it converges to incorrect results. We will present a new method that helps to improve the convergence by staying close to the SU(3) manifold. Here we will focus on pure Yang-Mills simulations and QCD in the limit of heavy quarks, which provide a testing scenario for these simulations.
Resonance theory for the dynamics of open dimers
Marco Merkli (Department of Mathematics and Statistics,University of Newfoundland, Canada)
We examine the dynamics of a dimer strongly interacting with noisy quantum reservoirs. This open system, a strongly coupled spin-boson system, is used to model excitation- and charge transfer in quantum chemical and biological reactions (redox, photosynthesis). We analyze the processes using a dynamical quantum resonance theory. Due to the strong coupling, ordinary methods (spectral deformation) cannot be applied, so we develop an extended Mourre theory to construct a resonance expansion of the propagator. In particular, we derive an expression for the reaction rates, proving the celebrated Marcus Formula of quantum chemistry.
Emergence of Classical Behavior in the Early Universe
Abhay Ashtekar (Institute for Gravitation and the Cosmos, Penn State)
In the inflationary paradigm, the very early universe is described using quantum field theory in cosmological space-times. In particular, the origin of the large scale anisotropies in the CMB is traced back to vacuum fluctuations of operators representing cosmological inhomogeneities. However, one then assumes that after a certain stage during inflation, dynamics of these inhomogeneities is well-described by the classical theory. This so-called `quantum to classical transition’ is at first puzzling and has drawn quite a bit of attention. In this talk I will first elucidate this issue, explain why some of the reasoning is incorrect, and arrive at a precise statement of why and how classical behavior emerges. Discussion will not assume any details of inflation, or even cosmology, and will be framed in the language normally used in quantum mechanics.
Axion cosmology from lattice QCD
Sandor Katz (Eotvos U, Budapest)
The strong CP problem of QCD can be solved via the Peccei-Quinn mechanism. The resulting pseudo-Goldstone boson, the axion is a natural candidate for dark matter. In order to quantitatively understand axion dark matter production two important QCD inputs are required : the equation of state and the topological susceptibility at high temperatures. Recent lattice calculations of these quantities will be presented and they will be used to constrain the axion mass in different axion production scenarios.
Reference : S. Borsanyi et al., "Calculation of the axion mass based on high-temperature lattice quantum chromodynamics’’, Nature 539 (2016) no.7627, 69-71, https://arxiv.org/abs/1606.07494
Causality without events
Michal ECKSTEIN (Uniwersytet Jagiellonski, Krakow)
Einstein’s causality is one of the fundamental principles underlying modern physical theories. Whereas it is readily implemented in classical physics founded on Lorentzian geometry, its status in quantum theory has long been controversial. It is usually believed that the quantum nature of spacetime at small scales induces the breakdown of causality, although there is no empirical evidence that would support such a view. In my talk, I will argue that one can have a rigid causal structure even in a `quantum spacetime’ without the local events. To this end I will draw from the mathematical richness of noncommutative geometry à la Connes and an operational viewpoint on physics. I will illustrate the general concept with an `almost commutative’ toy-model and discuss the potential empirical consequences.