Publications

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Engineering of anyons on M5-probes via flux quantization

Hisham Sati, Urs Schreiber

SciPost Phys. Lect. Notes 107 (2025) · published 4 November 2025 | · pdf

These extended lecture notes survey a novel derivation of anyonic topological order (as seen in fractional quantum Hall systems) on single magnetized M5-branes probing Seifert orbi-singularities ("geometric engineering" of anyons), which we motivate from fundamental open problems in the field of quantum computing. The rigorous construction is non-Lagrangian and non-perturbative, based on previously neglected global completion of the M5-brane's tensor field by flux-quantization consistent with its non-linear self-duality and its twisting by the bulk C-field. This exists only in little-studied non-abelian generalized cohomology theories, notably in a twisted equivariant (and "twistorial") form of unstable Cohomotopy ("Hypothesis H"). As a result, topological quantum observables form Pontrjagin homology algebras of mapping spaces from the orbi-fixed worldvolume into a classifying 2-sphere. Remarkably, results from algebraic topology imply from this the quantum observables and modular functor of abelian Chern-Simons theory, as well as braid group actions on defect anyons of the kind envisioned as hardware for topologically protected quantum gates.
Lecture notes on large deviations in non-equilibrium diffusive systems

Bernard Derrida

SciPost Phys. Lect. Notes 106 (2025) · published 29 October 2025 | · pdf

These notes are a written version of lectures given in the 2024 Les Houches Summer School on Large deviations and applications. They are are based on a series of works published over the last 25 years on steady properties of non-equilibrium systems in contact with several heat baths at different temperatures or several reservoirs of particles at different densities. After recalling some classical tools to study non-equilibrium steady states, such as the use of tilted matrices, the Fluctuation theorem, the determination of transport coefficients, the Einstein relations or fluctuating hydrodynamics, they describe some of the basic ideas of the macroscopic fluctuation theory allowing to determine the large deviation functions of the density and of the current of diffusive systems.
Simplified derivations for high-dimensional convex learning problems

David G. Clark, Haim Sompolinsky

SciPost Phys. Lect. Notes 105 (2025) · published 23 October 2025 | · pdf

Statistical-physics calculations in machine learning and theoretical neuroscience often involve lengthy derivations that obscure physical interpretation. Here, we give concise, non-replica derivations of several key results and highlight their underlying similarities. In particular, using a cavity approach, we analyze three high-dimensional learning problems: perceptron classification of points, perceptron classification of manifolds, and kernel ridge regression. These problems share a common structure—a bipartite system of interacting feature and datum variables—enabling a unified analysis. Furthermore, for perceptron-capacity problems, we identify a symmetry that allows derivation of correct capacities through a naïve method.
An introduction to large deviations with applications in physics

Ivan N. Burenev, Daniël W. H. Cloete, Vansh Kharbanda, Hugo Touchette

SciPost Phys. Lect. Notes 104 (2025) · published 23 October 2025 | · pdf

These notes are based on the lectures that one of us (HT) gave at the Summer School on the "Theory of Large Deviations and Applications," held in July 2024 at Les Houches in France. They present the basic definitions and mathematical results that form the theory of large deviations, as well as many simple motivating examples of applications in statistical physics, which serve as a basis for the many other lectures given at the school that covered more specific applications in biophysics, random matrix theory, nonequilibrium systems, geophysics, and the simulation of rare events, among other topics. These notes extend the lectures, which can be accessed online, by presenting exercises and pointer references for further reading.
Stochastic resetting and large deviations

Martin R. Evans, John C. Sunil

SciPost Phys. Lect. Notes 103 (2025) · published 16 October 2025 | · pdf

Stochastic resetting has been a subject of considerable interest within statistical physics, both as means of improving completion times of complex processes such as searches and as a paradigm for generating nonequilibrium stationary states. In these lecture notes we give a self-contained introduction to the toy model of diffusion with stochastic resetting. We also discuss large deviation properties of additive functionals of the process such as the cost of resetting. Finally, we consider the generalisation from Poissonian resetting, where the resetting process occurs with a constant rate, to non-Poissonian resetting.
High-dimensional random landscapes: From typical to large deviations

