Abstracts > Keynotes

Abstract. The big jump principle is a peculiar mechanism that triggers large fluctuations in stochastic processes with heavy-tailed distributions. The principle explains extreme events in a wide class of natural and man-made systems not in terms of an accumulation of many small subevents but solely as an effect of the biggest event, the big jump. The big jump principle is a well established mathematical result for sums of independent and identically distributed random variables with sub-exponential distribution. However its extension and application to more physical processes is still not well understood. By means of an effective approach, we show that the principle applies to a wide class of problems casted in terms anomalous transport, such as generalized Lévy walks and the Lévy Lorentz gas, also in the presence of stretched exponentials. We use the principle to derive the exact form of the tail of the probability distribution, providing a physical explanation of the processes driving the rare events.

Abstract. The sine-Gordon model appears as the low-energy effective field theory of various one-dimensional gapped quantum systems. Even though the model is integrable, in its applications as an effective description, integrability may or may not play an important role. Here we investigate the dynamics of generic, non-integrable systems in the sine-Gordon family at finite temperature within the semiclassical approach. Focusing on time scales where the effect of nontrivial quasiparticle scatterings become relevant, we obtain universal results for the long-time behavior of dynamical correlation functions. We find that correlation functions of vertex operators behave neither ballistically nor diffusively but follow a stretched exponential decay in time. We also study the full counting statistics of the topological current and find that distribution of the transferred charge is non-Gaussian with its cumulants scaling non-uniformly in time.

Abstract. The Eigenstate Thermalization Hypothesis concerns the properties of eigenstates of chaotic quantum systems. It has been developed by Berry, Deutch and Srednicki. Following their same general viewpoint, it has been recently generalized to include higher correlations that were hitherto neglected and are important for certain purposes. The enlarged framework is found to have close connections to the Free Probability construction that are promising and largely unexplored.

Abstract. Recently, accurate numerical and experimental observations suggested super-diffusive high-temperature equilibrium spin transport in Heisenberg XXX spin 1/2 chains (unitary rational 6-vertex model) with KPZ 2-point functions and dynamical exponent z=3/2. The phenomenon has been later conjectured to extend to arbitrary classical and quantum integrable systems with non-abelian global symmetries. The dynamical exponent z=3/2 has been explained via a self-consistent argument within the generalised hydrodynamics (GHD) picture of thermodynamic Bethe ansatz. I will discuss a simple integrable model on a discrete space-time lattice allowing for an arbitrary compact Lie group symmetry, exhibiting identical "mean KPZ physics".
In the second part of my talk, I will present a simple minimal interacting model - a reversible charged cellular automaton - with exactly solvable full counting statistics, analytically disclosing the divergence of scaled cumulants and critical behaviour. We argue that this exact solution can describe the behaviour of typical fluctuations in symmetric integrable systems.

Abstract. The real space renormalisation group approach for disordered quantum many-body systems, known as strong-disorder renormalization group or SDRG, turned out to be particularly suited to study entanglement properties in such systems. In the first part, I will review relevant literature showing how to use SDRG to get the behaviour of various entanglement measures in the ground state of random spin chains. In the second part I will describe how the method can be extended to the out-of-equilibrium scenario, as first done in [Vosk, Altman, Phys. Rev. Lett. 112, 217204 (2014)], and use this to derive analytic predictions for quantum information spreading in random spin chains.

Abstract. In this talk, I will discuss some recent results concerning the training and exploitation of Restricted Boltzmann Machines (RBM). RBMs are unsupervised learning models, whose main task is to generate new samples that resemble as closely as possible those contained in a given dataset. Formally, RBMs are very simple disordered Ising models, whose couplings and external fields are fitted via gradient descent (stochastic) dynamics. This means that if the training procedure succeeds, one ends with an effective model for the data whose typical configurations should be statistically similar, and yet different, to those belonging to the dataset. Furthermore, these trained effective Hamiltonians bring many opportunities for automatic pattern extraction of large databases if one knows where to look. In my talk, I will discuss some examples of these possibilities. Yet, despite their simplicity, training good RBMs is often a tedious and unstable task. I will show that these difficulties are a direct consequence of poor estimations of the negative part of the gradient, actually, the result of using non-convergent Markov Chain Monte Carlo simulations to estimate the model's equilibrium distribution. In addition, we observe that non-equilibrium samplings introduce strong memory effects in the model's Hamiltonian, that can be exploited to produce very high quality samples in short training times, only at the price of forgetting about fitting effective models with the "good" equilibrium properties (hence useful for interpretability). I will also show that RBMs learnt with clustered datasets, such as genomic or proteomic sequence datasets, are particularly hard to train due to their multimodal structure. We show that this difficulty can be overcome using multicanonical sampling methods. Finally, we see that RBMs trained in that way present significantly faster relaxational dynamics than RBMs trained with the standard PCD procedure.