Forum de Physique Statistique à l'École Normale Supérieure

Next seminar

Max McGinley  (18 February, 11h, L378)

Universality and complexity in early-time quantum dynamics

While the dynamics of many-body quantum systems can be extraordinarily complex, quantitative predictions can often be made by identifying appropriate statistical ensembles that capture the universal behaviour of a broad class of systems. In the context of dynamics, the late-time behaviour of scrambling systems without conservation laws are expected to be described by the spherical Haar ensemble—a uniform distribution over all states in Hilbert space. By understanding the key properties of Haar-random states, and the mechanisms by which they can emerge, we can understand the physics of a diverse range of systems in a unified way.

In this talk, I will describe new universal statistical theories that capture the dynamics of systems in regimes beyond Haar, focusing in particular on the states generated by early-time dynamics. These states, which are far from being thermalized, are much ‘simpler’ that Haar-random states, possessing short-range correlations and entanglement; nevertheless, their output distributions can still be complex, and classically hard to simulate. We argue that the behaviour of these early-time states can be captured by the so-called Scrooge ensemble [PRA 49, 668 (1994)], a more structured generalization of the Haar ensemble. As well as presenting evidence that the Scrooge ensemble describes the outputs of random constant-depth quantum circuits, I will show how our hypothesis accounts for the observed complexity of constant-time quantum dynamics, and predicts a dramatic susceptibility of these states to small amounts of noise. I will conclude by illustrating how the Scrooge ensemble could be used to describe other kinds of dynamics with beyond-Haar-random structure, such as the volume-law phase of monitored quantum circuits, and dynamics with conservation laws.

Upcoming seminars

Pavel Orlav (19 February, 11h, L378)

Classical thermalization and the Eigenstate Thermalization Hypothesis

Thermalization in isolated quantum systems is commonly understood through the Eigenstate Thermalization Hypothesis (ETH), which attributes thermal behavior to properties of individual eigenstates of the unitary time-evolution operator. Classical dynamics is also governed by a unitary evolution via the Koopman operator. In this seminar, I will explore whether an analogue of the ETH can be meaningfully formulated in the classical setting.

Based on arXiv:2602.02681

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25 February, Pierfrancesco Urbani

Separation of timescales controls feature learning and overfitting in large neural networks.

To understand the inductive bias and generalization capabilities of large, overparameterized machine learning models, it is essential to analyze the dynamics of their training algorithms. Using dynamical mean field theory we investigate the learning dynamics of large two-layer neural networks. Our findings reveal that, for networks with a large width, the training process exhibits a separation of timescales phenomenon. This leads to several key observations: 

1. The emergence of a slow timescale linked to the growth in Gaussian/Rademacher complexity of the network; 

2. An inductive bias favoring low complexity when the initial model complexity is sufficiently small; 

3. A dynamical decoupling between feature learning and overfitting phases; 

4. A non-monotonic trend in test error, characterized by a "feature unlearning" regime at later stages of training. 

Joint work with Andrea Montanari.

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3 March, Ana Lucia Retore

25 March, Laura Foini

1 April, Clément Hongler

8 April, Jean-Noël Fuchs

15 April, Sarah Loos