Valentina Ros

SciPost Phys. Lect. Notes 102 (2025) · published 13 October 2025 | · pdf

We discuss tools and concepts that emerge when studying high-dimensional random landscapes, i.e., random functions on high-dimensional spaces. As an illustrative example, we consider an inference problem in two forms: low-rank matrix estimation (case 1) and low-rank tensor estimation (case 2). We show how to map the inference problem onto the optimization problem of a high-dimensional landscape, which exhibits distinct geometrical properties in the two cases. We discuss methods for characterizing typical realizations of these landscapes and their optimization through local dynamics. We conclude by highlighting connections between the landscape problem and large deviation theory.
Les Houches lectures on flow networks in biology

Swarnavo Basu, Karen Alim

SciPost Phys. Lect. Notes 101 (2025) · published 10 October 2025 | · pdf

Flows are essential to transport resources over large distances. As soon as diffusion becomes time-limiting, flows are needed. Flows are key for the function of multiple human organs, from the blood vasculature to the lungs, the digestive tract, the lymphatic system, and many more. While physics governs the flow dynamics, biology's response to flows governs the flow network architecture. We start with the fluid physics of Stokes flow, the prerequisite to describe the flows in biological flow networks. Then we explore how the network adaptation dynamics of biological flow networks reorganize network architecture to minimize flow dissipation or homogenize transport, storing memories of past flows along the way.
Numerical aspects of large deviations

Alexander K. Hartmann

SciPost Phys. Lect. Notes 100 (2025) · published 30 September 2025 | · pdf

An introduction to numerical large-deviation sampling is provided. First, direct biasing with a known distribution is explained. As simple example, the Bernoulli process is used throughout the text. Next, Markov chain Monte Carlo (MCMC) simulations are introduced. In particular, the Metropolis-Hastings algorithm is explained. As first implementation of MCMC, sampling of the plain Bernoulli model is shown. Next, an exponential bias is used for the same model, which allows one to obtain the tails of the distribution of a measurable quantity. This approach is generalized to MCMC simulations, where the states are vectors of $U(0,1)$ random entries. This allows one to use the exponential or any other bias to access the large-deviation properties of rather arbitrary random processes. Finally, some recent research applications to study more complex models are discussed.
Many-body open quantum systems

Rosario Fazio, Jonathan Keeling, Leonardo Mazza, Marco Schirò

SciPost Phys. Lect. Notes 99 (2025) · published 14 August 2025 | · pdf

These lecture notes discuss the recent theoretical advances in the understanding of open quantum many-body physics in platforms where both dissipative and coherent processes can be tuned and controlled to a high degree. We start by reviewing the theoretical frameworks and methods used to describe and tackle open quantum many-body systems. We then discuss the use of dissipative processes to engineer many-body stationary states with desired properties and the emergence of dissipative phase transitions arising out of the competition between coherent evolution and dissipation. We review the dynamics of open quantum many body systems in the presence of correlated many-body dissipative processes, such as heating and many-body losses. Finally we provide a different perspective on open quantum many-body systems by looking at stochastic quantum trajectories, relevant for the case in which the environment represents a monitoring device, and the associated measurement-induced phase transitions.

13 citations
Lectures in quantum gravity

Ivano Basile, Luca Buoninfante, Francesco Di Filippo, Benjamin Knorr, Alessia Platania, Anna Tokareva

SciPost Phys. Lect. Notes 98 (2025) · published 7 August 2025 | · pdf

Formulating a quantum theory of gravity lies at the heart of fundamental theoretical physics. This collection of lecture notes encompasses a selection of topics that were covered in six mini-courses at the Nordita PhD school "Towards Quantum Gravity". The scope was to provide a coherent picture, from its foundation to forefront research, emphasizing connections between different areas. The lectures begin with perturbative quantum gravity and effective field theory. Subsequently, two ultraviolet-complete approaches are presented: Asymptotically safe gravity and string theory. Finally, elements of quantum effects in black hole spacetimes are discussed.

2 citations

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Publications

13 citations

2 citations